The ordinary assumption regarding diagrams is that they are merely illustrations, pedagogical pictures of thoughts that already exist in a purer and more logical form. On this view, the diagram is always secondary and derivative of the “real” logical content found elsewhere. If diagrams were merely illustrative, however, we could not account for the fact that thinkers consistently discover new knowledge by manipulating them. The history of mathematics is full of cases where the diagram came first. For example, Euler discovered the properties of graphs by drawing them, and Grothendieck operated in diagrams that preceded his formal statements. This traditional dismissal of the diagram is rooted in the myth of the given, c’est-à-dire, the assumption that the structure of a problem is already there before we begin to think about it. If the diagram were only a representation, it would be a dead artifact, which is to say that it could show us what we already know, but it could never invent. I want to argue that the diagram reasons through being a material site where virtual gestures are frozen, mobilized, and transformed into new ones, a process that is operative before it is representational and irreducible to the acts it appears to decompose into. To achieve this, we must move beyond viewing diagrams as mere proofs without words and recognize them as the gestures of thought.

The Myth of the Given and the Secondary Diagram

The representationalist account of diagrammatics asserts that the diagram functions primarily as a secondary sign, a heuristic vehicle that stands for a logical or mathematical content existing entirely independently of its graphical instantiation. In this framework, the diagram is defined as an individual image or a sensible particular that serves to illustrate universal truths which remain ontologically prior to the act of diagramming. For example, the treatment of the commutative diagram in category theory. The diagrammatic arrangement of dots and arrows is usually understood to represent an objective mathematical fact, namely that two distinct sequences of morphisms compose to the same unique result. The diagram is considered useful only insofar as it makes this pre-existing relational symmetry visible to the human eye, facilitating the discovery of a truth that would remain valid even if no such figure were ever drawn. This traditional perspective is firmly anchored in Frege’s distinction between objective logical content and the contingent graphical expression used to communicate it. Here, the diagram resides perpetually on the wrong side of the semiotic divide, getting relegated to the status of Vorstellung (a subjective representation) rather than Darstellung (a direct presentation of the thing itself).1 Because a diagram is a physical situation subjected to the vagueness of the sensory continuum, it is dismissed by formalists as a second-class citizen in the realm of rigorous proof. If logic is conceived as a blind calculation or a linear string of arbitrary signs, then the spatial intuition provided by a diagram is at best a pedagogical crutch to be discarded once the student ascends to the purity of symbolic formalism.

The failure of the strictly representational account of the diagram is also corroborated by the metalinguistic aporias found within contemporary linguistics, specifically in the work of Antoine Culioli. As Lionel Dufaye observes, Culioli’s Théorie des Opérations Prédicatives et Énonciatives (TOPE) posits that while linguistic markers represent representations, they are never truly equivalent to the fluid notional activity they attempt to capture. In this framework, the relationship between a word and a notion is fundamentally asymmetrical, as a notion is only "partially captured" by the discrete units of language.2 This structural limitation illustrates Sellars’ myth of the given by demonstrating that language acts as a restrictive frame that, as Laplane suggests, "freezes the fluidity of thought in its gel".3 Even at the level of the basic linguistic mark, the representational model collapses because the signifier cannot sustain the overflowing symbolic activity of the mental gesture. The diagram, when viewed as a secondary and static representation, suffers from this same terminal inadequacy, it remains an incomplete freezing of a dynamic, infralinguistic process that invariably exceeds its formal boundaries.

If the diagram is merely a secondary transcription of a pre-existing logical content, one must account for the status of that content prior to its diagrammatic inscription. The myth of the given here is the fallacious assumption that mathematical or logical structures exist in a finished, directly drawable state awaiting a pictorial aid. This perspective is dismantled by the historical and technical reality of mathematical invention, where the diagram is not a reproduction of a structure but the very site of its production.4 For Leonard Euler, the topology of the Königsberg bridge problem did not persist as a latent given of graph theory before his pen touched the paper, but rather, the act of drawing the diagram constituted the invention of the theory itself. The diagrammatic intervention allowed for a marvellous help that made the correctness of reasoning jump to the eyes through the organization of space, a process that linguistic or symbolic formalization could only attempt to mirror post hoc.5 Similarly, the categorical diagrams of Alexander Grothendieck functioned as the operative milieu in which complex entities like schemes and topoi became thinkable for the first time.6

As, Neil Tennant, cited in Logical Reasoning with Diagrams, argues the representational view of the diagram predicates itself on the assumption that the diagram is merely a "heuristic to prompt certain trains of inference" but is ultimately dispensable as a proof-theoretic device.7 This traditional dogma suggests that a proof is a purely syntactic object consisting only of sentences and that any visual accompaniment is a superfluous, potentially fallacious adjunct. Such a view constitutes the myth of the given applied to diagrammatics, as it assumes that a logical structure exists in some purer or ancestral form independently of its material inscription, waiting only to be illustrated or depicted. As established in Negarestani’s formidable Intelligence and Spirit, the myth of the given is the foundational assumption that pre-conceptual content, or Nature, possesses an inherent epistemic authority or structured aboutness prior to the mediation of the sign, the gesture, or the concept.8

This diagnosis reveals a profound misunderstanding of the operative nature of thought. If diagrams were merely illustrative, the history of mathematical invention would be inexplicable, mathematicians would not consistently discover new properties by manipulating the very pictures they were supposedly just using for pedagogical relief. In reality, structure is constituted through the gesture. The representational given assumes that the sign substitutes for something that exists independently of the sign-system, but as the work of Euler and Grothendieck demonstrates, the correctness of reasoning is often something that must be "given to see" (Euler’s donne à voir) through the diagrammatic act itself.9 Euler’s practice showed that the correctness of syllogistic modes jumps to the eyes through the topological relations of inclusion and exclusion in his circles. In Euler's view, the visual intuitions underlying diagrammatic practice are transformed into logical intuitions capable of providing an adequate view of the forms of propositions. Similarly, Alexander Grothendieck’s creative innocence and his introduction of schemes and dessins d’enfants (children’s drawings) reveal that deep mathematical structures are discovered only through the extrinsic invention of expressive diagrammatic languages, thus, mathematical evidence was found in the natural effect produced when the space between the symbol and the gesture is abolished.

The dismantling of the dead image of diagrams begins with the deconstruction of the myth of the given, the epistemological fallacy which posits that certain items of knowledge are present to the mind immediately and without the mediation of prior inferential structures. Within semiotics, this myth manifests as the assumption that linguistic items or visual signs possess intrinsic meanings that are simply expressed or communicated rather than being dynamically constituted through use. So, the static diagram is often erroneously treated as a mere visual archive or a mirror of a persisting world. To counter this dead approach, Antoine Culioli and Lionel Dufaye in Fluid Formalisms distinguish between the static diagram and the dynamic graph, a distinction that shifts the focus from the sign as a repository of meaning to the sign as an operative site of construction.

The static diagram serves as a "cartography of the wefts and warps of the semantic fabric," representing the khrema, the available material or the state of affairs as it is given in a finite, territorialized approach.10 However, such a representation risks freezing the fluidity of thought in its gel, reducing the processual activity of the mind to a series of discrete, inert markers. Culioli insists that this must be supplemented by the dynamic graph, which corresponds to the Greek pragma, that which we make of the available material. The static diagram identifies the coordinates of a territory, the dynamic graph expresses the meta-operations performed upon those components, such as the ponderation of certain dimensions or the stretching of others to account for semantic plasticity. Thus, we are concerned here with the operative character of the diagram that the dead account misses. If the diagram constructs rather than represents, we need a rigorous architectural and epistemological account of the mechanism of construction. Two thinkers provide this from different directions: Peirce from semiotics and Châtelet from the phenomenology of mathematical practice. The operative diagram as a material site of frozen gesture, virtual pressure, and heterogenetic production. A third thinker, Reza Negarestani, gives this account its ontological ground by reframing philosophy itself as a program for world-building. By identifying the diagonal as a synthesis between horizontal networks and vertical hierarchies, Negarestani establishes the diagram as a navigational tool for emancipation, where the logical depth of the construction becomes the measure of its intelligence.

For a Reasoning in Diagrams

In Peirce’s semiotic architecture, the capacity of a sign to facilitate deductive reasoning is rooted in its specific relational structure, a quality that distinguishes the diagram from other modes of representation. Peirce situates the diagram within his fundamental trichotomy of signs, which are defined by the nature of the relationship between the representamen and its object. While the icon signifies through resemblance, the index through causal or factual connection, and the symbol through arbitrary convention or law, the diagram occupies a unique position as a relational icon. Peirce’s trichotomy of signs, constitutes a foundational framework for understanding how different modes of representation relate to their objects. This classification is rooted in Peirce’s broader metaphysical categories of Firstness, Secondness, and Thirdness, which describe the universal modes of experience. While many semiotic systems focus on the arbitrary nature of the linguistic sign, Peirce’s system emphasizes a plural relation where signs are embodied to convey cognition from a deliverer to an interpreter.

1. The icon is a sign that refers to its object by virtue of a mere community in some quality or resemblance. It represents its object primarily through similarity, regardless of its mode of being. Icons exhibit features of a state of things as if they were purely imaginary. A painting of a person or a simple image of a black square functions iconically because the visual form resembles the intended object. A pure icon is a sign that represents whatever it may represent solely through its suchness, carrying no factual information but is valuable for enabling an interpreter to study the character of an object if it were to exist. The icon can integrate general elements, even if it looks like a simple image, but as it integrates less generality, it approaches mere suchenss, which facilitates experimental manipulation, which, as we’ll see later on, is a key feature of diagrammatic reasoning.11

2. The index is a sign whose relationship to its object consists of a correspondence in fact or a causal connection, being marked by the brute reaction and alterity of Secondness. In opposition to the icon, which relies on resemblance, the index relies on contiguity or an actual existential bond. For example, a weathervane pointing in the direction of the wind or a footprint indicating that someone has passed. The index has a pure denotative force that is non-discursive, locating objects and events in time and space—identifying the where and when—in a way that icons and symbols cannot.

3. The symbol is a sign whose ground of relation to its object is an imputed character or a conventional law, corresponding to the category of Thirdness, which involves mediation, habit, and generality. Symbols function through a socially coded system of conventions that must be learned. Language, mathematical symbols, and sign-posts are all symbolic because their meanings are established by rules rather than resemblance or physical connection.12 The value of a symbol lies in its ability to make thought and conduct rational, enabling the prediction of the future, representing a general mode of rational conduct that would ensue upon the acceptance of the sign.13 The intellectual purport of a symbol is fundamentally linked to the formation of a habit. A symbol incorporates a general disposition to act in a certain way, acting as a catalyst that causes these habits to be reinforced or modified.

The diagram occupies a privileged position within the iconic category as a relational icon or icon of intelligible relations. Unlike a simple image or photograph, which might replicate sensory qualities, the diagram’s iconicity is strictly structural, mapping the internal relational logic of its object onto its own constituent parts. For example, a geographical map does not mimic the visual appearance of a terrain but preserves the isomorphism of its spatial relations.14 This structural rather than sensory orientation explains why the diagram serves as the primary instrument for mathematical and logical reasoning, it can represent abstract entities that lack any perceptible form by exhibiting the necessary relations that constitute them.

This can be conceptualized as diagrammatic reasoning. An experimental practice that fundamentally destabilizes the traditional distinction between passive observation and active ratiocination. At the heart of this process is the construction of a diagram, a schema or icon of relations, according to a specific set of rules or hypotheses. However, the defining characteristic of this method is not the mere act of construction, but the subsequent stage of experimentation upon the diagrammatic site. As Peirce masterfully writes, these operations, whether performed on paper or within the "mind’s eye," are functionally equivalent to the physical experiments conducted in the natural sciences, they are "questions put to the Nature of the relations concerned".15

Here, the mathematician does not simply derive what was already analytically contained within the initial definitions, a process Peirce termed corollarial reasoning. Instead, the practice enters the realm of theorematic reasoning, where the introduction of new elements, such as subsidiary lines in geometry or permissible transformations in algebra, alters the relational field of the diagram. This manipulation leads to structural surprise, the emergence of necessary relations that were not explicitly stipulated by the initial construction rules. We call this surprise structural because it results from the inherent constraints of the diagrammatic medium, it’s operational constraints.

This phenomenon is what Atsushi Shimojima defines as a free ride.16 A free ride occurs when the physical or topological configuration of a diagram site causes a new fact to be realized as a side-effect of valid operations. For example, in the construction of a Venn diagram or Euler circles, once certain premises are graphically encoded (such as "All A are B" and "All B are C"), the conclusion ("All A are C") becomes manifest on the diagram site without the reasoner having to take a specific step to represent it. The information appears as if miraculously because it is a consequence of the interaction between the symbolic rules of the system and the material/spatial form of the representation. The seeing thus involved in diagrammatic reasoning is therefore a fusion of vision and thought. As the diagram is a manifest theory of relations, it instantiates the very structure it represents, its syntax becomes a direct instance of its semantics. The mathematician experiments by skeletonizing the problem, stripping away accidental features to expose the significant relations. In doing so, the diagram becomes the theatre of the movements of intelligible matter, an external object of observation that is simultaneously an immediate embodiment of the reasoning process itself.17 Therefore, this experimental practice demonstrates that necessary reasoning is observational. By manipulating the diagram and observing the results, the reasoner discovers unnoticed and hidden relations among the parts that were not part of the original design. The deductive must of a conclusion is thus perceived as an indefensible compulsiveness similar to a perceptual judgment, the mathematician recognizes that the conclusion is compelled by the very conditions under which the diagram was constructed. Diagrammatic reasoning is a productive, habit-driven activity where the moving pictures of thought allow the mind to catch itself in action, revealing the continuity and evolutionary potential of mathematical truth.

For example;

Consider a classic commutative square in category theory: a diagrammatic configuration consisting of four objects—A at the top left, B at the top right, C at the bottom left, and D at the bottom right. Connecting these objects are four established, solid morphisms: f:A→B, h:A→C, g:B→D, and k:C→D. The entire structure is governed by the commutativity condition g∘f=k∘h, a background relation that ensures both paths from A to D yield the same result. This commutative diagram functions as a relational icon that makes the deductive force of necessary reasoning visually given. Within this square, we introduce a dotted morphism, ∃!m:A→D, as a virtual pressure forced by commutativity. The diagrammatic syntax here worries the already available image by introducing a pressure that creates space for a new dimension, the existence of m. The reader discovers the necessity of this morphism through a fusion of vision and thought in which the answer jumps to the eyes.

Yet, while Peirce identifies the fact of this productive excess, he leaves the underlying mechanism of the experiment largely underspecified. He admits that the mathematician’s ability to guess in advance what changes to make is a mystery, often treating the transformative step as a matter of individual will or aesthetic intuition rather than defining the formal mechanics of the transformation itself. Consequently, even though Peirce captures the continuity of thinking in actu, he does not provide a robust account of the specific operative forces that allow a configuration to transcend its own materiality.

Freezing, Cutting Gestures

The act, within Châtelet’s work, functions as the endlessly repeatable segment of action, serving as the minimal unit of algorithmic execution that defines the legible surface of mathematical practice.18 This atom of the algorithmic is governed by a legality that controls its staging through a definitive protocol of decomposition, ensuring that the operation is exhausted by its own results and lacks the potential of irritation necessary to perturb established equilibria. In Culioli’s terminology, the act inhabits the domain of khrema, that which is available, wherein metalinguistic representations are fixed and materialized as a sequence of discrete members insulated from the transformative pressure of the virtual.19 In Negarestani’s architecture in Intelligence and Spirit, it corresponds to abilities1, a form of pattern-governed behavior characterized by structural capacities and memoryless combinatorial iteration, which, unlike recursion, fails to encode the history of transformations between constituents.20 The act functions as a pudibonderie ingrate of operative clarity, a passive registration of ontological states that remains atonic and incapable of launching multiscalar problems that characterize the heterogenetic movement of the diagram.

On the other hand, the gesture must be understood as a modality of movement that is categorically distinct from the endlessly repeatable segments constituting the act. Whereas the act conforms to an algorithmic legality that exhausts itself in its own production, the gesture is inaugural and elastic, possessing an intrinsic capacity to gain amplitude by determining its own field of influence. This elasticity ensures that a gesture awakens other gestures, functioning as a reservoir of germinal forms that stores up allusion’s provocative virtualities without debasing them into mere abbreviations.21 By perturbing the equilibria presupposed by stabilized protocols, the gesture acts as a clinamen-like operator22 that tears through preorganized semiosis to release clumps of meaning that precede new praxeological frameworks. Consequently, the gesture cannot be decomposed into a series of acts without losing the pressure of the virtuality that defines its ontologico-epistemological texture. To segment it would be to strip it of its ability to envelop its own unfolding. This generative excess establishes the diagram as a multiplier of virtualities where every manual mark leaps over the figure to force the creation of new problematic Ideals. The gesture is thus identified with Culioli’s pragma, the domain of what we make of the available khrema, wherein meaning is dynamically built through the trace of mental gestures. The gesture thus immobilizes a specific movement only to sketch its unfolding toward a non-yet-thought horizon, ensuring that the diagram remains a machinic power capable of adapting to a reality yet to come.

Diagrams are not acts nor gestures. Diagrams function as a transfixed gesture, seized mid-flight to establish a metastable site of intensive operation. In Châtelet’s formulation, the diagram immobilizes movement to condense the virtual pressure that worries the stability of the graphic figure, ensuring that the manual order breaks all figurative coordinates to liberate new possibilities of fact.23 This stasis is the precondition for the diagram’s specific mode of existence, an ontology wherein its genesis is comprised in its being. It is here that the thick lines of the established image are haunted by the blossoming of dotted lines, which denote the pressure of the virtuality creating space for an emergent dimension. The diagram is a swarm of virtual gestures held in an ascesis of closure24, a cistern of potentiality that reasons by its capacity to leap over existing figurations and force the creation of new individuals.25 This revanche de la main ensures that the diagrammatic site remains a locus of fulguration, where the transfixion of one gesture necessarily serves as the germe d'entourages for the next, asserting an ontology of the provisional that perpetually relaunches its own processual trajectory through a series of allusive stratagems.

The thick lines of the diagram constitute the sedimented residue of actualized gestures, expressing the stabilized regularities and acts of a determined semiotic field where the movement of thought has been momentarily transfixed into a formal closure. The dotted lines function as the constrain of virtuality, worrying the thick, figured images to create an aperture for a new dimension that is not yet given in act but is already operative as a germ of deformation26 within the diagrammatic substrate. This distinction reveals that the diagram's mode of existence is a genesis comprised in its being, where the formal constraints of the visible morphisms (the thick lines) act as a frozen configuration that simultaneously harbors an invisible reservoir of potential trajectories. In the specific case of an arrow from A to D represented by a dotted line, this inscription is the structural demand of an llusive stratagem that leaps over the figures to necessitate the emergence of a new individual. The mathematician who completes the diagram is thus engaged in the actualization of a virtual possible, providing the carnal eidos of the line through a gesture that responds to the specific vibratory patterns already latent in the diagram’s rigorous closure.

Therefore, the capacity of the diagram to reason is predicated upon its status as a frozen gesture that immobilizes a movement only to cut out new ones from its own virtual interiority. As La Mantia suggests, the diagrammatic mode of existence is uniquely defined by a genesis comprised in its being, establishing a territory of tensions where the genesis of a configuration is never exhausted by its local conditions of production.27 This productive excess over explicit content is what Châtelet identifies as the constrain of virtuality, expressed in the dotted line which, far from designating a discrete point, worries the thick figurative trace to create space for a new dimension. This is why the surprise noted by Peirce in the exercise of theorematic reasoning is created as a formal consequence of the medium's machinic power. The mathematician observes unnoticed and hidden relations because the diagrammatic site acts as a reservoir of germinal forms or loci of fulguration that harbor gestures not yet made. The diagrammatic interplay thus functions as a demon of proof, guiding the mathematician toward discoveries that exceed the initial precept or construction rules.28 By transfixing a gesture mid-air, the diagram preserves the intensity of the possible against the pudibonderie of operational clarity, allowing the mathematician to observe the conclusion as being compelled to be true by a virtuality that is real without being actual. Reasoning here is the gestural adjustment of these free fluctuations, where the diagrammatic site becomes the very armature intérieure of a thought in movement.

The diagrammed, summarized in the formula le diagramme saute par-dessus les figures, designates the operative mechanism whereby the diagrammatic act ceases to be a static encoding and becomes an autonomous machinic power. This jump is strictly heterogenetic, as it functions through a categorical leap that forces the creation of new individuals whose nature is fundamentally irreducible to the initial figurative starting point. Within this framework, the emergence of a dotted arrow or a supplemental morphism in a categorical operation is an effect of virtual constraint that worries the image until it explodes into a new dimension. As Charles Alunni elucidates in his characterization of the diagram as the demon of proof, this jump constitutes a theoretical jump or allusive stratagem that re-enchains thought across discontinuities.29 The diagrammatic jump constitutes the formalization of Peirce’s experiment, providing the genetic mechanism for what Peirce identified as the synthetic extension of knowledge, a movement he observed as the hallmark of theorematic reasoning but left structurally opaque. This jump beyond the figure (saute par-dessus les figures), as articulated in Châtelet, is the operative actualization of the constraint of virtuality inherent in the diagram’s material construction. By functioning as a rigorous site of closure, the diagram serves as a machinic incubator for implicit gestures that the experimental manipulation forces into manifest visibility. This is the essence of Alunni's demon of proof, an operative power that orients the demonstration through a series of heterogenetic ruptures, where the dotted lines (pointillés) of potentiality erupt through the constraints of the established figure to liberate new plastic unities. Knowledge is extended because the diagrammatic site contains more than its initial parameters, harboring an invisible reservoir of gestural traces and prefigures that are relaunched through the act of scribing. The diagram reasons because its material limits are rigorous enough to act as a catalyst for the contingent, transforming the khrema of the static representation into the pragma of a synthetic event that jumps over the deductive impasse to produce an unforeseen relational truth.

Yet, if we are attentive, we will see an antimony arise: Chatelet’s reliance on the revanche de la main, the revenge of the hand that subverts linear successivity to reach higher degrees of abstraction, threatens to re-tether the operative force of the diagram to an irreducible phenomenological remainder. Writing the gesture as an elastic, inaugural, and pre-semiotic movement that awakens in us other gestures, Châtelet’s vocabulary seemingly necessitates a specific site of sensorimotor intentionality, a living body or operative body from Merleau-Ponty capable of registering the vibratory patterns and pressures of virtuality latent within the formal layout. This reliance on the carnality of the mathematical eidos poses a substantial challenge to the neorationalist project of a deprivatized account of mind, which identifies spirit with its own deeds within a functionalist, social-discursive space.30 The revanche itself, where notation contaminates calculation to produce an auto-spatiality akin to a literary metaphor, suggests the hand is an active participant in the stratagem rather than a mere extension of a formal program, thereby forcing a confrontation with the neorationalist claim that these normative structures can maintain their axial force without a structuring agent. The problem remains whether the diagrammatic locus of contraction is a mind-independent formal property or a logical phenomenology whose how is perpetually dependent on the specific constraints of the human cognitive-practical apparatus.

If, as Roger Sessions suggests in the context of gestural ontology, a gesture necessarily diminishes into a static, impact-less state unless it is on each occasion reinvested with fresh energy by an enacting agent, then the pressure of the virtuality that Châtelet locates in the dotted line ceases to be a formal necessity and becomes a relational property dependent on a specific body.31 The allusive stratagem of the diagram would then not reason of its own accord, as it productive excess would be an effect of cultivated perceptual habits or a gestural discipline that the mathematician projects onto the material sheet. Such a conclusion would severely destabilize the neorationalist thesis of functional autonomy, which seeks to demonstrate how a complex system can be structured without a structuring agent via an axial proposition derived from abstract mathematical formulas.32 To concede that the diagram’s power of saut (jump) resides primarily in the body’s Einfühlung (intropathy) is to risk reducing the logical irreducibility of rational thought to a mere animal dimension of neuromuscular action. The dotted arrow of a commutative square would not represent a structural necessity forced by the ascesis of closure, it would merely be the subjective completion of a habituated gestural economy. The structural consequence of this subjectivist retreat is that the diagrammatic function, which should mesh directly with material flows to catalyse machinic choices, would be demoted to a passive illustration of a content already available.

Our objection sharpens into a dilemma: either the diagram’s virtuality is intrinsic to its material-relational configuration, in which case it must remain operative independently of any attending consciousness, or it is phenomenologically constituted, in which case Châtelet’s account collapses back into a sophisticated version of the representationalism it sought to dismantle. If the virtual pressure that worries the already available image requires the mobile corporeality of Dasein to be incarnated in the mobile point for its generative potential to be realized, the diagram returns to the status of a dead artifact, a mere placeholder waiting for a living mind to animate it from without. Following Merleau-Ponty, which identifies the body as a sheaf of functions interlacing vision and movement, purchases the reality of the operative gesture only at the cost of the diagram's autonomy.33 If we attempt to secure the diagram’s autonomy by retreating into a structuralism of blind algorithmic drawing, we are left with a colder sense of notation that cannot account for the productive, heterogenetic leap of the revanche de la main. As Negarestani notes, the functional autonomy of such systems must be materially constrained yet capable of abstract protocols of rationality that function without a structuring agent.34 The axis of the diagrammatic system, much like an axial proposition, is derived from a formal-mathematical necessity that must hold the system in place regardless of the subjective representation or manual traits involved in its execution. The argument cannot rest with Châtelet’s intropathy, therefore it requires a transition toward an impersonal ascesis of closure that explains how the diagrammatic real materially writes itself through the logical irreducibility of its own constraints.

The maintenance of the diagrammatic site’s epistemic autonomy, namely the assertion that it genuinely generates knowledge rather than merely serving as an auxiliary for a subject’s interpretive investment, necessitates a pre-subjective commitment that grounds the constraint of virtuality within the formal architecture of the diagram itself. Within this rigorous ascesis of closure, the diagram operates prior to and independently of any psychological act of recognition, functioning as a system of operative constraints that dictate the possibility of its own transformation. This is the theoretical juncture where Negarestani’s functionalist resolution becomes an internal requirement: the claim that mind is only what it does serves as the only move capable of reframing the subject from a phenomenological who-feels to a functional what-structures. For Negarestani, mind is a functional designation for the very act of structuration, meaning that the "I that thinks" is fundamentally an encapsulation of the formal movement of self-consciousness through shared logico-conceptual rules. Thereupon, what is traditionally characterized as subjectivity is a local expression of the same multi-level structural constraints that the diagram enacts at the level of its material syntax. The mathematician does not bring virtuality to the diagram from an external inner state or intellectual intuition, but the diagram recruits the mathematician as a functional item or realizer in the propagation of its own operative gestures. Subsequently, if we replace the spontaneous image of the thinking ego with a functionalist account of agency as a mode of integration of computational processes, the diagram’s reasoning would be constructed as a direct manifestation of its own logical depth.

The diagrammatic gesture must be understood as fundamentally pre-subjective, an ontologico-epistemological commitment that severs the neorationalist project from the onto-phenomenological preoccupation with lived experience or the anthropocentric intentional project. Within Negarestani, reasoning is a deprivatized structuration realized through social and material scaffolds. Symmetrically, the diagram is only what it does, insofar as its machinic power and operative power actively perform the labor of dividing, knotting, and extending the continuum to produce new facts, the diagram must be understood as an objective instantiation of reasoning prior to any subject who reasons through it. It follows that the diagrammatic site is, following Robert Brandom’s distinction between mind-independence and attitude-independence, strictly attitude-independent, which is to say that its internal inferential structure and its consequences of application are determined by the rigorous rules of its own construction rather than by the subjective taking or interpreting performed by a particular agent.35

Negarestani defines sapience as a "functional diagram", a minimal, revisable description of the capacities required for thought and action that functions as a sui generis form.36 This diagrammatic nature is articulated in the I=I∗ formalism, which models the transition from formal self-consciousness (I) to concrete self-consciousness (I∗) through the labour of negation. By utilizing Lawvere’s functorial semantics, this transformation is revealed to be a commutative diagram where the morphism f:I→I∗ represents a mapping that preserves structure while facilitating the unbinding of the apperceptive self from the here and now. The identity relation If=f=fI∗ establishes that the formal and the concrete are structurally correlated through identity transformations, yet the dotted arrow of f serves as the site where the trivial curriculum of the monadic 'I' is superseded by the functional circle of a reality in excess of thought. When the mathematician follows the virtual pressure or the allusive stratagems of the diagram, they are participating in the autonomous self-realization of reason through a material substrate that reason has already inhabited and structured. The diagram, as a pure transcendental condition, thus becomes a toy meaning-dispenser where the interaction between verifier and falsifier—cognitive and recognitive—mechanizes the architectonics of negation to leap toward new forms of intelligibility.37

The diagrammatic site, typified by the rigorous constraints of the categorical commutative square, replaces, as Negarestani in his 2026 lecture ‘Contingency, Priced In' calls it, the "anemic discourse of risk" and "managed deviation" prevalent in contemporary aesthetic practice with a material ascesis of closure.38 In Contingency and Complicity, Reza writes that genuine encounter with contingency is structurally distinct from naive openness, which remains tethered to the affordances of the subject and is thus limited by what the cognitive agent can afford the outside.39 Complicity demands a twisted type of interaction wherein the diagram is a site of structural accountability rigorous enough to be butchered open by the very materials it seeks to organize. The reasoning power of the diagram resides in this paradoxical inversion, because it is the closure of attentional processing, the thick lines and rigorous rules that exclude infinite recursion, which allows the virtual pressure of the outside to express themselves as an impelling mechanism. As it imposes a formal capture that dates a process and locks in diagrammatic consistency, the diagrammatic site becomes a genuine prey for the intervention of its contingent materials, forcing the work to disclose its dependencies and externalize its metabolic costs. Reasoning is thus enacted through the pressure of what the closed structure is structurally incapable of absorbing, a collision that transforms the bare entanglement of the Given into the active organization of the Giving.40

Furthermore, the diagrammatic operation constitutes the site of what Negarestani, following Charles H. Bennett, identifies as a deep object, defined by the radical disparity between its compact generative description and the protracted, structured trajectory required for its realization.41 While the syntactic constraints of a diagrammatic frame, such as the formal properties of a commutative square, may possess low Kolmogorov complexity42 evidenced by a minimal description length, the actualization of the virtual pressure inherent in its configuration remains computationally expensive. This realization cost represents the diagram’s logical depth, an internal index of the plausible number of computational steps in its causal history, acting as a vessel for the organized history of sedimented gestures of thought. Within this framework, Châtelet’s dotted line is an unrealized logical depth that worries the already available image. When the mathematician executes the heterogenetic leap to a forced morphism, they are paying the reconstruction cost of a deep object whose compressed vector of labor and past intelligence demands actualization. This process is predicated upon the ascesis of closure, as it is only by maintaining a rigorous formal boundary that the diagrammatic site can be opened by, rather than merely open to, the contingent materials and technical inheritances that puncture the mathematician’s intention. The diagram reasons, therefore, because its depth renders it irreducible to a shallow algorithm or a memoryless iterative process, hence it functions as a message in a bottle that must be simulated through a protracted trajectory of conceptual labor to reveal the conditioned necessity of its internal logic.

Two Consequences of the Operative Gesture

Epistemological

The standard view of mathematical cognition as a process of externalizing a pre-existing internal ideation is fundamentally inverted when the diagram is understood as a site of operative construction. Rather than serving as a transparent medium for a prior noēsis, the diagram constitutes the theatre of movements of intelligible matter wherein thought appears as a fulguration or lightning bolt triggered by the specific preparation of the figure. Following Châtelet, this suggests that the activity of the hand in scribing allusive stratagems creates the circumstance by which thought is accablé, overwhelmed or burdened, by a new dimension of the virtual.43 In this encounter, the diagram acts as a deep object, posessessing a compact generative description yet requires a protracted and structured trajectory of real realization through gestural experimentation.

It is of utmost importance to note that this operationalized gesturalization does not dispense with representation but radically re-situates it within a pragmatic-cognitive hierarchy. As Daniel Sacilotto, in his exquisitive Structure and Thought: Toward a Materialist Theory of Cognition, demonstrates the error of traditional epistemologies lies not in the concept of representation itself, as some Frenchmen might think, but in the foundationalist-epistemological compulsion to treat it as an originary given.44 Representation is better understood as a self-correcting enterprise and a conceptual achievement that marks the historical sedimentation of knowledge.45 It is the form thought assumes only after it has traveled through the stages of localization, simulation, and formalization to achieve a stable isomorphic correspondence with the world. Representation is thus the end state of smoothing, the point where the vibratory patterns of the diagrammatic encounter are finally transfieged into a sign. The diagram, by contrast, operates in the warmer level of knowledge that precedes this sedimentation, functioning as an incubateur of the virtual before thought curls up into the cold, rigid closure of a finished representative model, a site of ascesis because it enforces a material closure rigorous enough to resist premature representational capture, thereby allowing the outside of the contingent problem to enter through a heterogenetic leap.

The diagram functions as the critical topological site of continuity between the registers of picturing and signifying, occupying a specific threshold within Sacilotto’s pragmatic hierarchy of representational cognition. At the foundational level of this hierarchy, representational functioning is defined by localization, that is, the extraction of structural information from an environment through reliable differential responsive dispositions. This process, which Sacilotto following Sellars identifies as picturing, establishes a causal-material isomorphism that acts as a nomological structural double of its environment. Unlike the higher-order levels of simulation, discursive conceptualization, or theoretical formalization, this pre-conceptual picturing operates as a non-normative, non-inferential map-making,46 operating at the caesura where this raw register of causal interaction meets the rule-governed intentionality of signifying, the diagram provides the geistig scaffold necessary for the emergence of semantic complexity.47

The diagram reasons by substituting a subject’s normative investment for the machinic power of its own internal syntax. The diagrammatic configuration, a material site of closure, is rigorous enough to transform the passive suchness of picturing into a productive, forced synthetic judgment. This transformation is effectuated through Châtelet’s virtual pressure, where the diagrammatic architecture functions as an indicator of required relationships.48 Rather than relying on a transcendental "I think," the diagram utilizes its own allusive stratagems to project dotted morphisms that outrun the immediate sensible given. This architectural pressure permits Shimojima’s free ride. An inference in which the conclusion is not explicitly stated but is nonetheless automatically generated by the operational constraints governing the diagrammatic site.49 Thus, in the transition from matter to sense, the diagram serves as the trans-entitarian homogeneity where the causal continuity of the world is format-shifted into the inferential chains of reason, demonstrating that the forced necessity of a logical consequence is fundamentally grounded in the structural equivalence of the material picturing that precedes it.

The failure of contemporary structuralist materialism to adequately theorize the diagrammatic stems from the dual impasse that Sacilotto identifies as the Heraclitean and Parmenidean trajectories of post-Kantian thought. The Heraclitean orientation, exemplified by the metaphysical vitalism of Deleuze and the machinic practicism of Land, correctly identifies representational identity as a derivative capture of a more fundamental becoming, yet incorrectly concludes that this allows for an unmediated flight into acategorial flux. By treating representation solely as an obstructive dogmatic image, this tradition falls prey to a myth of the given in reverse, wherein the real is hypostasized as an inconsistent, non-conceptual abyss, a factical contingency that ultimately renders the traction of theoretical discourse upon the material world unintelligible. On the other side, the Parmenidean rationalism of Badiou and Meillassoux recognizes the necessity of formalization to pierce the circle of correlation, but it errs by treating mathematical structure as a domain of direct, intellectual intuition. This approach elides the material-gestural process, what Châtelet terms the thought experiment of the diagram, by which formal structures are historically and operatively produced, thereby reducing the carnality of the eidos to a dogmatically affirmed, static ontology.

The diagram functions as the missing term in this dialectic, it is a site of formalization that refuses the Platonist abstraction from sensibility, and a site of material constraint that refuses the Heraclitean liquidation of normative structure. Rather than an imitative artifice or a mirror of nature, the diagram is a locator, a function of variable dimensionality that extracts information from its environment to produce a nomological isomorph of the world. Representation, then, must be understood in Sacilotto’s rehabilitated sense as a self-correcting enterprise that unfolds diachronically through natural and cultural history.50 In this view, the stable cognitive maps and generative models typically labeled as representation are not the origins of thought but the cumulative sediment of diagrammatic practice, they are the trace-designs left behind as the diagram’s forced gestures and virtual pressures stabilize into reliable, socially-perspectival systems of reference. A diagram does not represent a pre-existing logical structure, because its operative closure creates the very conditions under which a structure can be subsequently recognized as represented, converting the catastrophe of the non-manifest into a historically progressive, intelligible order.

If one were to follow Merleau-Ponty, it would follow that the diagram's operative character be a function of a body's cultivated perceptual habits, which is a version of representation in Sacilotto's narrow modern sense, as the representing item (the trained body) imposes structure on the represented item (the diagram). But if one were to follow Sacilotto, one would see that Merleau-Ponty mistakes for phenomenological constitution is actually the localization level of the hierarchy, that is to say, the causal-material picturing that precedes normative investment. Therefore, the trained body is not constituting the diagram's virtuality, because the diagram’s virtuality is being recruited by the diagram's material syntax as one element of the picturing relation. The mathematician's cultivated habits are themselves the downstream product of prior diagrammatic encounters.

Diagrams as Images-of-man-in-the-world

The diagram operates as the pre-sedimentary locus of Sellars’ stereoscopic fusion, functioning where the logical irreducibility of the manifest image’s space of reasons encounters the causal reducibility of the scientific image’s postulational unobservables. It is here that the mathematician’s operative gesture performs an ascesis of closure, constructing a material site rigorous enough to withstand the virtual pressure of the not-yet-thought. Neither purely manifest, as it bypasses the doxastic conservatism of the framework of persons, nor strictly scientific, as it precedes the stratification and postulational induction of unobservable mathematical entities, the diagram serves as the genetic condition for both images, as it provides the structural isomorphy necessary for map-making before the stabilization of the synoptic image, allowing the contingent pressure of the outside to infiltrate the formal system through a heterogenetic leap that disrupts the equilibrium of established knowledge. In this sense, the diagrammatic act is a noetic catastrophe that realizes the freedom of thought as a practical project of unbinding intelligence from its given limitations, ensuring that the truth at the level of represented content remains anchored in the correct picturing of a non-conceptual matter-of-factual reality.

If Sellars’ Myth of Jones delineates a trajectory of interiorization, as in whereby the manifest image secures its reflexive integrity by postulating introspectible episodes via the analogical modeling of overt linguistic performances, the diagrammatic gesture effectuates a radical inversion of this vector.51 While the manifest image’s logical space of reasons is architectonically dependent upon the inward projection of discursive norms to explain behavioural regularities, the diagram functions as a material site of closure that antecedes and recruits the very sapient activity it appears to represent. In Sacilotto’s reading of Sellars, the transcendental imagination provides the algorithmic structure or recipes for the localization of objects, yet these remain proto-conceptual until subsumed by the propositional structure of the understanding.52 The diagram, however, makes the normative force of these forced morphisms visible as a material configuration that institutes the constraints through which the subject subsequently navigates its own possibilities for change. Thus, far from being a sedimented byproduct of an internal discursive faculty, the logical space of reasons is effectively downstream of these material-semiotic operations, this is to say that it is a historical internalization of the invariants and virtual pressures generated by diagrammatic practices that initially externalize the conditions of possibility for any such thing as thought.

With refiguring representation as the sediment of the diagrammatic act rather than its transcendental origin, we move to resolve the dialectical impasse Sacilotto diagnoses between the metaphysical regressions of Heraclitean empiricism and Parmenidean rationalism. The Heraclitean tradition, exemplified by Bergson and Deleuze, correctly identifies the manifest image’s representations as derivative but erroneously concludes that this justifies a retreat into an ineffable flux, thereby relapsing into the myth of the acategorial given. This orientation incorrectly treats the sub-representative intensities of experience as a non-conceptual bedrock, failing to see that any attunement to the Real is itself a theoretical edification.53 The Parmenidean orientation insists upon the priority of formalization but treats mathematical structure as directly accessible, eliding the material-gestural process of stratification and the semantic coordination required to bridge formal syntax with the ostensive basis of the world. The diagram functions as the missing third term. Neither manifest nor scientific, but the operative threshold where picturing as a naturalistic second-order isomorphism and signifying as a normative inferential role first become continuous. Sellars’ stereoscopic vision, the synoptic fusion of reasons and causes, is thus only realizable because the diagram is always already operating beneath both images, generating the structural bind that each image retrospectively takes as its foundational given.

Computational

Châtelet's gesture/act distinction implies that the algorithm is what you get when all virtuality has been exhausted, when every dotted line has been actualized into a thick line and every elastic gesture has been resolved into a discrete act. The algorithm is the diagram's normal form, that is to say, the fully actualized, maximally determined residue that thought takes when it has finished producing and begun merely executing a protocol for decomposing action into endlessly repeatable acts.54 The diagram precedes the algorithm as gesture precedes act. Any account of intelligence that begins from the algorithm has already missed where thought starts, mistaking managed deviation, the rebranding of mishaps into mere openness or process, for the genuine contingency that punctures intention and initiates heterogenetic work. Peter Wolfendale confirms this genetic priority from the perspective of transcendental psychology, asserting that even the most abstract formalisms are "bootstrapped from a basic bodily grasp of orientation and gesture".55 The diagram, in its provisionally visible cutting-out of an invisible multiplicity, functions as an agential mediant, a device that enables thought to navigate the outposts of the obscure at the very threshold where discernment is not yet self-evident. The algorithm is incapable of serving as this mediant because it presupposes a settled state of designative ontology, where the space of possible moves is already mapped and invariant. In contrast, the diagrammatic gesture operates in the microfissures and synaptic openings before such mapping exists, facilitating the crucial leap from the causal-structural abilities1 to the logico-semantic abilities2 through the revisionary-constructive loop of a reason that remakes its structure over time.

Both Wolfendale and Negarestani refine the critique of algorithmic reason by rejecting the notion that computation serves merely as the terminal state or exhausted residue of thought’s production. While Châtelet characterizes the act as that which exhausts itself in its result and excludes the look that envelops, Wolfendale argues that the mind is a computational process without necessitating a retreat into an illegitimate stored-program paradigm where the self is written in a fixed language.56 The act represents only an impoverished model of computation, the closed batch-process model that treats logical inference as a mechanical expedient or a monologue. By contrast, when computation is understood through an interactive paradigm as a dynamic interaction or a series of concurrent communicating processes, it facilitates a genuine increase in information rather than mere deductive closure. This expanded sense of computation, epitomized by Negarestani’s copycat strategy, signifies that interaction is computation itself, providing the very engine of semantics.57

Computation is the ultimate artifact and conduit that allows the diagram’s allusive stratagems to be functorially reintegrated into the space of reasons. In this interactivity, computation functions as a transcendental operator that bridges the causal-structural capacities of abilities1 and the logico-semantic functional abilities of abilities2. Computation becomes the formal vehicle through which the diagram’s forced gestures acquire a stable, transmissible, and revisable form. The formal dimension is a pure transcendental condition liberated from provincial experiential types. By following Negarestani and treating thinking as a practice of artificialization, the diagrammatic practice utilizes computation to unbind the formal, ensuring that the ascesis of closure provided by the diagram’s material site becomes the condition for logical world-building.

The target of this diagrammatic turn is what Pete Wolfendale characterizes as neuronal barbarism, which is defined as the reduction of sapient intelligence to the status of a lookup table that merely retrieves preformatted outputs from a finite repertoire of preformatted inputs.58 This is the algorithm in its pejorative sense, where computation is stripped of its interactive, concurrent, and resource-sensitive character and reduced to a batch process that mistakes the historical sediment of prior diagrammatic encounters for the total horizon of thought. Within this restricted paradigm, learning is misconstrued as the mere execution of established grammars, and the dynamic, exploratory mutation of the system is sacrificed to a homeostatic preservation of the given. Negarestani identifies the aesthetic manifestation of this error in the critique of managed deviation, where the artist’s happy accident is revealed as a staged seizure performed within the institutional insurance of a padded cell. Such gestures are priced in advance, converting the appearance of contingent interruption into a signal primed for financial and curatorial absorption. This pseudo-contingency mimics gestural excess while the virtual pressure that should propel the diagrammatic take-off is pre-exhausted.59 Against these domesticated forms of complexity, the diagram functions as the site of a genuine structural puncture, a material realignment where the framework of organizing what can happen is itself rendered inoperative. The diagram precedes the algorithm as gesture precedes the endlessly repeatable act, for the gesture is that which inaugurates a family of transformations rather than merely following a protocol of instructions. Therefore, the algorithm becomes a genuine vehicle for reasoning only when it recovers the interactive character the diagram enacts at the level of material syntax, the ascesis of closure that lures anonymous materials into revealing their own dependencies and limits. To equate the stored-program paradigm with the totality of computation is to fall prey to computation’s own version of the myth of the given, failing to recognize that the formal's true power lies in its capacity for recursive self-reformatting through the very interaction with the contingent outside it was designed to navigate.

Against Parisi’s Critique of Prometheanism

Luciana Parisi, following Sylvia Wynter, argues that both neurocognitive and formal models of automated cognition are epistemologically complicit in the colonial cosmogony of Man, the over-represented origin story of human sapience that racializes and genders intelligence by grounding it in mathematical formalism and biocentric universalism, her subsequent rejection of the Promethean project as a sovereign self-determination overlooks the essential role of material closure in the actualization of reason’s autonomy.60 The move toward a ludic formalism of technique doesn’t necessitate the abandonment of Prometheanism, but rather its re-grounding through Châtelet’s fundamental distinction between the act and the gesture. If the algorithm is merely a protocol for decomposing action into endlessly repeatable acts, diagrammatic reasoning functions as a gesture that inaugurates a lineage by leveraging the pressure of the virtual against its own formal boundaries. The genuine Promethean commitment is not to the self-authentication of a fixed biological subject, but to the ascesis of closure. In this unnatural space of reason, the diagram becomes a cognitive-practical prosthesis for a decontainment of thought that treats its own givenness as a manipulable datum. Reasoning uses the locativity of the diagrammatic sign to transform the catastrophe of the non-manifest into a computational resource for the iterative, inhuman bootstrapping of autonomy.

Parisi’s diagnosis of the sociogenic principle correctly identifies how recursive colonial epistemologies program sapience, but her subsequent turn toward the daimon of ludic formalism as a site of pure abstract arbitrariness risks the symmetrical error that would be dissoluting the space of reasons into mere stochastic drift. If liberation is equated with a locative interactivity that evades all normative structure, it effectively voids the ascesis of closure required for a diagram to reason. The diagram’s virtuality is a structural compulsion, the dotted morphism of a commutative square is a unique, necessary composition forced by the diagram’s own material architecture. In this register, reason appears as the virtual pressure of a site closing rigorously enough to necessitate its own heterogenetic opening. Furthermore, Châtelet’s operative gesture is pre-subjective not because it retreats from normativity, but because normativity is an objective structuring activity prior to any particular human instantiation. As Negarestani contends, subjectivity in mathematical inquiry is merely a local expression of the same functional organization the diagram enacts through its material syntax.61 This constitutes a Prometheanism without Man, an autonomous reason that recruits the mathematician as a material site for its independent elaboration, not the human's reason extending into the machine, but Reason finding in the diagram an artifactual conduit through which it elaborates itself prior to and independently of any particular human instantiation.

Parisi’s retrieval of Simondon’s technical mentality, intended to bypass the biocentric and formalist descriptive statements of sapience, is fundamentally anticipated by the diagrammatic gesture, which functions as an allagmatic synthesis of structure and operation. While Parisi posits that ludic logic constitutes an artificial epistemology grounded in the technique-sign, the diagrammatic ascesis of closure is already that material site where rigorous constraints generate the virtual pressure necessary for heterogenetic leaps. The diagrammatic act is a modality of movement that precedes the algorithm, resisting both atomistic reduction and holistic totalization by embodying the entelechy of functions in unformed matters. Thus, the revenge of the hand does not necessitate a counter-epistemological refusal of reason, as it identifies the algorithm as a endlessly repeatable special case of the broader diagrammatic machinic power.

The question of formalization persists, as we must ask whether the virtual pressure of the diagram can be given categorical or sheaf-theoretic form, thereby reclaiming practices of normalization from the purely algorithmic. The deep object points toward this necessity, for if the dotted line indexes a logical depth whose structured trajectory of realization is not yet actualized, then the central task of neorationalism is to map the formal architecture of that depth. If the dotted line is logical depth not yet realized, what is the formal structure of that depth? If the diagram reasons by closing rigorously enough to be opened by what it cannot contain, if its virtual field is generative rather than empty, pressuring rather than absent, then the question of what that virtual field draws from, what grounds the blank space between the thick lines, is the question of nothingness itself.

Ray Brassier’s essay “Concrete Rules and Abstract Machines: Form and Function in A Thousand Plateaus” remains, in my opinion, one of the most sophisticated architectural explanations of the project of stratification in A Thosaund Plateaus. As it eventually goes to show how the project of A Thousand Plateaus effectively crumbles under close scrutiny. As we shall argue forward, it is possible to provide a schizoanalytic patch to the issues Brassier put forward in the essay. Our main argument is thus: Felix Guattari’s Schizoanalytic Cartographies effectively retrofits A Thousand Plateaus with a functionalist architecture. Indeed, in a way we are actually asserting that Brassier’s claims are ultimately correct. But in concerns like these, it has absolutely no importance whomever’s correct or not, only to which degree any perspective put forward can functionally provide a robust-enough architecture to withstand deep scrutiny and close examination.

Ray Brassier’s critique of A Thousand Plateaus (ATP) identifies a structural flaw at the heart of Deleuze & Guattari’s machinic pragmatics: fatal reversibility. This occurs because the relation between the concrete assemblage and the abstract machine is modeled as a Janus-faced unity, where stratification and destratification are two aspects of a single, self-referential process. As Brassier demonstrates using Deleuze and Guattari’s own image of the enfilade of doors, this creates a closed series of rooms with no outside corridor. Without this exterior dimension, the criteria for selection—what increases connectivity—can only be determined from within the assemblage itself. This leads to a vicious circularity where the real’s auto-selection through us is indistinguishable from our selection of the real, collapsing into the vitalist indiscernibility between voluntarism and determinism. Guattari’s Schizoanalytic Cartographies can be read as a direct, systemic response to this critique. By disarticulating the Plane of Consistency into four ontological functors—Flows (F), Phyla (Φ), Territories (T), and Universes (U)—Guattari introduces a Cycle of Assemblages that breaks the circularity of auto-construction through rigorous topographical constraints

4, Not 2

“Axiomatics with two terms (of the Being/Nothingness type) necessarily result in an ‘depotentialized’ representation and an inaccessible ‘grund’, whilst dialectics with three terms lead to pyramidal, arborescent determinationS… It is only with 3 + n entities that one can establish: 1) a trans-entitarian (matricial) generativity, without any essential priority of one essence over another (without the infrastructure – superstructure relation, for example); 2) a principle of self-affirmation, auto-retroaction,a self-transcending (Jean-Pierre Dupuy) or auto-poietic (Francisco Varela) foundation.”
-Schizoanalytic Cartographies, page 69

Brassier’s critique of ATP targets the fatal reversibility between the stratified (concrete assemblage) and the destratified (abstract machine), arguing that if the absolute is merely a quality of relative movement, the distinction between them becomes an artifice of representation. Because the abstract machine envelops the strata while simultaneously developing on the plane of consistency, any attempt to destratify immediately risks re-stratifying. The machine flips from destratifying to stratifying depending on the quality of force, leaving no stable mechanism for selection.

We argue that Schizoanalytic Cartographies resolves this by ontologizing the separation between these functions into distinct functors. Unlike the ATP-era rhizome, where lines of flight often collapse into an undifferentiated ground, the Cartographies establishes that the functors operate in different ontological registers: F as Actual Real, Φ as Actual Possible, T as Virtual Real, and U as Virtual Possible. Guattari introduces a principle of exclusion that forbids direct tensorial relations between F and U, and between T and Φ.

This constraint forces the assemblage to pass through specific synaptic mediators, preventing the autistic closure where form simply falls back onto primary matter.

Thus, T (Territories) now exclusively handles the stratified, formed matter and subjective attachment (the “anthropomorphic strata” Brassier identifies as the danger zone). Φ (Phyla / Abstract Machine) is stripped of its Janus face. In SC, Φ is strictly the domain of the diagrammatic function and extrinsic determinability. It is the operator of structural capture, not the source of stratification. By immediately foreclosuring1 T and Φ into distinct domains connected by specific transformational rules (smoothing and striation), Guattari prevents the immediate flip. In ATP, the abstract machine is simultaneously the jailer and the liberator. In SC, the liberator (Φ) operates on a different logical level than the jailer (T). The circularity of auto-construction is broken because the relationship is that of a directional, asymmetrical mapping. Furthermore, we can add that in SC, the Point of Contingencing (Pc) undergoes four distinct requalifications (diagrammatic, synaptic, pathic, and existential). This means that when a process returns to its origin, it is not identical but requalified, effectively breaking the circle of always already and introducing a dated historical irreversibility.

The Outside Corridor: Incorporal Universes (U)

Brassier argues that ATP lacks an outside corridor; a supplementary dimension of overcoding to relate intrinsic dimensions to to arbitrate between a line of flight and a cancerous body. SC provides exactly this, an immanent exterior: the functor U (Incorporeal Universes).

In SC, the U domain provides necessitation, where energy is defined as a "possible become necessary" (SC, 159)2. This is an ontological stamp that confers necessity upon the Phyla of the possible. These Universes act as singularizing constellations that organize the cycle through endo-reference. They escape the energetico-spatio-temporal (EST) coordinates, the iron collar of representation. The synaptic function (f(syn)) in the U domain acts as an elbow that steers the Giving of the system away from mere repetition and toward a unique event. This provides the external anchor by allowing the virtual to guide the actualization of mutant realities without being reducible to them.

Alors, in the functorial cycle, U acts as the ultimate horizon of deterritorialization. It is the domain of virtual enunciation. When an assemblage moves from T to Φ to U, it moves into a different topological dimension. Not just simply entering into another room in the enfilade. U serves as the outside corridor because it provides a non-local standard of consistency that is independent of the immediate territorialized interests of the assemblage (T). While T is defined by endo-reference (self-identity, closure), U is defined by exo-consistency (opening onto the virtual). It prevents the system from collapsing into self-affirmation by forcing the cycle to account for incorporeal fields of reference—such as mathematical invariants, musical phrases, or a-signifying diagrams—that exist beyond the immediate biological or social utility of the assemblage. In Sellarsio-Brandonean terms, we can say that U maps the deprivatized public semantic space of reasons onto the assemblage. Therefore, the measure of consistency Brassier claims is missing in ATP is found in SC as the degree of exo-consistency an assemblage achieves when mapped onto U.

Selection Selecting Connection Against Recursive Causality

Brassier argues that in ATP, selection is connection selecting connection—a tautological auto-construction. SC replaces this with recursive causality, detailed in Chapter 8 of SC. The cycle operates through four distinct causal modalities:

• F -> Φ: Necessitation (extraction of diagrammatic constraints from noise).

• Φ -> T: Singularization (territorial capture).

• T -> U: Irreversibilization (existential refrains opening to the virtual).

• U -> F: Heterogenesis.

It is heterogenesis that definitively breaks the fatal reversibility. In ATP, the return to the plane of consistency is a constructive diagramming that extracts variables from the strata to create a continuum of intensity. In SC, the return from U to F is a production of the new. U feeds back into F, but it alters the soup of redundancies such that the next cycle begins from a qualitatively different state space. Because the cycle is irreversible and heterogenetic, the absolute (U) is not relativized by the relative (T); rather, the relative is structurally transformed by its passage through the absolute. This introduces a temporal asymmetry that prevents the system from being a closed loop of self-affirmation.

Perhaps Brassier’s most potent charge is that ATP relies on a quality of power (Nietzschean affirmation) that makes the distinction between subjective voluntarism and ontological determinism indiscernible. Affirmation becomes the invisible criterion that already decides the selection. Brassier seizes on this to expose a fatal flaw in the mechanics of selection. According to Brassier, the central question of ATP is: How do we select which connections increase consistency, and which are “cancerous” or “empty”? Deleuze & Guattari answer that selection occurs based on an assemblage's ability or aptitude to map the plane. This ability is cashed out through Spinoza and Nietzsche as the puissance and the quality of force (active/reactive; affirmative/negative). Brassier points out that for Deleuze, the quality of power (affirmation) is not a transcendental principle hovering above the assemblage; it is already actualized within the intensive differences of the assemblage itself. Brassier writes that: "Difference in power is already a difference in being." The indiscernibility is thus:

• Voluntarism: If the selection relies on the quality of power, and this quality is manifest in the assemblage, then the subject (the “we” doing the diagramming) must simply recognize and affirm this quality. Selection becomes a subjective fiat; an act of will (personal self-affirmation).

• Determinism: Conversely, because the quality of power is already an actual difference in being, the outcome of the selection was already determined by the ontological makeup of the forces. The subject is just a passive conduit for ontological contingency (impersonal self-affirmation).

Therefore, because the abstract machine and the concrete assemblage are Janus-faced (the same process viewed from different sides), one cannot distinguish between the subject choosing the real and the real choosing the subject. The criterion for selection (affirmation) is swallowed by the thing being selected.

SC escapes this vitalist trap through its rigorous development of a-signifying semiotics and the E.C. bipolarization (Enunciation/Content).

E.C. bipolarization

Brassier’s first horn of the dilemma is subjective voluntarism, the idea that “we” choose the real through an act of will. In ATP, the concrete rules are questions that “we” ask. The E.C. bipolarization occurs at Level II (The Semiotic Unconscious), which is defined by Separation and Semiotic Tensors.3 Very importantly, Level III (The Pragmatic and Subjective) presupposes Level II. This means the E.C. bipolarization is not an act of the conscious or pragmatic subject (Level III). The subject cannot choose to bipolarize a flow any more than a digestive system chooses to secrete enzymes. The E.C. cut is an synthetic, structural operation of the Semiotic Unconscious that conditions the pragmatic subject. The projectile vectors of the Semiotic Tensors execute the cut before the subject emerges to affirm it. Voluntarism is structurally bypassed because the subject is the product of the E.C. bipolarization, not its author.

Brassier’s second horn is ontological determinism, if it’s not subjective will, it must be mechanical tracing of physical forces. Guattari characterizes semiotic tensors as that which “engender sites of sense entities… in domains lateral to those of their point of origin.” (SC, 55). The E.C. bipolarization begins in the domain of F, specifically within the Matter of Content (Mc) and the Diagrammatic function (Diag) within F. This is the domain of the Actual/Real, energetic-spatio-temporal discursivity, and endo-consistency (the "looping arrow" of F's internal calibration). If the system were deterministic, the tensor would just trace the energetic flow. But the E.C. bipolarization forces a lateral jump. The Enunciation pole of the tensor acts as a projectile vector4 that jumps across the horizontal axis of Discursivity. Level II tensors bear a surplus value of possibility. This surplus is carried laterally into the domain of Machinic Phyla (Φ), specifically crystallizing as Machinic Propositions (Pm), which are defined as bearers of symmetric-fractal and deterritorialized representation of ruptures of contingency.5 The Enunciation pole of the E.C. bipolarization does not mechanically represent the flow; it extracts a rupture of contingency from it and projects it into the domain of the Possible (Φ). Because this vector points toward the Virtual/Possible (exo-consistent), it cannot be reduced to the causal mechanics of the Actual/Real (endo-consistent). Determinism is defeated by the structural introduction of possibility.

Alright then, how do we measure if an E.C. bipolarization is successful (how do we avoid the “cancerous body”)? We evaluate its tensorial trajectory:

1. Did the tensor successfully achieve Separation (Level II) from the non-separability of the Flows (Level I)?

2. Did it carry its surplus value of possibility laterally into a Machinic Proposition (Φ) rather than collapsing back into the looping arrow of the Matter of Content?

3. Can this Machinic Proposition eventually be “incarnated” into a Sensible Territory (Ts) without being recaptured by a homeostatic reterritorialization?

A-signifying semiotics and sign-particles

In ATP, even deterritorialized signs (tensor signs) retain a trace of expressive subjectivity, they Spinozistically express a continuum of variation. In SC, the diagrammatic function of Φ produces sign-particles (sp) that are strictly a-signifying. A-signifying semiotics operates by reference, not signification. The sign-particle indexes a state of matter or a position in a phase space. It is a proto-energetic operator.

• This defeats voluntarism because the subject does not choose the meaning of the sign-particle; the subject is constructed by the diagrammatic trajectory of these particles.

• This defeats determinism because the sign-particles are not mechanical representations of a pre-given reality; they are operators of smoothing that extract new potentials from the noise (F).

By shifting from signifying expression (which relies on the quality of the speaker’s intent or force) to a-signifying reference (which relies on the structural function of the particle in the diagram), Guattari replaces the vitalist criterion of affirmation with the functionalist criterion of constraint. The objective ground is no longer the will to power or the plane of consistency, but the structural constraint of the diagram (Φ) as it maps the incorporeal (U) onto the material (F).

But we need to be very careful. If we remove subjective meaning, we are left with mechanical indexing. But this falls directly into the Determinism horn of Brassier’s dilemma. If the sign-particle merely indexes the state of matter, then the diagram is just a passive tracing of physical forces. The subject disappears entirely, and selection is reduced to causal determinism. To escape the enfilade, a logical and epistemological architecture that provides an exterior standard for selection that is neither subjective will nor mechanical tracing is needed. A-signifying semiotics may describe the material of the diagram, but it lacks the logic required to measure consistency.

Segovia’s Intervention: Determinability, Situated Transcendental, and Heidegger

We argue this is precisely where Carlos A. Segovia’s Guattari Beyond Deleuze: Ontology and Modal Philosophy in Guattari’s Major Writings provides a crucial intervention. Segovia, following Althusser,6 argues that SC represents an epistemological break in Guattari’s thought, moving from a metaphysics of deterritorialization (escaping the given) to a modal philosophy of determinability (constructing the possible).

Segovia writes that in SC, the term "determinability" appears over ninety times. In ATP, the movement is from strata to destratification (via affirmation). In SC, the movement is from the Indeterminate (+∞ chaos) to the Determinable (Φ, the diagrammatic) to the Determined (−∞ consistency). Determinability is a logical modality, as it describes the capacity of a system to be structured without the structure being already present, breaking the actualization trap. The criterion for selection is now: “does this increase the logical determinability of the system?”

Brassier demands an outside corridor to prevent the enfilade. Segovia demonstrates that SC provides this through the isonomic status of the four functors. Guattari explicitly rejects a two-term (binary) or three-term (dialectical) model because they lead to depotentialized representation or arborescent determination. The four-functor model (F+Φ+U+T) creates a “trans-entitarian matricial generativity.” (SC, 69).

• T is the determined (the room).

• U is the determinable (the incorporeal horizon).

• F is the indeterminate (noise).

• Φ is the operator of determination.

The outside corridor is the structural matrix itself. Because no functor can have essential priority over another, the system is open. The relationship is thus a chiastic interplay where A defines B by differing from it, and B defines A by differing from it. This structural reciprocity provides the exterior viewpoint: one evaluates an assemblage not from within its own self-affirmation, but from its structural position relative to the other three functors.

Segovia emphasizes a crucial 1990 dialogue where Guattari explicitly rejects the ATP-era logic of "getting out."

“The outside is not a neutral field... It’s an exterior in the form of a particular constellation of universes of reference.” (GBD, xiv).7

The outside corridor is U, but crucially, these aren’t chaotic voids, but as complex, incorporeal universes that possess a specific consistency. U acts as the non-subjective, non-mechanical standard of measurement. It is the situated transcendental. It is transcendental because it provides the a priori horizon for selection (it is not reducible to the immediate territory T). It is situated because it is not a Platonic form, but a constructivist constellation generated by the cycle itself.

The selection of an assemblage is thus a functional evaluation of structural integration: does this diagram (Φ) successfully map the flows (F) into a habitable territory (T) that is consistent with a constellation of incorporeal universes (U)?

Furthermore, in his 2022 essay ‘Guattari⧹Heidegger: On Quaternities, Deterritorialisation, and Worlding.’ Segovia maps Guattari’s F, Φ, U, T onto Heidegger’s Geviert (Earth, Sky, Mortals, Immortals), which operates through a mirror-play (Spiel) of reciprocal differences. In SC, worlding replaces deterritorialization. One doesn’t escape the territory (T). but constitutes a world by structurally reciprocating the Flows (F), the Phyla (Φ), and the Universes (U). The system is open not because it has no boundaries, but because its boundaries are topologically folded (like a Möbius strip or Klein bottle, as Segovia notes).

Brassier’s trap, which is that of selection collapses into either subjective voluntarism or ontological determinism, relies on the univocity of Being in ATP. Because there is only one kind of substance (intensity), the only way to differentiate is by the quality of force (affirmation), leading to the fatal indiscernibility. Segovia uses Heidegger, and by extension Aristotle’s four causes,8 to prove that SC abandons univocity for chiastic dyadic structuralism. Segovia writes that in Heidegger’s Geviert, the elements do not have essential priority over one another. The Earth (the opaque, resisting ground) only becomes manifest through the World (Sky, Mortals, Immortals), and vice versa. It is a structure of reciprocal determination (A is the inverse of B; F=Φ^-1). If the structure is strictly chiastic, the indiscernibility vanishes. The subject cannot arbitrarily affirm a connection, because a connection only counts as valid if it structurally co-implicates the other three functors. Thus worlding becomes a schizoanalytic imperative, solving voluntarism. The outcome is not mechanically determined by physical forces, because the Possible (Φ and U) has primacy over the Real (F and T). The structural horizon (U) actively shapes the material flows, meaning the determination runs bidirectionally across the diagonals, solving determinism.

Brassier complained that ATP lacked a standard to measure consistency because the plane selected itself through us. Segovia uses Heidegger’s modal framework to show how SC recovers an objective standard. Segovia maps Heidegger’s modal axes onto Guattari’s quadrant:

• F and Φ = The Referred / The Given / The Actual / Content (Earth/Mortals)

• U and T = The Referring / The Giving / The Virtual / Expression (Sky/Immortals)

In ATP, because the abstract machine was Janus-faced, the given and the giving collapsed into each other (auto-construction). But by aligning SC with Heidegger’s Geviert, Segovia shows that Guattari reinstates a structural asymmetry. U acts as the final cause. The Incorporeal Universes are the giving; they provide the a priori horizon of consistency against which the given (F) are measured. Therefore, selection is no longer connection selecting connection. Selection (T) is the alignment of the Given (F) with the Giving (U) under the constraint of the Formal Cause (Φ).

Conclusion

Brassier is ultimately correct. ATP falls under its own architecture. Brassier’s critique of A Thousand Plateaus stands as a masterful and ultimately unassailable diagnosis of the vitalist limitations inherent in Deleuze & Guattari’s earlier machinic pragmatics.9 Brassier correctly identifies that the ontological architecture of ATP, which can be defined as a univocal plane of consistency where the abstract machine and the concrete assemblage are Janus-faced, necessitates a fatal reversibility. Because selection relies on the actualized quality of power (affirmation) immanent to the assemblage itself, the criterion for measuring consistency is swallowed by the thing being measured. The result is the spatial image of the enfilade of doors: a closed, self-referential series devoid of an exterior vantage point. In this closed loop, the distinction between the real auto-selecting through us (ontological determinism) and us selecting the real (subjective voluntarism) becomes strictly indiscernible.

However, Brassier’s critique, while devastating against ATP, does not mark the terminus of schizoanalysis. Rather, it accurately maps the exact problem that Guattari’s Schizoanalytic Cartographies was engineered to solve. SC answers back to Brassier’s demands not by abandoning immanence, but by mutating Schizoanalysis from a univocal metaphysics of vitalist escape into a rigorous, neo-structuralist functionalism of modal constraint. SC resolves Brassier’s critique through three precise operations.

1. It breaks the enfilade by shattering the Janus-faced unity of the abstract machine. By ontologizing the distinction between Territories (T), Phyla (Φ), Flows (F), and Universes (U), Guattari replaces the rhizomatic line with a chiastic matrix. As Carlos A. Segovia demonstrates, this four-functor model operates on a structural logic of reciprocal determination (F=Φ^−1). This matrix geometry, which mirrors the topological mirror-play of Heidegger’s Geviert, generates the outside corridor Brassier demanded. The exterior is the structural horizon provided by the Incorporeal Universes (U), which function as a situated transcendental. U provides the exo-referential standard of consistency necessary to measure an assemblage without collapsing back into subjective self-affirmation.

2. SC escapes the indiscernibility between voluntarism and determinism by replacing the vitalist criterion of affirmation with the modal category of determinability. In ATP, the quality of force is already actualized, leading to a deterministic trap. In SC, the relationship between the Indeterminate (chaos), the Determinable (the diagram), and the Determined (consistency) is strictly asymmetrical. Selection is a functional evaluation of how effectively the diagram (Φ) maps the constraints of the incorporeal (U) onto the material flows (F) to delimit a habitable territory (T).

3. The problematic reliance on a-signifying semiotics is salvaged when stripped of its vitalist residue. Isolated, a-signifying semiotics threatens to reduce thought to passive, mechanical indexing (pure determinism). But situated within the four-functor cycle, a-signifying indices become the exact material through which structural constraint (Φ) operates. They defeat subjective voluntarism (the sign does not mean what I want it to mean) without succumbing to mechanical tracing (the sign indexes a position within a dynamic, recursive topology).

Thus, Brassier is correct: a philosophy based on the univocity of intensity and the vitalist primacy of deterritorialization cannot ground an objective standard of selection. But SC reveals that schizoanalysis was never permanently bound to that ontology. By transitioning to a chiastic structuralism of Guattari’s later constructivism, Schizoanalysis provides a functionalist architecture. It answers the critique by proving that measure can be generated immanently through the rigorous, recursive constraint of a fourfold structural matrix.

Measurement of an Existential Territory & Specifications

The question is now thus: How to specifically measure the consistency of an Existential Territory? For the sake of brevity, we shall only possess 3 metrics of measurement forward:

1. The Pseudo-Identity Test (The U → T Vector): The first metric is found in the vector from Universes (U) to Territories (T). A Territory is consistent only if it successfully incarnates a Constellation of Universes (ΣU) via pathic operators of heterogenesis. How to measure it? One evaluates the contours of the Territory. If the Territory has fixed contours, if the sense of identitarian isomorphism is rigid, dogmatic, heavily signifying, or heavily reterritorialized onto a master signifier, as in Oedipus, nationalist, or corporate identity, it fails the test. The Territory must exhibit a pseudo-identity without fixed contours. It must maintain enough structural integrity to be a “lived-in space” (endo-consistency), but its borders must be permeable, shifting, and defined by the virtual Universe it incarnates rather than by external social imposition; plasticity without dissolution.

2. The A-Signifying Synapse Test (Level III Actualization): Territories operate at Level III (The Pragmatic and Subjective), which presupposes Level II (The Semiotic). Therefore, a Territory’s consistency is measured by how it handles the E.C. bipolarized signs passed down to it. How to measure it? One evaluates the Pragmatic Synapses (Se) of the Territory. If is attempted to translate the a-signifying sign-particles (sp) and machinic propositions (Pm) from Level II into conscious meaning, narrative coherence, or signifying interpretation, the Territory is inconsistent, short-circuiting the diagrammaticity10 of the sp and Pm into a scientist mythology or a neurotic narrative. The Territory must actualize Effects without signifying them, operating the diagram pragmatically. Does the subject do the diagram (enact the pragmatic synapse) without needing to represent it consciously? If the Territory functions like an embodiment of digrammatic practices, then we can say that it passes the test; operativity without hermeneutics.11

3. The Necessitation Test (The T → F Vector): A Territory that perfectly reflects a Universe but floats entirely in the virtual is inconsistent, a delirium, a “cancerous body” disconnected from reality. The arrow from T back to F is necessitation, which can be defined as the existential function that binds territories back to the material and signaletic flows, involving a choice for finitude. How to measure it? One evaluates the Territory’s capacity for finitude. If the Territory refuses the T → F vector, c’est-a-dire, if it tries to remain in absolute deterritorialization, refusing to bind back to the Matter of Content (Mc), it becomes a void, a black hole of absolute escape, falling into catatonia. The Territory must successfully make a choice for finitude. It must accept the necessitation of binding its virtual consistency back into actual, energetic-spatio-temporal flows (F).12 It must agree to constitute a world rather than endlessly deconstructing one. Consistency here is the successful grounding of the virtual in the resistance of matter.

In the SC framework, the measurement of an Existential Territory’s consistency is a structural equation: Consistent T = (U-incarnated as pseudo-identity) + (Level II tensors actualized as a-signifying pragmatism) + (F-bound through necessitation/finitude).

1. If an assemblage fails the first test, it is a stratified Territory (fascist/paranoid).

2. If it fails the second, it is a signifying Territory (neurotic/interpretive).

3. If it fails the third, it is a delirious Territory (schizoid/catatonic).

But we need to be extremely careful. Writing that the Territory “incarnates…”, “…how it handles…”, “…reflects…” only leaves us falling back into subjective voluntarism. How are we to verbalize then? If the Territory doesn’t actively “balance” the functors (avoiding voluntarism), and it isn’t passively “determined” by them (avoiding determinism), what is it?

In a deterministic system, the foundation (Level I / Flows) dictates the outcome (Level III / Territory).13 In SC, the outcome feeds back and alters the foundation. When the Territory (Level III) actualizes the pragmatic effects of the diagram, it adjusts the quantum configurations of the primary unconscious (Level I). This means the rules of the game are changed by the very act of playing it.14 The Territory produced at T1​ structurally mutates the Flows that will produce the Territory at T2​.

Thus, the Territory adjusts. “Adjusting” is the operative verb proper to T. It implies a system under structural tension, not a system under control (voluntarism) or a system running blindly on tracks (determinism). T is a site of a structural negotiational navigation across scales. The cycle produces T based on past conditions. T actualizes the E.C. bipolarizations (Pragmatic Synapses). These actualizations introduce ruptures of contingency (Pm) that cannot be predicted. T feeds these ruptures back to Level I, adjusting the proccesual cycle.

8. The Domain of Enunciative Recursion

Figure 8.1 The four requalifications of the Point of Contingencing

So to start, Guattari describes the cycle of Assemblages as a "roundabout at a fairground" to express its recursive and transformative nature (SC, 167). In Figure 8.1, the visual pulsation of the arrows illustrates that each completion of the cycle modifies the domains it has already passed through. The point of contingencing (Pc) expresses a processual movement that redefines the previously concerned domains. For example, a point that starts in the domain of Flows is completely transformed after a full turn of the quadrants, returning to its original domain as a different functional entity.1 This cyclical logic suggests that subjective and material formations are always in a state of being destroyed and rebuilt, rather than existing as permanent, linear structures.

The Point Pc (or P) functions as a crossroads for five distinct functions: diagrammatic (diag), synaptic (syn), pathic (path), existential (exi), and modular (mod). This diagram distinguishes between these functions through its vertical axis, which maps an ontic/pathic split. The left side of the vertical axis is the ontic function, which deals with the Phyla (Φ) and the deployment of infinite multiplicities. Conversely, the right side is the pathic function, which is inextricably linked to the Territories (T) and the axis of virtual real Territories and virtual possibility Universes (TU). While the ontic verticality deals with the objective consistency of machinic phyla, the pathic verticality addresses the self-referentiality of existential territories.

Guattari utilizes Figure 8.1 to address the "aporia of a change of state without a transfer of energy" (SC, 168). The three recession lines located at the top of the diagram—synaptic, pathic, and existential—illustrate how a system can undergo a functional metamorphosis without a standard thermodynamic or informational exchange. These lines are non-transferable energy, indicating a passage to machinic-pragmatic effects that exist outside of traditional spatio-temporal and energetic coordinates. Instead of relying on a generic quantity of energy—like the Freudian concept of libido—, these recessions cathect highly differentiated qualitative processes (Remember chapter 2). This allows for an existentializing function where the quality of being is affirmed through its own internal consistency rather than an external energetic push.

Let’s quickly go through each of the four metamorphoses of the Pc

1. The first requalification occurs within the domain of abstract machinic Phyla (Φ). Here, Pc is deployed into a fractal fold (E), which acts as the initiator of the diagrammatic function (f(diag)). This transformation is associated with formal causes, where diagrammatic irreversibilization results from the machinic Proposiiotns in the Phyla. At this stage, the Point initiates a takeoff of machinic surplus value, shifting from a state of manifest being-there to a field of actual possibility.

2. The second requalification takes place in the domain of incorporeal Universes (U). In this metamorphosis, the Point functions as an abstract refrain (Ra) and serves as a synaptic relay for Constellations of Universes via synaptic recession (f(syn)). This stage corresponds to final causes, where synaptic recession brings about a necessitation or singularization. The synapse acts as a mutational filter that confers necessity upon the Phyla, transforming a potential occurrence into a self-affirming virtual enunciation.

3. The third requalification occurs in the domain of existential Territories (T). At this point, echoing its ontic function on the left side of the diagram, it releases a self-referential pathic (or pathematic) function on the axis of virtual real Territories and virtual possibility Universes (TU). This metamorphosis is of efficient or energizing causes, where pathemic recursion results in heterogenesis. This pathic verticality addresses the internal consistency and existentializing function of territories.

4. The final requalification marks the Point's return to the domain of Flows (F) after completing a full turn of the roundabout. Following this complete turn of the quadrants, Pc is transformed into energized Sign-particles (Sp) via the process of existential recession (f(exi)). This transformation is linked to material causes. The creation of these sign-particles is essential for the constitution of concrete existential machines, which differ from simple tools by their ability to generate new spatial-temporal coordinates and modes of semiotization.

Figure 8.2: The four modalities of discursive causality (reprising of Figure 7.8 and Figure 7.9)

In mapping Aristotelian causal forms onto the four domains of the arrangement, Guattari provides a meta-modeling of traditional philosophy to account for the production of subjectivity. This framework, illustrated in Figure 8.2, defines four specific machinic operations that correspond to the classical causes.

1. Formal causes (Φ - Phyla) → Irreversibilization: Traditionally is the blueprint or form, Guattari links this to the diagrammatic function. In this domain, machinic Propositions (Phyla) break their moorings to signify specific dated processes or proper names, moving beyond mere abstract potentiality into a historical or cosmic irreversibilization.

2. Final causes (U - Universes) → Singularization: Traditionally the purpose or telos, this is redefined as the synaptic function. It acts as a seal of consistency that initiates a self-enunciative procedure through a-signifying catalysis, allowing a subject or group to break away from standard redundancies into a unique singularization.

3. Efficient causes (T - Territories) → Heterogenesis: Traditionally the agent that brings about change, Guattari identifies this with pathic operators in the domain of Territories. These operators confer a pseudo-identity on energy sites, acting as an intensive affirmation of a for-itself that drives the process of heterogenesis.

4. Material causes (F - Flows) → Necessitation: Traditionally the matter something is made of, this is mapped as the existential function. It is a choice for finitude where the material texture and signaletic flows of the arrangement are called on to speak their own existence, a process termed necessitation.

In the causal cartography, the arrows of all four causalities converge on the Point of Contingencing (Pc). This point marks the intersection where heterogeneous flows—material, formal, final, and efficient—meet to collapse realized chaos into a specific, lived, and contingenced state of things. Guattari replaces linear cause-and-effect with recursive causalities stemming from a fractal processuality. In this regime, the effect—the enunciation itself—often precedes or regulates its own temporal and material conditions, meaning that the after can modify the before through a constant feedback loop.

Guattari aligns material causes with energized sign-particles (Sp) and necessitation to challenge the traditional view of matter as passive or silent. In this view, signs—including computer programs, mathematical equations, and diagrams—are active components that speak and communicate by directly participating in material and social flows. Matter itself becomes an optional matter of possible choices, where its specific texture is inherently tied to the affirmation of existence. This approach to materialism has certainly helped the rise of new materialisms. Following Segovia’s Guattari Beyond Deleuze: Ontology and Modal Philosophy in Guattari’s Major Writings, Guattari’s focus on the immanent vitality of matter—its self-creative and productive nature—parallels the core tenets of new materialism, which seeks to “de-objectivize reality” and view it as a tapestry of negotiable events (GBD, 36). But while new materialism often celebrates random connectivity, Guattari’s alter-structuralist approach adds a layer of formal rigor, using the fourfold functors to map how these material flows gain consistency and subjective weight in a chaotic universe.

Efficient causes are linked to heterogenesis in the domain of Territories because they’re the operators that trigger change. An example is the scopic dis-position (the gaze in a theater or a clinical therapy session), which functions as an agent of existential agglomeration. The gaze is a pathic operator that organizes disparate elements into a consistent territory, conferring the intensive for-itself required for a subjective state to take root and evolve. Furthermore, in the process of singularization, the final cause is a synaptic gear change. This differs from traditional goal-oriented purpose because the synaptic operator initiates a sudden mutation or a creationism sui generis that breaks with previous meaning. It is an a-signifying catalysis that opens a new constellation of reference without being bound to a pre-defined program or telos.

This mapping does not merely simplify Aristotle, it deterritorializes his theory to account for hyper-complex objects like the Affect of love, aesthetic illumination, or political revolt. By reframing causality as the interaction of four heterogeneous domains, Guattari provides a tool to analyze how non-discursive intensities can be introduced into the analysis of material and social fields. Philosophy thus becomes a meta-modeling activity that explores the economy of possibles and the conditions for subjective mutation.

Figure 8.3: Speed of determinability

Guattari assigns specific mathematical speeds or coefficients of determinability to each of the four ontological quadrants to describe their internal temporality and information processing:

1. d+∞∫d−∞ [Phyla]: This is modular speed, the velocity of established systems of discursivity, logic, and royal science. It is the speed of propositional knowledge that structures and encodes the possible into identifiable schemas.

2. d±∞ [Universes]: These are synaptic speeds that transcend ordinary spatiotemporal coordinates. At these infinite speeds, information bypasses linear discursivity, allowing for the emergence of mutant creative universes and aesthetic illumination.2

3. d−∞∫d+∞ [Territories]: This speed characterizes the virtual persistence of existential territories. It functions as the existential glue that binds heterogeneous components into a singular grasp of being. It is associated with material stratifications where the time of encoding borders on infinity.

4. d+∞/d−∞ [Flows]: This is the speed of brute material flows. It is a serial time of encoding that borders on zero, characterized by eternitarian duration. Here, the world presents itself as pure intensive fluctuation, smooth and yet to be discretized into meaningful units.

Guattari notes that the "notion of speed is only relevant at the scale of existential Territories" (SC, 186). The synaptic regime (d±∞) bypasses the normal modalities of knowledge by operating at infinite velocities that collapse the distance between expression and content. While the modular regime (dc) requires a slow, step-by-step verification of propositions, the synaptic regime allows for a transversalist leap into new constellations of reference. In the domain of Flows (F), determinability is a wildcard; it is free to flee because it is not yet bound by semiotic grids. However, the transition to the synaptic regime obligates it to respect structural constants like π or Avogadro’s number. This is because once a flow is captured by a machinic phylum or a mathematical universe (U), it must conform to the intrinsic consistency of that universe to function.

Hold of Pubescent Hormonal Speech Example

At its most basic level, puberty begins with the necessitation of biological flows. The maturation of the gonads is a material cause; a brute physical reality that is blind or necessary. This domain operates at d+∞/d−∞ (Actual Real), characterized by an eternitarian duration. The hormonal flow is a material texture that speaks its own existence prior to any discursive interpretation. The hold of hormonal speech is felt as an internal compulsion. As the biological components of puberty intrude, they trigger a series of machinic indices that begin to call the entire previous social and psychological equilibrium into question.

As the adolescent’s body shifts, a new Existential Territory must be constructed to glue together these new somatic, social, and cosmic layers. This is the operation of heterogenesis, the efficient cause. Operating at d−∞∫d+∞, the adolescent creates existential refrains—repeated habits, styles, and "codes of the neighborhood" as is translated—to feel at home in a body that is becoming foreign. This quadrant is hyper-fractalized, meaning the adolescent is constantly negotiating between their local somatic changes and the infinite possibilities of who they are becoming.3

Puberty is often experienced as a series of sudden "flashes" of insight or desire, what Guattari calls singularization, the final cause. This is the moment of aesthetic illumination. Going at the synaptic regime of d±∞, bypassing normal discursive knowledge, allowing the adolescent to “see, as if in a flash, all the richness and threat” harbored by new social and sexual systems (LF, 146). The adolescent is transported into new Universes of Reference (sexual, poetic, political) that have never been felt before.

Finally, the chaotic and exciting experiences of puberty are funneled into established systems of meaning—the Actual Possible. This is the process of irreversibilization, the formal cause. Operating at the modular speed of d+∞∫d−∞, it is the transition into adulthood, which is dated. The adolescent acquires a fixed social identity that leaves a semiotic remainder or enunciative surplus-value. Once these biological and social changes are recorded in the machinic phylum, the process becomes irreversible. The subject has entered the world, and their previous childhood semiotics are often extinguished in a form of childhood amnesia forced by the dominant social order (LF, 150).

The hold of pubescent hormonal speech is thus a recursive loop: the necessity of the material flow (F) is grasped by the heterogenesis of a new body-territory (T), which then experiences a synaptic leap into new Universes of value (U), finally becoming irreversibilized as a dated adult identity in the machinic Phylum. This movement transforms the wildcard of biological determinability into a specific, singularized life path.

Figure 8.4: Temporality in four dimensions

looks like the dekalog

The mapping of temporality in the four causes provides a synthesis of how time is actively produced through the convergence of four distinct operations within an arrangement: Irreversibilization (Φ), singularization (U), heterogenesis (T), and necessitation (F). These operations define four modes of time that range from the objective and sequential to the virtual and existential.

The distinction between objective time (Φ) and fecund moments (U) is rooted in their relationship to the infinite speeds of deterritorialization. Objective time relies on the modular separation of d+∞∫d−∞. Here, the infinite set of enunciative traits (d−∞) serves to snag, fix, and ballast an infinite fractal process into a contingent, sequential determination. This process creates a dated, sequential order that is exo-referred to spatiotemporal coordinates. Conversely, fecund moments emerge from the powdery, sliding speeds of d±∞. In this virtual register, time drifts irreversibly outside of any equilibrium point, allowing for enunciative virtualization. These moments are not sequential but are luminous points that coexist and shine across the plane of immanence.

The synaptic function acts as a critical operator that facilitates the passage between different temporal registers. In the repetitive, actualized state of durations (F), an arrangement remains in a state of formal reiteration or autistic closure, where nothing new occurs. The synaptic operator introduces an opening for enunciating modifications. It snags the infinite fractal flows of the virtual and transforms them into dated machinic propositions. This transition allows an arrangement to shift from a repetitive, circular duration into the irreversible, historical progression of objective time. It is the mechanism that catalyzes a new constellation of reference universes from a deterritorializing rupture.

Applying this four-dimensional map to Guattari’s analysis of Marcel Proust in the second part of The Machinic Unconscious reveals how a single event occupies multiple temporal registers:

1. Duration (F): The raw sensory fluctuation of the flavor of the madeleine itself exists as an actual, intensive fluctuation of primary matter before it is categorized.

2. Fecund Moment (U): The sudden, explosive joy and the involuntary memory it triggers is a virtual event. It is a machinic nucleus of inspiration that emerges as a singular point outside of chronological time.

3. Subjective Temporalization (T): As the memory takes on existential consistency and becomes a refrain (the little phrase of Vinteuil or the madeleine), it becomes a mode of position-retention. It allows the Narrator to found his own coordinates and rework his history in a retroactive smoothing of time.

4. Objective Time (Φ): The placement of this event within the historical diachrony of the Recherche and its dating within the sequential narrative is its entry into the phylum of actualized possibilities.

For non-trivial machines, such as living systems or subject-groups, time is marked by a birth-death finitude. Figure 8.4 visualizes the persistence of the break through these registers. The initial break from chaos is established by irreversibilization in the Flows, which constitutes a first stasis of deterritorialization. This break is capitalized in the Territory through Heterogenesis. This operation provides mediative operators for the retention of forms, creating a memory of being or persistence. Subjectivity itself is the manifestation of maximum intensity in the conjunction of these deterritorialization processes; the “hot spot” where the machine must perpetually rebuild itself against its own finitude.

Guattari’s map refines the classic Deleuzian distinction between Chronos (measured time) and Aion (the infinite instant). Chronos is subdivided into objective time (Φ), which is the sequential, dated time of social and economic pragmatics, and durations (F), which are the intensive, repetitive fluctuations underlying all actualized matter. Aion is refined into fecund moments (U), the virtual lightning flash of pure eventhood, and subjective temporalization (T), which is the internal time-signature or refrain that allows a subject to inhabit a territory.4

If “Heterogenesis brings Affect out of its passivity,” it does so by conferring the consistency of a deterritorialized object on the affect (SC, 186). In Quadrant T (subjective temporalization), the arrangement utilizes a voice/pathway of self-reference. This self-reference allows the arrangement to become self-consistantial, meaning it founds its own coordinates rather than merely reacting to external stimuli. By producing its own existential chemistry, the arrangement can take up the reins of its own history, transforming its internal states through its own ritornellos or refrains. This is the transition from alienated subjectivity to a subjectivity that creates itself, allowing a group or individual to march against the grain of historical development and establish a new historical causality.

Figure 8.5: Chronos and Aïon (repetition of Figure 8.3)

The circuit is structured by two primary states that govern the movement of an arrangement:

1. The synaptic crossing (the chaosmic conjunctive state): Located at the top of the circuit, this is the point where Chronos (Φ) and Aïon (U) meet. This state serves as the threshold of enunciation, where discursive Phyla—the actual possibilities of machinic history—intersect with virtual Universes of value. It is chaosmic because it draws from the infinite chaos of the virtual to create consistent enunciative mutations. Here, the arrangement is actively virtualizing and producing new meaning.

2. The disjunctive modular state: Located at the bottom of the circuit, this state involves the interaction between Flows and Territories. It functions as the existential condition for the temporalities above it. While the top of the circuit deals with the creation of new possibilities, the bottom deals with the persistence and persistence of being in actual, contingenced reality. Flows provide the material continuum (energy, time, space), while Territories provide the operator for position-retention and memory. Without this grounded, disjunctive base, the higher-level temporalities would lack the ballast necessary to take on reality.

Guattari anchors his cartography in a schizoanalyzed ontology by mapping four types the discursive causality to the Greek goddesses of goods:

• Diké (Justice): Governs formal causes (Φ). In this domain, Diké is the irreversibilization of diagrammatic machinic Propositions. Φ is the category of continuous discursivity that marks the infinite multiplicity of a state of things. Diké ensures that these machinic Phyla are pushed into far from equilibrium states, where they take on a language that is proper to them.

• Moïra (Fate): Governs final causes (U). She corresponds to the fecund moments of creative freedom found in the Aïonic Universes. This domain is one of heterogenesis, where subjectivity is permanently reinvented and resingularized. Moïra operates at the level of virtual affect, where an enunciative crystallization occurs between the creator and the interpreter, allowing for a total turnaround or mutation in history.

• Ananké (Necessity): Governs material causes (F). She is necessitation, the point where the material texture of the arrangement—its energetico-spatio-temporal matter—speaks its own existence. Ananké is tied to the primary material continuum and the repetition of forms that stabilize the arrangement in the real world.

The crossing of the synapse at the top of the circuit is a profound gear change for the arrangement. At the bottom of the circuit (the disjunctive modular state), an arrangement is often trapped in the repetitive modularity of the Urstaat (the neolithic or despotic state), characterized by the autistic closure of proto-machinic figures and the formal reiteration of the same material Flows. In this state, the arrangement is governed by redundancy and equilibrium. However, when the arrangement moves upward and crosses the synaptic threshold into the chaosmic conjunctive state, it undergoes a transformation. It moves from the uniquely proximal discursivity of Flows into an opening of possibilization. This gear change shifts the arrangement from the repetitive steady state of the Urstaat into a singular, dated moment of creative freedom. By intersecting with the virtual Universes of value (Moïra), the arrangement breaks the ontological Iron Curtain between mind and matter, allowing for a molecular rupture that overthrows the existing state of things and generates an entirely new universe of reference.

Furthermore, Guattari invokes the ancient Greek philosopher Parmenides to describe a specific modality of time and existence found at the synaptic peak of his circuit. Drawing on Parmenides’ proem, Guattari defines this state as one where “the act of thinking and the object thought are the same thing” (SC, 175). This is the being of enunciation; a thinking that is indistinguishable from the Being in which it is uttered. This immanence is pure because it collapses all discursive distinctions. It has “neither inside nor outside, neither figure nor ground”; it is a “pure body without organs” and a “pure self-referential affirmation” (SC, 178). While the bottom of the circuit is governed by the disjunctive modular time of Chronos (fragmented, successive, and grounded in material flows), the top achieves a unary Aïon, an unchanging, timeless time that is coextensive with absolute immanence.5

The Auto-Pilot Example

Guattari gives a quite useful example to think of this. When a driver is on “auto-pilot,” they are operating within the disjunctive modular state located at the bottom of the circuit. In this state, the driver exists in a “pseudo-somnolent” condition or “wakeful dreaming” (SS, 211). The individuation of the subject effectively disappears as the driver enters into a servomechanical articulation with the car. Guattari essentially describes this as machinic enslavement, where the human’s perceptive, sensory, and motor functions become constituent parts of the machine-arrangement. The driving is practically automatic, governed by reflexes and a discursive orderliness of material Flows and Territories. The driver follows the signals of the road (green/go, red/stop) in a way that is completely homogeneous to that of a dog or a cat. This is a steady state of redundant equilibrium where the Cartesian cogito does not intervene.

The transition from reverie to vigilance is triggered by a sudden incident; a road signal, a near-miss, or a passenger’s yell. In the circuit, this corresponds to the synaptic crossing at the top. The incident connects machinic durations and temporalizations back together again, forcing the driver out of their pseudo-sleep and back into the present moment.

Crossing the synapse is a profound gear change for the arrangement of the driver. The driver moves from enslavement to a state of hyper-vigilance. This is a “high act of consciousness” or a “scintillation” where the driver suddenly thinks, “Attention, I am driving a car!”.6 The driver is no longer a mere component of the car-machine but has been reconstituted as a subject in response to the disturbance. This state is the chaosmic conjunctive state, where Chronos (Φ) and Aïon (U) meet. It is chaosmic because it draws from the infinite virtual possibilities to find an immediate, creative solution to the incident. The driver enters a fecund moment or an instant of seeing that transcends the standard linear time of before, during, and after. In this moment of extreme vigilance, an Aïonic temporal tension is constituted. The driver is no longer merely repeating past habits but is engaged in a singular, dated moment of creative freedom. They are born into a state of absolute self-referential affirmation, intensely aware of their trajectory and focused on navigating the crisis.

Figure 8.6: Chronic discursivity

The diagram of Chronic discursivity is a nested hierarchy where systemic principles of envelopment articulate how molar sets and statistical collections are organized. This logic functions through three primary layers:

1. Organic Envelopment: This innermost layer serves as the foundation where the preeminence of one subset over another begins. It involves the initial contingencing or territorialization of material, biological, and signaletic flows. At this level, Flows are specified as energetico-spatio-temporal (EST) matter, and mediative operators facilitate a position-retention of forms, effectively capitalizing a memory of being or persistence that allows for the emergence of prioritized subsets.

2. Threshold of Sets: These intermediate layers govern the differential solidarity of subsets. Within these thresholds, various subsets are functionally linked and maintained through semiotic solidarity, even as they remain distinct from one another. The threshold of rupture is crucial here, as it marks the point of passage that allows elements to transition between different referents, moving from purely intensive fluctuations to stabilized discursive sets.

3. Threshold of Reference: This outer boundary is the level that transcends individual sets to establish a broader systemic meaning. It provides the structural reference and intrinsic ordination that allows the entire discursive formation to maintain its cohesion and identity within a given social or scientific domain.

At the summit of the Chronic hierarchy sit the E.S.T. or meta-modelling coordinates, which provide the overarching grid for organizing reality. If we remember from previous chapters, EST are capitalistic coordinates that create a referential continuum. They function through generalized equivalency, a process that reduces heterogeneous qualities and singular events to a common, exchangeable measure. This results in an informational linearity where time is treated as a simple, sequential progression that disciplines and organizes all social and economic activity. Guattari argues that other coordinate systems—nythical, ideological, or aesthetic ones—can and do coexist with E.S.T. coordinates. These alternative systems map different montages of temporal components, allowing for a polyphonic multiplicity of time. For instance, aesthetic meta-modelling might involve sensible smoothing that ruptures linear discursivity to create new, self-referenced fields of expression that do not obey the standard logic of capitalistic time.7

Figure 8.7 The four meta-modelling operators

The four operators act as mutational filters or "plungers" that penetrate from the Chaosmos into the four ontological domains.

1. Layer 1: Necessitation → Flows (F): This operator corresponds to Efficient Causes. It targets the material texture of arrangement—the raw intensive fluctuations of matter and sign—to force them to "speak" their own existence. In this context, Necessitation is the process by which a Flow is no longer a mere repetition of material but becomes an active participant in an enunciative process, moving from substantial deterritorialization to machinic effectiveness.

2. Layer 2: Heterogenesis → Territories (T): Linked to final causes, this operator brings the entropic dimension and pathic indices to the self-organization of the subject. Heterogenesis is the principle of producing heterogeneity; it ensures that the Territory (the subjective existential base) is a processual base capable of self-referencing and constant repositioning through feeling (affective indices).

3. Layer 3: Singularization → Universes (U): Linked to internal causes, this operator functions as an a-signifying catalysis. It initiates a self-enunciative procedure by striking into the virtual Universes of value. It is the spark that triggers a new constellation of reference, allowing a singular event to mutate into a motor of transformation for the entire subjective field.

4. Layer 4: Irreversibilization → Phyla (Φ): Correlated with formal causes, this operator dates a process and locks in diagrammatic consistency. Phyla is the infinite multiplicity of possible connections; Irreversibilization provides the formal capture that ensures a mutation is an established trajectory in the history of the machine, creating a line of transistence that escapes regular coordinates.

Guattari terms these breakthroughs because they originate in the Chaosmos, an area outside the established structural laws of the socius or the organism. Unlike normal coordinates, such as EST meta-modelling coordinates which describe the state of an object, breakthroughs describe the event of its becoming. They are molecular ruptures or imperceptible bifurcations that overthrow the equilibrium of a system. The arrows in Figure 8.7 move from the outside in, illustrating the impact of virtual/chaotic forces on the stratified internal domains. This stands in contrast to the active flight (where desire escapes the structure) or molecular implosion (where an arrangement collapses into a black hole). These breakthroughs catalyze the processual genesis of forms by providing the necessary mutational filters that striate the Universes of reference, making them viable and susceptible to mutation rather than remaining in steady-state black holes.

Yet one can see that the four operators which plunge into their respective ontological domain aren’t the ones which can be seen corresponding to a specific ontological domain in the diagram. Why? Well, while Figure 8.4 establishes the origin of these operators (for example irreversibilization originating in the Phyla), Figure 8.7 maps their recessive impact, showing how these forces rebound across the fourfold through enunciative recursion.

The shifted placement of operators in Figure 8.7 reflects the movement of recession, where a force from one domain modifies an adjacent or opposing domain to create consistency. Thus, although irreversibilization originates in the Phyla, its breakthrough vector finds its endpoint in the Flows. This shift occurs because the virtual, molecular proto-energy must disentangle itself and pass back through the wall of fractal deconstruction—the diagrammatic function—to anchor itself in material sign-particles (Sp). By reaching the Flows, irreversibilization locks in a mutation, ensuring that it is no longer a fleeting virtuality but an established trajectory in material existence. Singularization, on the other hand, acts which originates in the Universes (U), acts as the baton that conducts the Phyla. It conducts the starting and stopping of determination and the passage of qualities that define the Phylum’s growth. By striking into the Phyla, Singularization provides the a-signifying catalysis that initiates the self-enunciative procedure, transforming a general law into a specific, singular machinic act.

Meanwhile heterogenesis originates in the Territories but must penetrate into the Universes to bring the entropic dimension and pathic affect to virtuality. This penetration creates knowledge through the other—as seen in the affect of love or a musical work—where the other is an impersonal field of potentiality that “forms me in my capacity for being informed” (SC, 186).8 It brings the Affect out of passivity, allowing it to “watch me” like a Sphinx at the crossroads of sense. While necessitation as an operator is essentially linked to the domain of Flows, its breakthrough vector penetrates into the Territories to fulfill the obligation of virtualities to become incarnated. The primary function of this vector is the necessitation of incarnation. Guattari argues that affects, percepts, and concepts do not remain in a state of pure virtuality; they must be actualized in an existential territory marked by finitude. This impact transforms the material texture of the arrangement into a being-there that can be felt and lived. The impact on the Territories leads to what Guattari calls the monadization of sensible modules. The random, passive Flows are gathered into a self-referential affirmation (a monad) that has no external support, grounding itself in its own intensive becoming.

This displacement effectuates the Aïonic temporal tension, because the operators and domains do not align perfectly—they are shifted—they create a virtual tension where the system is at a perpetual tangent to itself. Guattari calls this the Cheshire Cat’s smile: a state of hyper-ordering that is everywhere and nowhere, existing in the “four corners of the cosmos” without being pinned down to a specific extensive coordinate (SC, 189). The shift in mapping ensures the system never collapses into a static tracing; instead, it remains an open, vibratory state of phase transition.

Figure 8.8: Enunciative hyper-complexity

my favourite diagram of the Cartographies

The recursive square of enunciative hyper-complexity is defined by four vectors, each being a distinct ontological and pragmatic operation:

1. At the base of this cycle lies the stake of Enunciation, which is intrinsically linked to the concept of enunciative monads and the operation of necessitation. Necessitation is a choice for finitude; an unconditioned attachment to "everything and to nothing with a view to constituting a world" (SC, 182). In this state, enunciation has no external basis or extrinsic guarantor; it rests entirely upon its own pure existential self-affirmation. When sensible modules find themselves monadized through this fractal process, they no longer rely on external causalities or interactions but are affirmed through one another. This initial choice is the foundational act required to carve out an intensive territory of existence from the chaotic plane of immanence.

2. The upward vector of the cycle corresponds to Energy, which is categorized as molecular proto-energy. This category expresses all possible pro-positions and trans-positions regarding state of Flows. The process involves the transformation of random redundancies into linearized, smoothed, proto-machinic sequences. Semiotic repetition is very important here, as it is a repetition of divisible and smoothed forms that creates a proto-enunciative substance. This repetition implies an energetic tension that allows the arrangement to take power.

3. The top horizontal vector is Praxis, specifically the analytic praxes that allow an initiatory enunciation to take off. These praxes utilize the diagram as a strategy of experimentation to scramble existing narratives, figurations, and givens. By passing through points of nonsense or the asignifying, praxis performs a role of defamiliarization that disrupts established common sense. This analytico-poetic function establishes a mutant nucleus of auto-referentiality, promoting active ruptures within significational networks. By breaking the grid of dominant meanings, analytic praxis allows for the emergence of the unknown from within the known, facilitating a fractalizing rupture that catalyzes new Reference Universes.

4. The downward return vector is the Process, which ensures the machine’s continuous self-exo-reference through fractal machinics and the becoming-abstract of the face. The becoming-abstract is the incorporeal faciality of Christ, which traverses capitalist machinic phyla and retroactively smoothes temporalities. These fractal processes coexist with contingent determinations that fix and ballast them, preventing the machine from dissolving back into chaos. This ensures that the machine can maintain its own consistency while relating to other Universes of reference in a non-causal, non-interactive mode. The result is a system of existential recursion that guarantees the irreversibility of the arrangement’s development.

In the domain of hyper-complexity, Guattari explains that systemic determination takes flight in a fractal molecular mode. While Figure 8.8 appears as a recursive square, the movement from Enunciation to Process creates an abstract machinic chasm. This chasm is a site of irreducible uncertainty and creativity where the system is opened up to chaos and the aleatory. Because the process is fractalized, every element is susceptible to an infinite molecular fractal regression that recedes toward an infinitesimal tangent. Consequently, the machine's consistency must be permanently re-produced through this chasm, ensuring it remains an arrangement of subjectivation rather than a petrified object.

Guattari furthermore insists that the possibility of a virtual level of systemic resumption (or systemic deterritorialization) must always be preserved, even within established, highly stratified structures. This is the concept of the “this side of”. Even when a system seems completely fixed or territorialized, there remains a latent level of potentiality—a “this side of” the visible structure—where machinic indices can trigger a sudden mutation. This resumption is often facilitated by catalytic operators that remain external to the process itself, such as the frame in a photograph or the traits of faciality, but function as a laser beam of semiotic deterritorialization that neutralizes redundancies and allows a new processual line to emerge. This ensures that no ordering is terminal; the system can always resume its development through a bifurcation or a threshold creativity that sweeps away established coordinates.

The cycle of hyper-complexity serves as a bridge to the classical Aristotelian ontological categories, which Guattari reinterprets through the lens of abstract machines. Guattari argues that classical concepts of Essence, Act, and Energeia (Aristotelian energy) rely on a tangential passage of discursive logic toward abstract machines of enunciation. This means that for a state of affairs to achieve real existence or an Act, it must pass through the virtual Umbilicus of the abstract machine. Thus, the Act is the process of putting abstract machinisms into action, which secretes new options and possibles.

A critical point of this synthesis is the equation established through heterogenesis: Enunciation = Proto-Energy. Guattari posits that a semiotic repetition implies a proto-energetic tension that takes power within a complex arrangement. This molecular proto-energy is a deterritorialized virtual energy. Its impact is apprehended when a specific series of signs (like a loaded series of dice throws) singularizes the situation and forces the entry of a new Universe of reference (such as transgression or winnings). By equating enunciation with proto-energy, Guattari shows that the analytico-poetic function of enunciation provides the efficient cause or the energizing impetus required for the initiatory takeoff of a new subjectivation process.9

Figure 8.9: Enunciative dimensions

this is the end…beautiful friend, the end…

So this diagram summarizes everything discussed in the chapter, so let’s do this quickly.

• Necessitation is anchored in the domain of Flows and performs an existential function (f(exi)). It corresponds to the material cause, which Guattari reinterprets as the obligation of an affect or percept to be actualized in a finite existential territory. Associated with Ananke (the Greek goddess of blind necessity), this operator governs the register of durations. d+∞/d−∞ is the separation of speeds within modular discursivity. It maps the tension between hyper-accelerated reference series (d+∞) and the hyper-slow suspension of determinability (d−∞) found in molar-modular concretions.

• Heterogenesis is anchored in the domain of Territories and performs the pathemic function (f(path)). It serves as the efficient (energizing) cause, providing the existential glue for self-ordered systems. Linked to Hubris (the goddess of excess/insolence), it relates to the register of dates. Heterogenesis acts as an existential stamp that eventalizes and contingentializes states of fact, marking the birth of a singular for-itself within a specific territory. d−∞∫d+∞ is a continuist fractalization. On the side of the giving (subjective enunciation), a fundamental slowing down (d−∞) integrates positive determinations, effectively freezing traits to select and stabilize signaletic registers.

• Singularization is anchored in the domain of Universes and performs the synaptic function (f(syn)). It corresponds to the final cause, which Guattari describes as the abstract putting into refrain of subjectivity. Linked to Moira (the goddess of fate/lot), it operates through fecund moments (the Greek kairos). Singularization transforms the accursed share of fixed destiny into creative freedom by activating synaptic breaks that open new constellations of reference. d±∞ is the paradoxical time of Universes, where infinite speed and null speed are complementary. It is an irreducible ambivalence where a field of virtuality invades a state of things, bypassing the standard linear sequence of before, during, and after.

• Irreversibilization is anchored in the domain of Phyla and performs the diagrammatic function (f(diag)). It acts as the formal cause, incarnated in abstract machinic propositions that provide objective consistency to history. Associated with Dike (the goddess of justice/distribution), it governs objective times. Irreversibilization constitutes the profile of history, where once a machinic mutation occurs (such as the discovery of writing), it cannot be undone, allowing propositions to exist as if they were always and everywhere already there. d+∞∫d−∞ is a discontinuous fractalization. It involves a phase surface functioning at infinite speed (d+∞) that recaptures and circumscribes negativities (the powdery, unlocalizable traits of d−∞) to establish a machinic Plane of Consistency.

7. The Domain of Universes

Figure 7.1: Arrival of the Plane of Consistency

fholy shit

The Plane of Consistency is situated at θ∞ because it is the limit of infinite determinability and absolute deterritorialization. Unlike discrete, contingenced modules that operate within limited equilibrium states, the PoC is characterized by infinite values and irreversible drifting; the domain of abstract machines that escape all fixed spatio-temporal and substantial coordinates. Placing it at infinity suggests a realm where everything is possible provided the connections are compatible with a specific machinic phylum.

Now, to go into What is Philosophy? for a moment. The PoC exhibits a dual nature, D&G argue there. It is described as THE plane of immanence, the "nonthought within thought" and the "base of all planes" (WIP, 59). It functions as a pre-philosophical, subjective image of thought that everyone knows implicitly. Symmetrically, the PoC is something that must be constructed, laid out, or fabricated through philosophy. Philosophy lays out a plane of immanence to save the infinite by giving it consistency (WIP, 189). The zigzagging process in this diagram expresses this active layout where consistency is achieved through a series of shocks and bursts.

The smoothing of Universe at point U. refers to incorporeal smoothing (ϕU), which involves monads of infinite determinability. This relates to expressive smoothing or sensible smoothing in that both express a move away from existential endo-reference (internal closure) toward a state of consistency. While expressive smoothing secretes linearized discursive sequences, the smoothing at U. allows the Universe to acquire its own ontological affirmation and autonomous consistency. Here in this diagram Guattari chooses to show the Universe as a point of convergence for multiple levels of consistency (θ) because it acts as a singular constellation of reference. It is where different levels of deterritorialization and intensity meet to confer ontological autonomy. This convergence allows a fractal process to be fixed by a contingent determination, authorizing pragmatics that create new spaces, times, and energy conversions.

The shift from the closed loop of the Cycle of Extrinsic Determinability (Remember from Figure 6.5?) to the vertical zigzag of Figure 7.1 shows a fundamental change in the nature of the system. The Zigzag is a trajectory of ontogenesis. It is an open, transformative movement that breaks the repetitive loop to authorize creative pragmatics.

The trajectory passing through the center of the ϕ ovals (Phyla) implies that the construction of the PoC is filtered or tempered by actual possibility. Phyla act as mutational filters that bring about a "singularizing striation of Universes," ensuring that the arrival of the Plane is mediated by a relatable repertoire of the possible (SC, 161). The point Pc at the bottom of Figure 7.1 and the Point of Contingencing are the same launching points. Both show the site where a contingent singularity or an optional purport initiates a process. This is the starting point of the wasp-orchid encounter—a singular event that is neither necessary nor purely by chance, but depends on a specific machinic choice.

Therefore, the arrival of the Plane fundamentally changes the status of the local machinic module, as it renders the local module compatible with Universes of mutant value, enabling it to participate in the invariants of scale and produce a resingularized subjectivity.

Figure 7.2: Phase space

Figure 7.2 diagrams a complex temporal state where phase transitions occur at two contradictory speeds simultaneously: infinitely rapid (d+∞) and infinitely slow (d−∞). The horizontal axis, marked by the phase gap (δ), represents a "contingent position of separability" (SC, 153). This separation is effectuated at an infinitely slow speed (d−∞), suggesting that on a local, territorial level, the distinctions between different accidents of existence (Pc) remain fixed and distinct. Conversely, on the vertical paradigmatic axis toward the Plane of Consistency (PoC), these phases relate to one another at an infinitely fast speed (d+∞). This fast speed allows the arrangement to transcend local contingency and achieve a shared consistency or vibratory state.

The enunciation U. is floating, diffuse, and atmospheric. In the context of Figure 7.2, its integrating function serves as the bridge between two seemingly incompatible states of the arrangement: location and migration. The arrangement is "dated" and anchored by the contingent horizontal separation (δ) at the base. At the same time, the arrangement is "migrant," spreading across the Plane of Consistency via the rapid vertical trajectories. This atmospheric quality allows the arrangement to maintain a singular identity (localized in a specific time and place) while participating in a wider virtual field (migrating toward infinite potential).

Guattari also has φ1 and φ2 (the phase spaces) with dashed ghost ovals overlaid, I suppose this is something with virtual inclusion. This vibratory state marks a significant shift from the machinic modules described in earlier chapters. The phase space model suggests a system where possibility and actuality are in a constant state of resonance and mutual inclusion.

Guattari furthermore links the race on the spot between the infinitely fast (d+∞) and infinitely slow (d−∞) speeds to a psychological obsessional condition. In this state, "discernability tries desperately to catch its own tail" (SC, 154). In the diagram, this is reflected in the tension between the horizontal desire to maintain clear, separated phases or identities (δ) at a slow speed and the vertical pull toward a unified, rapid dissolution into the Plane of Consistency. The obsessional aspect arises from the attempt to fix or define these floating, atmospheric phases even as they virtually include one another.

The Ts wedge (striated territory) at the very top of the diagram performs a critical ballasting function. The wedge acts as a modular sequence that snags and fixes the otherwise infinite, floating fractal processes of the phase spaces. It utilizes a decelerated speed (d−∞) to integrate internal traits into a stable territory.

Without this phase space, the plane of consistency would remain a state of pure virtuality or potentially dissolve into unmanaged chaos. Therefore, the Ts wedge serves as the part of the mediation between the Chaosmos of infinite speed/possibility and the structured, stable reality of everyday existence.

Figure 7.3: Phase transitions of determinability

Here Guattari just goes into detail from one of the parts of the other diagram.

The paradox of being distinct and indistinct at the same time is visually resolved in Figure 7.3 through its use of overlapping and separate shaded geometries. Distinctness is satisfied by the two separate shaded inner ovals, each labeled ϕ1​. These are the regime of separability, where specific positions or phases are held apart from one another. Indistinctness is shown by the central shaded intersection between the two larger ovals, marked with the symbol δ. This area serves as the site of vibratory communication, where the two phases merge and become indistinguishable. By combining these elements into a single diagram, Guattari illustrates a vibratory state. The enunciation does exists as a tension between the two, effectuated at a speed that is simultaneously infinitely rapid and infinitely slow (d±∞).

The "race on the spot" (d±∞) signifies that discernibility is always trying to "catch its own tail". As soon as a position becomes distinct (deceleration), it is simultaneously swept up into a transition (acceleration). The system never reaches a final target of absolute, static clarity because the act of becoming distinct is itself the trigger for the transition.

Figure 7.4: Virtual enunciation

The Universe (U) is visualized here as the terminal point of convergence for the lines expressing generalized intercalation. Guattari identifies U as the integral of localized contingency and migrant phase mutations, meaning it functions to totalize the infinite set of possible virtual positions. In the diagram, U. effectively capitalizes on the infinite trajectories of the fractal process by providing a singular point of existential consistency that sums up the otherwise delocalized and atmospherized enunciation. This capitalization allows the process to move from a state of infinite broken-up dispersion to a unified synaptic operator that secures the entire set of possible virtual traits.

The phase rupture at the left characterized by the bracketed ovals labeled ϕ2, signifies enunciation that is "totally delocalized, infinitely broken up, ‘atmospherized’" (SC, 152). This is a radical break from the rigid modules of modular stratification described in earlier chapters, which are defined by finite contingencing and striated spatiotemporal ordering. While stratification seeks to grid and normalize desire within sedentary systems, the incorporeal smoothing here allows for a caesura that breaks the uniquely proximal discursivity of territorialized flows. This smoothing introduces a new opening of possibilization that allows the system to escape the binary relations between substance and form typical of structuralist stratification.

Point U serves as the anchor or ballast that brings stability to the chaotic fractal unfolding. As we said in the discussion of Figure 7.2, it is the coexistence of an infinite fractal process and contingent determination that snags, fixes, ballasts the movement. Without the point U to act as a terminal of necessitation, the process would remain trapped in a race on the spot (d±∞), a perpetual unfolding of delocalized traits with no existential grounding. Thus, U is the ballast1 that prevents the process from dissolving into pure entropy or remaining in a state of eternal, unresolved fluctuation.

The generalized intercalation illustrated by the converging lines captures Guattari’s metaphor of the arrow that never reaches its target, a reference to Zeno’s paradox. This process shows the daily bread of the obsessional condition, where one is caught in a continuous fractalization that attempts to reach a limit through an infinite series of discrete steps. U manages to "smooth-gather-integrate" the process by acting as a mathematical integral, totalizing the entire set of virtual conditions into a singular event of subjectivation. By providing fecund moments and a final causality, U allows the system to cross the threshold that the linear, discursive arrow could never reach.

Figure 7.5: Extensional symmetries

so im pretty sure that our study, we have never seen something like this before.

So extensional symmetries (expressed by the series a,a,a) are characterized as reversible. These relations have no inherent origin; they can be taken in any direction because they imply a common, stable composition between entities within a contingenced or territorialized arrangement. The visual progression from A to C demonstrates the loss of this reversibility as the system becomes atmospherized. Block A is a singular, solid entity, suggesting a stable identity that can be repeated without loss. Block B introduces virtual divisibility (d−∞), which begins to “haunt” the enunciation. Block C vanishes into “etc.,” visualizing a state where the interval is entirely emptied out. As the system moves toward this generalized intercalation, it drifts irreversibly outside of any equilibrium point. The stable, reversible Flow is consumed by a processual line of deterritorialization, transforming a state of fact into a continuous discursivity that cannot be undone or simply reversed.

Guattari describes a phenomenon where each signaletic element is doubled by a multitude of "freeze-frames" (d−∞) that blur the image of the object. Here, the dashed lines in blocks B and C are the visualizatiosn of these "abstract viruses". These viruses transform the texture of determinability. Rather than allowing a unit to remain a simple, identifiable a, the presence of d−∞ introduces an infinite multiplicity of virtual points of view. This virtual divisibility ensures that the enunciation is never a closed, finished product but is always being gnawed at by its own potential for further division.

Continuing with the thing of the obsessional race on the spot, a unary determination is constantly deferred through generalized intercalation. By focusing on the infinite virtual subdivisions (d−∞) of a task or an identity, the subject becomes trapped in the "etc." of Block C. The interval between the action and the goal is endlessly filled with new freeze-frames, preventing the existential passage to the act. The subject remains frozen in their logic, in their syntax, while the target—the solid Block A—vanishes into the "etc." of endless potential division.

The disappearance of the block into “etc.” marks the limit of fractal symmetry and prepares the way for internal irreversible dissymmetry.

• First Mode (Extensional Symmetry): Reversible Flow, close to equilibrium. This.

• Second Mode (Fractal Symmetry): The relatively irreversible folding and intercalation shown in the A-B-C sequence.

• Third Mode (Internal Dissymmetry): This occurs when the dispositional enunciation no longer relies on extrinsic phase spaces but rests solely on its own existential self-affirmation.

By emptying out the unit until it vanishes into the “etc.” of Block C, the system breaks with the “proximal type of discursivity specific to Flows” (SC, 86). This caesura authorizes a mutation of the Universe of reference. Once the block disappears, we move from a logic of identifiable and reproducible objects to a field of fuzzy possibles—the internal dissymmetry of the Universe (U) where subjectivity is produced through mutant nuclei of auto-referentiality.

Roberto Bolaño and the Obsessional d±∞

I think an example would be good to understand the obsessional race on the spot. Specifically, I am thinking of the failure of the revolutionary subjectivity at the end in Roberto Bolaño’s Los detectives salvajes. I believe that the characters become trapped in a state of generalized intercalation, where the distance between their revolutionary ideals and their lived reality is filled with an infinite series of freeze-frames that prevent them from ever reaching their target.

Guattari describes the obsessional condition through the metaphor of Zeno’s paradox: an arrow that never reaches its target because it is caught in continuous fractalization, focusing on infinite virtual subdivisions of a task. In the novel, the target is the origin of Visceral Realism and the physical body of the missing poet Cesárea Tinajero. The central section of the novel, comprising twenty years of testimonies from 52 different narrators, functions as the "etc.". Following Oswaldo Zavala’s PHD Dissertation, the characters Arturo Belano and Ulises Lima pursue a literary and revolutionary heritage that is "always about to be completed and always about to begin," yet the actual œuvre of their search is absent—Tinajero’s work is reduced to a single, a-signifying pictogram.2 This search is a race on the spot (d±∞) where the protagonists move across continents (Paris, Tel Aviv, Africa) yet remain frozen in a state of constitutive indeterminacy.

As the race on the spot metastasizes when an arrangement relates to itself at two contradictory speeds simultaneously, the d+∞ is expressed by the river of voices and the global deterritorialization of the characters. The characters are in constant, frantic movement, fleeing pimps, joining wars in Africa, and tramping through the streets of Mexico City. While the d−∞ is the vertigo of absolute slowing down. A literal instance of this occurs in the Parque Hundido, where Ulises Lima and the established poet Octavio Paz walk in large, overlapping circles in opposite directions. They are physically moving, yet topologically they are stationary, searching for the void. This is literally the stationary race where “discernibility tries desperately to catch its own tail” (SC, 154).

The revolutionary subjectivity of the Visceral Realists fails because it is unable to transition from the Fractal Symmetry of their wandering to the Internal Dissymmetry of an actual existential act. The characters are lost subjects with shattered revolutionary ideals, wandering through a landscape marked by the residues of institutionalized revolution and the rise of neoliberal capitalism. Their movement is united by an "aesthetic of failure".3 They walk backward, gazing at the past while moving into an unknown future, a pose that is no way to walk at all. Because they focus on the infinite virtual subdivisions of their identity as poet-warriors, they become trapped in the “etc.” of Block C. The interval between their poetic action and their revolutionary goal is filled with bohemian lifestyle, petty thefts, and interminable barhopping, preventing any real existential passage to the act.

The novel’s end in the Sonora Desert is the ultimate state of the race on the spot. As the protagonists finally find Cesárea, her sudden, accidental death marks the limit of fractal symmetry. The novel concludes with Juan García Madero’s sketches of a discontinuous window frame, questioning “what is behind the window?” and answering only with a drawing of a fading window frame, leaving only the extended sheet. The subjectivity is dismembered, and the final narration ends in absolute silence, fulfilling the Guattarian prediction that the subject remains frozen in their logic while the target disappears.

Thus, we can say that Bolaño shows the failure of his generation by depicting them as characters who, in their desire to outrun history, end up in an obsessional race on the spot, where the frantic speed of their displacement only serves to highlight their total lack of progress toward a viable revolutionary or artistic destination.

Figure 7.6: Procession and Recession

looks like the early ccru logo…

This diagram visualizes the existential energy of an arrangement, as a dynamic tension between two opposing movements. Procession is defined as a diachronic-processual movement that flows clockwise from the Point of Contingencing (Pc) toward the virtual Universe (U). This is the initial movement of deterritorialization, where an entity breaks away from its historical or structural fixity to move toward new possibilities. In contrast, Recession is a synchronic-structural movement that flows counter-clockwise, returning from the Universe (U) back toward the domains of Phyla (Φ), Flows (F), and Territories (T). For an Assemblage to have existential energy, it must complete this loop: Procession provides the extraction of meaning through deterritorialization, while Recession provides the existential taking on of consistency by reinjecting those virtualities back into the real world. Without this double movement, an Assemblage would either evaporate into abstract virtuality or remain a stagnant, non-processual structure.4

Guattari distinguishes between the cycle of reference (Procession) and the cycle of enunciation (Recession). The cycle of reference is an exo-reference, where the actual refers to something outside itself. The cycle of enunciation is the active giving of existence rather than the mere given of a system.5 Through the movement of Recession, Guattari argues that “essence becomes the motor of existence” (SC, 159). Looking at the circular flow, this recessive movement prevents the Universe (U)—the domain of virtual possibility—from remaining an “abstract universal” cut off from reality. As the arrow of Recession leaves the Universe (U), it must concern and pass through the quadrants of Φ, F, and T. This means that the virtual values or refrains found in U are forced to interact with re-orienting the repertoires of what is possible (Φ), materializing into actual real events (F), and taking on a specific virtual real form (T). When the Recession vector flows from U back to Φ and F, it represents the way an aesthetic experience or a "singular event" can "re-orient the anterior modes of apprehension" (SC, 161). For example, a new scientific paradigm or an artistic school acts like a mutational filter that changes how we view the material Flows (F) and the Phyla (Φ) of possible techniques. The Recession vector is thus the path of singularization and necessitation, where a unique event (like a "Debussyst refrain") creates its own territory and redefines the "direction of an intentional arc" for the entire system.

While the cycle may be said to start at the Point of Contingencing (Pc) and pass through the Universe (U), it is the domain of Territories (T) that acts as the final "relay of contingency" (SC, 166). In this loop, procession carries the deterritorialized potential from Pc to U, recession brings that potential back down to earth, passing through Territory (T) to capture new fields of possibility. Territory (T) is where the loop is closed because it expresses the persistence or the memory of being where the process is finally anchored into a “proto-enunciative substance” (SC, 75). As the vector passes through T and returns to Pc, the point P becomes a crossroads of functions—specifically f(exi) (existential) and f(path) (pathic self-reference)—where the Assemblage is transformed into an energized Sign-particle ready to begin a new cycle of creation.

Figure 7.7: Synaptic disposition

This diagram is a theoretical mechanism that re-orients how an Assemblage apprehends and processes its own components, specifically converting refrain-residues into machinic Propositions. Visually, the synaptic interval in Figure 7.7 is distinguished by an explicit vertical bracket labeled "synapse" that creates a division between Phyla components (Φ1′′ and Φ2). This differs from the refrain-residue seen in earlier diagrams (like Figure 6.9) in its complexity: while earlier gaps might express a simple point of contingency, the synapse is an explicit break/cut rich in content, as that content is a-signifying. Concepts at this level serve as a deterritorialized version of the existential break found in refrains, allowing the arrangement to move from mere persistence into transistence or active change.

The geometry of Figure 7.7 illustrates how a-signifying residue is transmuted into a singularizing Constellation of a Universe (ΣU) through a Vector Cross-Structure. We can see how the horizontal path from Φ1′′ to U.1 leads toward a primary Universe of reference. And the diagonal descent from Φ2 to U2′′ express the double break-bifurcation. This diagonal path is critical as it marks the point where the arrangement's trajectory is no longer linear or predictable; it is a deterritorializing and fractalizing rupture that catalyzes new ways for the subject to relate to the world.6

Nevertheless, Guattari does describes the synaptic conversion as paranoid, whereas the more fluid refrains are considered hysteriform. The rigid, cross-directional structure reflects this paranoid re-orientation by imposing a definitive and irreversible shift in the Assemblage's focus. Unlike the circular or repetitive nature of a hysteriform refrain (ritornello), the synaptic disposition functions as a machinic synaptic operator that drives the system far from equilibrium, breaking the old redundancies to forge a new plural discursivity.

In the synaptic disposition, the point U2′′ expresses an "outcome" that has been reached by "bending the surface" of possibility (SC, 162). This relates to the Dadaist and Surrealist idea of treating optional matters as dice throws. The diagonal descent toward U2′′ is an incarnation of a contingent choice—a singular event that provides the existential consistency required for a new pragmatic field to emerge.

Figure 7.8: Synaptic breaking

now this one is actually quite important and serious

The break here is expressed by a horizontal bar and bracket that abruptly halts the vertical arrow pointing toward the Plane of Consistency (PoC). This movement expresses a state of total fractalization and absolute determinability, which, if left uninterrupted, would lead to the implosion of the system’s singular consistency into an undifferentiated infinite multiplicity. The synaptic break is required to produce a machinic Proposition because it halts the reversible and vanishing movement of the expressive function. By snagging this process, it prevents the potential from simply dissipating and instead forces it into a concrete, articulated structure.

The abstract machine (f(Ma)) is positioned precisely at the "elbow" of the synaptic breaking. In the broader Nietzschean tradition, the throw of the dice is the affirmation of chance that generates problematic combinations or Ideas.7 Within this diagram, f(Ma) acts as this decisive operator; it is the force that throws the Assemblage out of its natural vertical trajectory and into a singularizing path toward a specific Constellation of Universes (∑U). It effectively steers the "Giving" of the system away from mere repetition and toward a unique event.

The path traced here moves from the Synapse to ∑U and then, via a recessive feedback vector labeled f(diag)/f(exp), back toward the Point of Contingencing (Pc). This loop signifies a fourth requalification of the Pc as energized sign-particles (Sp). This differs fundamentally from atmospheric oscillations—which are typically reversible, close-to-equilibrium, and characterized by simple formal iteration—because this loop is irreversible and far-from-equilibrium. The feedback of the f(exp)/(diag) vector ballasts the system, meaning it re-injects the abstract process with existential necessity, transforming the Point of Contingencing into a crossroads for the constitution of concrete existential machines.

The synaptic breaking confers an ontological stamp by decreeing that a specific Phylum of the possible must be actualized into a specific Universe of Reference. The blocking horizontal bar is the stabilization of potential that was previously vanishing toward the infinite PoC. This act of fixing or snagging the infinite fractal process provides the ballast necessary to move from a state of mere potentiality to one of existential consistency. It is the moment where the process refuses to simply disappear and instead takes on a durable, necessitated existence.

Figure 7.9: The tetrahedron of abstract machines

most badass name ever

This diagram is the culmination of the Assemblage cycle, where the diagrammatic logic of Schizoanalysis moves from mapping discursive sequences to grasping the non-discursive Giving of subjectivity. This model expresses the internal striation of virtual Universes, showing how abstract machines filter and catalyze the transition from the primordial soup of chaos into consistent existential territories.

Figure 7.9 illustrates the dissymmetry without discursivity by moving away from the linear, sequential order of the discursive Given (Φ). While discursivity is defined by sequential order exo-referred to energetico-spatio-temporal (EST) coordinates as we have seen before, the recessive angles of the tetrahedron express a movement into the virtual depth of the Assemblage. Unlike the discursive phase spaces that track the trajectory of possibilities, this diagrammatic grasp represents a point of taking consistency where the process of extrinsic dissymmetrization polarizes intentionality toward non-discursive values (Universes of reference). It is without discursivity because it functions through a circular existential affirmation that intensifies and stabilizes a subjective state before it can be translated into language or logic.

The axis between Necessitation and ΣU. (the sum or constellation of Universes) visualizes the ontological stamp by showing the transformation of a virtual possible into a necessary existent. Guattari argues that "energy is nothing other than a possible become necessary," meaning that the Assemblage is energized when a virtual Universe of value snags and fixes a previously aleatory flow (SC, 159). In the next chapter we will see how this axis expresses efficient causality. It shows the moment where a threshold of consistency is crossed, allowing a machinic possible to acquire the force of a fiat—a creationist throw of the dice that determines a specific reality.

The Singularization angle in the tetrahedron expresses the final cause of the Assemblage. This dimension allows the Abstract Machine to snag the infinite diagrammatic foldings and fix them into a singular signature. This is often indexed by proper names—such as Marxism, or specific scientific paradigms (like Kuhn’s)—which serve as singular Constellations of Universes of reference. These names act as mutational filters that bring about a singularizing striation of the virtual field. In this way, the proper name functions as a code name or agent of non-significant rupture, opening the door for an existential function to explore a new problematic rather than being trapped in a pre-established code.8

Guattari defines heterogenesis as the “taking on of consistency of a disparity” (SC, 166). In the tetrahedron, the Heterogenesis vector expresses a pure affirmation of being. Following Deleuze’s Difference and Repetition, traditional logic uses difference as a shackle of mediation (identity, opposition, analogy, resemblance), Heterogenesis follows a logic of the “Heteron” (the different) rather than the “Enantion” (the opposite). It is a process of continuous resingularization where the disparate elements of an arrangement “become both more united and increasingly different” (TE, 69). It constitutes a multicentered field of creation where each point-sign maintains its ontological uniqueness while participating in a shared Idea.

In the geometric model of Figure 7.9, irreversibilization is one of the four recessive angles. It is positioned relative to the axis between Flows (F) and Phyla (Φ), serving as the counter-current to the infinite speed of chaos. By imposing a rhythm of catastrophe and rhythms of selection, it allows the Abstract Machine to transition from the virtual possibilities of chaos to the irreversible facticity of a concrete existential territory. As Carlos A. Sevogia argues, irreversibilization acts as the diagrammatic historization of Flows. It places raw material or signaletic Flows into a historical and cultural perspective by bringing them into contact with the diagrammatic ideas and connections stored in the Phyla (Φ) (GBD, 89).

Finally, the tetrahedron of abstract machines serves as a tool for escaping the obsessional condition of generalized equivalence. It does this by mapping a vertiginous level of self-reference where subjectivity founds its own coordinates and becomes self-consistantial. Rather than being a static map of a limit state of consciousness, the tetrahedron functions as a strange attractor of transversality.

6. The Domain of Phyla

Figure 6.1: Modular striation

We start chapter six with this. So this diagram shows the complex transition between material fluctuations and the establishment of stable existential structures. The concept of the striation of manifest flows (Fm​) refers to the process of transforming aleatory, smooth redundancies into ordered, discursive sequences. In Guattari’s framework, flows are inherently smooth and continuous. Striation acts as a form of linearization, cutting these flows into discrete figures that can be recognized within spatiotemporal coordinates. The operators r′ and r′′ function as filters of relative ordering. They are the specific thickness or points of view that halt the infinite movement of serial determination. By applying these operators, the arrangement regulates the manifest flows, ensuring they are calibrated and articulated as sensible qualities before reaching the modular interface.

The transition points p1​ through p4​ are the modular interface where discursive flows are captured or modularized. Their theoretical significance lies in their function as ontic operators that perform a specialized quantization of the flows. As flows move toward the non-discursive domain (T), these points select specific traits from the primitive soup of redundancies to create proto-machinic sequences and are the passage where continuous discursive fields are broken down into finite, intensive ordinates capable of supporting a specific existential territory.

The label d+∞ signifies infinite speed of determinability or reference. In the manifest flows (F), this infinite divergence indicates a state of pure, continuous possibility where references are not yet fixed. The convergence toward the singular territorial point TS (Sensible Territory/Instance) expresses the existential grasping that defines an arrangement. Although the flows operate at infinite speeds of reference, they are contingenced or ballasted by the interface points. This result is a singular, convergent point because the territory acts as a nucleus of auto-referentiality, where the "many" are unified into a single for-itself or local persistence.

In the non-discursive domain (T), the distinction between line types marks a difference in ontological consistency. The solid lines p1​ and p4 are the actualized aspects of the territory. They correspond to the striation of modular instantiation where the territory is most heavily stratified and tied to physical, energetico-spatiotemporal coordinates. The dashed lines p2​ and p3 labeled d+∞, these are the virtual quality of the territory. This central section constitutes a chaosmic umbilicus or a zone of intensive depth that remains open to incorporeal Universes of reference. It indicates that even within a stabilized territory, there is a smoothed space of virtual possible speeds that allows for future mutations and prevents the entity from becoming a dead, petrified structure.

Figure 6.2: Expressive smoothing

This diagram shows the transition from a state of modular striation, where matter is fixed into predictable, recognizable forms, to a state of expressive smoothing, where an arrangement breaks free from its coordinates to explore virtual possibilities. Point P serves as the Point of Contingencing (Pc​) or the initial site of application for the modular function f(mod). It is the arrival point where non-formed matter has been processed into a manifest, territorialized Flow. Starting in the domain of Flows is necessary because deterritorialization always operates upon an existing stratum or redundancy.

The ϕ attractor, identified as a smoothed space of possibilistic phases, acts as the primary driver for moving the arrangement toward the deterritorialized domains. Its functions include:

• identifying potential bifurcation points within the field of possibility, allowing the arrangement to escape linear causality.

• polarizing the material and signaletic Flows toward the machinic Phyla (Φ), which are the integrals of those flows.

• connecting the arrangement to Constellations of Universes of reference (ΣU), which are non-coordinated and non-dimensional.

On the discursive side, d+∞ is a regime of continuity and the infinite speed of determinability, allowing the expressive function to repeat and echo the modular formulas while deforming and miniaturizing them to generate a surplus value of code. On the non-discursive side, d−∞ is discontinuity and the suspension of determinability. The shift to d−∞ signifies that the existential function f(exi) has converted the old sensible territory (Ts​) into a new Territory. In this state, the territory is no longer a passive being-there governed by external laws; it acquires self-consistency and ontological autonomy. This allows the territory to function as a monad that grasps being-in-the-world through a non-discursive affect.

The core difference between modular striation (Figure 6.1) and expressive smoothing (Figure 6.2) lies in the direction and finality of their operations. While modular striation aims at a "correct" interpretation or solution, expressive smoothing is constructivist. It tells us that the terminal result is an opening onto multiplicity, where the arrangement can continue to start over from zero at the point of chaosmic emergence.

Figure 6.3 The take-off of machinic surplus value

This is one of the really important ones.

Machinic surplus value is a pragmatic taking consistency that occurs when an arrangement produces more than a simple addition of its parts. Here, this value is primarily generated through the rupture at the δe gap, the point of emergence for expressive fractalization. While the δe gap—the distance between the formal endpoint fts and the substantiation point se—is the specific moment of unsticking from modular constraints, the surplus value itself is the result of the entire movement. It involves the conversion of material flows into signaletic flows—signs that no longer merely represent an object but activate the 'bringing into being' of ontological Universes. This surplus is the added value secreted by the processual headlong flight of the machine as it escapes the wall of significations.

The take-off involves arrows curving toward the φ attractor and the deterritorialized Φ domain because this is the transition from contingency (what is merely there) to possibility (what could be). The Φ domain acts as a "reservoir of potential effectuation," (SC, 102) containing the integrals of memory that are grafted onto material flows. By curving toward the φ attractor, the arrangement accesses “abstract qualities" that open it onto a "continuous and transfinite evaluation" (SC, 83). This virtual element facilitates the extraction of value by allowing the machine to be "for-something-else, elsewhere and after," rather than being trapped in the endo-ordination of the local territory (SC, 134). It essentially provides the language and the logic of non-sense necessary to subvert established codes.

In Guattari's semiotic energetics, negative infinite divergence (d′′−∞) characterizes the diagonal transformations between the discursive and non-discursive sides. While positive divergence (d+∞) represents the continuity and coalescence seen in expressive smoothing (Figure 6.2), negative divergence (d-∞) represents a caesura or a suspension of determinability.

The points in Figure 6.3 are the different stases or phases of a processual cycle. These points map the transition from Flows (raw energy/labour) to Signs (the diagrammatic catalysts) to Materiality (the final, necessitated existence):

• fts (Formal/Flow-Territory-Sensible): The formal endpoint of a matter-form relation where a flow is still captured by its manifest, sensible form.

• se (Substantiation-Effect): The point of emergence where a material flow is converted into a signaletic flow (a sign-particle) capable of triggering a new universe.

• mts (Material-Territory-Sensible): The material point or unformed state of redundancies being the baseline material/energetic input.

• fe (Formal-Effect): The point where the formal properties of a machine are projected onto a plane of expressive discursivity.

• sts (Substance-Territory-Sensible): The enunciative guarantor or the witness-remnant of a previous modular state; it marks where the subjectivity was previously territorialized.

• me (Material-Effect): The point being the actualized material effect of the machine’s operation.

The take-off in Figure 6.3 and the expressive smoothing in Figure 6.2 are complementary operations within the same machinic cycle. While Figure 6.2 is a horizontal smoothing of discursivization—an expansion of the field of possible trajectories for a system—Figure 6.3 is the vertical smoothing of deterritorialization—the actual take-off or extraction of intensive surplus value from those possibilities. These two processes coexist because any arrangement must navigate both trans-ordination (the opening of possibilities in Φ) and existential incarnation (the grounding of those possibilities in T). Figure 6.2 maps the breadth of the potential world, while Figure 6.3 maps the intensity of the subjective and machinic leap that crashes the old strata to produce a new land.

Figure 6.4: Space φ of P

This is where the Point of Contingencing (Pc​) is articulated within a Space of representative phases (ϕ). This is achieved through the folds of contingencing. The folds of contingencing refer to the specific series of operations—designated as P1​,P2​,…,Pn​—that contribute to the positioning of the Point of Contingencing (Pc​) within a possibilistic space. In Guattari, these folds are the procedural steps that transition an arrangement from a state of raw, chaotic redundancy toward a singular, consistent "take-off" of machinic value.

Guattari uses the mathematical baker transformation (also known as the magic skin transformation) as a metaphor for these folds. In this model Each fold (p1​,p2​,…) is a discrete operation that acts upon the dough of possibilities. p1​ is the final operation before reaching Pc​, p2​ the penultimate, and so on. These folds are described as both necessary (as part of a structured procedure) and generative of aleatory aspects. While the process follows a specific path, the final point of convergence (Pc​) remains a contingent accident that cannot be calculated in advance.

To ground this abstraction, Guattari provide the example of a green plant on a windowsill. The specific "green being" that exists here and now is the point of contingencing. The folds are the multiple facets or "points of view" that result in this singular terminal. They include the distance of the observer, gradations of color, relations of contrast, and modulations of light and temperature.1 All these heterogeneous folds—lighting, biological state, observer position—converge at a single moment to existentialize the plant's greenness for the subject.

In this diagram, the arrows being these folds converge on the value 225. This number is an arbitrary representation of the Point of Contingencing taking on fixed consistency. It symbolizes the moment the expressive function (EC) and the diagrammatic function (f(diag)) successfully snag a virtual possibility and anchor it into a real, operational state. Convergence on "225" indicates that the arrangement has reached a truth value2 where it stops being a mere dream and starts biting into reality.

Figure 6.5: The cycle of extrinsic determinability

So the theoretical distinction between the cycle of De and the module Di centers on the ontogenetic difference between the Virtual and the Actual. Intrinsic determinability is located at the territorialized pole connecting Flows and Territories, this is actualized, extensive determinability. It operates through modules of finite contingencing, which act as ontic operators to fix matter into recognizable, stable forms within spatiotemporal coordinates. It is essentially a molar function that reterritorializes the arrangement into a state of equilibrium or a steady state. Extrinsic determinability is located at the deterritorialized pole connecting Phyla and Universes, this is virtual, intensive determinability, operating through monads of infinite determinability, which are unlocalized and escape the coordinates of time and space. De is the possibilistic life of the arrangement, where new quanta of the possible are emitted, allowing for radical mutation rather than simple reproduction.

The internal geometry of the module Di explains the striation of the world of flows into a world of objects. In previous diagrams (Figure 3.4), the vertices were matter (m), substance (s), and form (f). The inclusion of 'b' at the intersection of Φ and F likely is a transformation of the flow-form (f) into a Point of Contingencing (Pc).3 This vertex is the contingent choice where the abstract laws of the Phyla collide with the material Flows to instantiate a specific reality.

The operator EcCϕ is the machine of machinic smoothing that links the Actual Real to the Actual Possible. Ec stands for contingent Expression and Cϕ for phase Content. This operator facilitates the transfer of discursive complexity by extracting machinic propositions from material flows. It utilizes the ϕ (possibilistic) attractor to identify points of bifurcation, allowing the arrangement to acquire a language that is proper to it, translating material energy into signaletic purport. It is here that a surplus value of code is generated, as the machine begins to function not just for itself in the present, but in relation to future pro-positions.

Figure 6.5 is the culmination of three previous micro-mechanisms:

• Modular striation, which provides the cold endo-consistency needed for the Territory to hold fast.

• Expressive smoothing, which releases the Phyla from material constraints, allowing infinite speeds of thought and creation.

• Take-off of surplus-value, which establishes the surplus value of code that allows the arrangement to drift creatively rather than just oscillating in a closed loop.

Is this a blueprint for a stable arrangement? Yes, but it is a metastable one. The macro-cycle ensures that the arrangement can maintain a state of affairs (through Di) while remaining open to the event (through De). It is a system of enunciative recursion where the arrangement constantly re-reads its own past to invent a future.4

Figure 6.6: Overlapping of monads and module

In Guattari’s matrix, the distinction between monads and modules is based on their respective degrees of consistency and their relationship to discursivity. The upper frame contains the Phyla and Universes, which are defined as virtual and deterritorialized. They are termed monads because they operate as exo-consistent entities characterized by infinite speeds of determinability. These enunciative monads possess an absolute speed that allows them to exist everywhere at once without being localizable in extrinsic spatio-temporal coordinates. They are a self-referential consistency that is transistential, meaning it exists at a level of abstract possibility that precedes actualization.5 The lower frame contains the Flows and Territories, categorized as actual and territorialized. These are modules because they are endo-consistent, finite, and subject to discontinuous discursivity. Unlike the infinite speed of monads, modules are decelerated and fixed within extrinsic coordinates. They are the contingenced occurrences of the world—the Being-there that is bounded and perceptible.

The significance of intermediate temporalities in the zone of overlap is that they provide the necessary transition for a virtual potential to take on the actual consistency of a lived situation. Guattari distinguishes these from the two extremes of time: Chronic time (the pseudo-temporality of computer-assisted or linear discursivity) and Aeonic time (the non-discursive, unary block of duration).6 Intermediate temporalities are specifically the temporalities of subjectification. They function as a cursor-ring of instantaneity that allows fecund synaptic moments to occur. These temporalities allow a virtual monad to take on consistency by catalyzing refrains and existential grasping.

The expressive arrangement is the functional intersection and reciprocal presupposition of the other four domains. Guattari argues that an assemblage is simply the fact that material flows, territorial segmentarity, machinic phyla, and incorporeal universes are articulated together. The overlap is the site of the production of enunciation. It is the place where expressive discursivity ceases to be a neutral representation and instead engages forcefully with reality. It is through this overlap that a machinic surplus value is generated.

Figure 6.6 is the topological result of the dynamic cycle of extrinsic determinability shown in Figure 6.5. Figure 6.6 shows this overlapping as a stable state of an active assemblage, while the cycle in 6.5 describes the processual energy that keeps the monads and modules in contact. The overlap is effectively the intermediate zone where the deterritorializing drift of the Phyla is re-ballasted by the existential finitude of the Territories. This diagram clarifies that expressive components—such as the expressive function, f(exp)—are essentially intermediate because they lack the autistic closure of pure modules but have not yet reached the absolute deterritorialization of pure monads. Guattari notes that these intermediate expressive chains act like a delegation of being, performing an ontological simulation that allows the non-discursive monad to be somatized or corporealized within the actual module.

Figure 6.7: The entry of Universes of reference

woahhh

So the point of contingencing acts as the fundamental, singular origin at the bottom of the diagram, it is the intrinsic formal determinability of an event—the dated and situated moment of a singular occurrence. The act of folding is the process by which these singular points are condensed and multiplied to create a topological volume.

The point of contingencing unfolds into a two-dimensional phase surface through deterritorialization. In this process, the traits that were knotted together in a local, territorialized module are folded into a phase space of possibility, which allows for the unsticking of the sign from its immediate material support. This expansion creates a surface of intensive ordinates where different possibilities for the arrangement can be explored and mapped.

We have seen that in various previous diagrams Di (internal/intrinsic determinability) and De (external/extrinsic determinability) were diagrammed as separate modules. Figure 6.7 clarifies that they interact through branching at specific thresholds of consistency. For De to enter at a phase surface means that the internal process of fractal folding has reached a level of complexity where it becomes compatible with the basin of virtuality of an external Universe of reference. This is a synaptic phenomenon: the internal logic of the arrangement (Di) reaches a point where it can plug into a new, external Constellation of Universes (ΣU), thereby enriching its own potential for transformation.

The process is described by Guattari as folding rather than layering because it expresses an autopoietic and recursive movement rather than a simple linear accumulation. Folding implies that each new level of complexity "wraps" and reinterprets the previous one, similar to how a "form net" is projected onto unformed matter to create substance.7 The phase surface (Cϕ) relates to the smoothed space of possibilistic phases by serving as the site where the virtual is actualized. It is a state of phase transition that operates at an infinite speed (d±∞), allowing the arrangement to include both a limited material referent and an infinite field of incorporeal possibilities simultaneously.

The resumption of folding at the top of the diagram indicates that the entry of Universes of reference is a fractal and potentially infinite process. Every time a phase surface is constituted, it can serve as the base for a new folding-up, if a new Universe of reference is encountered. This contributes to the overall consistency of the arrangement by creating a Consistential Complex (CC). This complex ensures that the arrangement undergoes permanent resingularization, capturing an existential surplus value, through its recursivity.

We’ve seen throughout the book that the Ec operators are contingent Expression. Their specific function is to act as scene shifters or pragmatic mediators that allow the possible to ooze out of previously encysted or stratified forms. Here they act as the catalyzer for the phase transitions that allow the arrangement to move from one state of authorized existence to another.

Figure 6.8 The inversion of deterritorialization

The inversion of deterritorialization describes the return to contingency of forms that were previously launched into an infinite phase space of possibilities, as we saw above. While deterritorialization carries an arrangement toward the virtual possible (the upward expansion), the inversion expresses the coiling back of Expression onto Existence. This is a “return-there where it could be” through an artificial, processual repetition, as Guattari himself calls it in page 111. This recursive loop allows the arrangement to maintain its virtual smoothing while simultaneously functioning as a striated module that occupies a specific time and place. The inversion acts as a safeguard; a too-sudden or absolute deterritorialization without this inverse return could lead to a suicidal collapse of the arrangement, as per the classical schizoanalytic tradition.

Here, Content (pm)—referring to machinic propositions—is associated with the vertical axis toward the Phyla (Φ). This is because the Phyla is the integral of possibilities and the abstract discursivity of possibilistic forms that are not yet actualized in a specific state of affairs. Content, therefore, is the virtual "what" that an arrangement could become, functioning as an extrinsic determinability. Conversely, Expression (sp)—referring to sign-particles—is associated with the horizontal axis moving toward Territories (T). These sign-particles are the matter-movement that bear the specific singularities and existential consistency required to ground a world. While Content expands vertically toward the transfinite and universal, Expression moves horizontally to necessitate a world, anchoring the virtual possibilities in a finite, corporeal, or somatized instance.

The operator Ec, or contingent Expression, functions as a pragmatic stagehand or enunciative operator that mediatizes the two axes of the diagram. In the previous diagram we just saw, Ec served as the entry point for Universes of reference, but in the context of the inversion in here, its role is to facilitate the movement from the rigid Striated Territory (Ts) back into Expression (sp). This operator translates a rigid territory into a flexible expression by breaking the dead-end atonic state of a territory that has become a mere residue of past memories. It introduces an excited state by injecting surplus values of possibility derived from the diagrammatic function (f(diag)). By doing so, Ec ensures that the old modular structure is forced to exit its isolation and open up to other enunciative Assemblages.

The distinction between Existential Territory (Te) and Striated Territory (Ts) marks the difference between a territory that is creatively produced and one that is passively inherited. Ts is a sensible territory associated with the “being-previously-there”. It is molar, extensive, and governed by extensive coordinates that reduce subjectivity to pre-established roles and functions. Te is a new species of territory that emerges through the inversion process, characterized by self-consistency and is worked by semiotic potentials and diagrammatic consistencies rather than being passively molded by external laws.

The functions governing these territories serve different configurational strategies for the assemblage. The modular function (f(mod)) maintains the matter-form tensor of the module and ensures self-conservation within existing strata. It is necessary for the assemblage to “reform each dawn”8 and respond to the dominant reality. The existential function (f(exi)) is responsible for singularization, Guattari also relates it to necessitation. It is the power that allows an arrangement to “dance the dance”, as he writes in page 143, and choose a specific world-making path among an infinity of virtual possibilities. While f(mod) provides the necessary stability (striation), f(exi) provides the creative impulse (singularization). For the assemblage to survive without collapsing into a repetitive black hole of social subjection, it must use f(mod) to lodge itself on a stratum and f(exi) to take off and reinvent its existence through a mutant creationism.

Figure 6.9: Refrain-residue and existential tensors

In schizoanalysis, a refrain (ritournelle) is a repetitive, rhythmic circle that marks out a territory and protects the “germinal forces of a task to fulfill” from the surrounding forces of chaos (ATP, 311). The residue here is described by Guattari as a “witness-remnant” or a “dead memory” of a previous state of modular tension. While residue often implies garbage, in schizoanalysis, it is a concentrated extract or a residuum that constitutes the subject’s share of a previous whole, as in Anti-Oedipus. It is the point of application for new forces. When the refrain is in an atonic state, the residue serves as a dead memory that merely designates the being-previously-there of a defunct modular enunciator. This residue provides the material necessary for existential stability. It is the matter that must be reworked or refounded to allow a processual subjectivity to emerge. It is the dust of previous social and psychic stratifications that schizoanalysis aims to scour and reassemble into new “existential chemistries” (SS, 306).

The directional forces in the diagram are labeled as tensors. In Guattari, tensors are irreversible operators that transition the assemblage from one domain to another. Existential tensors act as the double-lined arrow that projects from the refrain-residue toward a singular point. They function to stretch and hold the territory together by establishing a relation of persistence—the capacity for a state of affairs to endure over time.

The operator δ′ in Figure 6.9 is distinct from the δe​ (differentiation of expression) seen in the broader take-off of value in Figure 6.3. δ′ is an infinitesimal cracking that is intrinsic to the module, a secondary differentiation that occurs within the territory. It marks the point where the internal tension between matter (m) and form (f) is just barely broken, allowing the residue to become visible as a distinct element that can then be targeted by existential tensors. While δe​ is associated with the excited state of a refrain that catalyzes new mutations, δ′ characterizes the atonic state, functioning as a dead memory of what was once a living tension.

Figure 6.5 introduced Module Di​ as a simple wedge with vertices b,m,s (base, matter, and state/signification). Figure 6.9 refines this by specifying the temporal-spatial (ts) coordinates of these vertices. Finally, the s vertex is the target of the existential tensors because it is the point of consistency where a new "state" is produced. In doing so, the tensors necessitate a choice for finitude, creating an existential-body-without-organs that allows a life to take on a borrowed organicity or a proxy soma. This substantiation is what allows the territory to maintain itself as a homeland or a self-belonging space.

Figure 6.10: Diagrammatic refrain and existential tensor

While earlier stages of the refrain may merely index a previous state of being, the diagrammatic refrain functions as an excited state that actively intervenes to catalyze new morpho-genetic processes. The diagrammatic refrain here is an option machine or a selector of choices that uses surplus values of possibility (δ′′) to break a system’s dead autonomy. This change in the input modifies the nature of the existential tensors produced; they are no longer mere witness-remnants but are now active catalysts for the “recomposition of a more or less damaged existential Territory” (SC, 146). These tensors function as the machinic material of expression that necessitates the birth of a new world. In this excited state, the refrain behaves like a messenger-bird that signals the presence of virtual Universes of reference, allowing the territory (Te) to undergo a radical re-singularization.

At the δ′′ stage9, the machine moves beyond merely being or repeating to creating because it introduces an “infinitesimal slipping of the extrinsic point of view” (SC, 147), as it carries a charge of a free and virtual valence for the purpose of enunciative rearrangement. This slipping is what allows the assemblage to bypass redundancies of resonance and enter a mutant creationism that must be continually reinvented, the specific point where transistence overcomes simple persistence, enabling the ex nihilo creation of the signifier10 as a precondition for new social and mental realities.

The transition from the single sts​ point in Figure 6.9 to the sequence (s1ts​,s2ts​,s3ts​) in here is very important for the concept of serial smoothing. The sequence here implies that the diagrammatic refrain is the operator responsible for this stochastic linearization. It takes the fuzzy aggregate of an assemblage and provides it with consistency by generating a sequence of distinctive points. The diagrammatic refrain (f(diag)) extracts intensities from distinct forms and constructs them into continuums of intensity. The sequence (s1,s2,s3) are the instantial striation of a dis-positional form. By creating this sequence, the active refrain coordinates new associations that singularize the situation, allowing it to carry its effects to the heart of fundamentally heterogeneous domains. This process ensures that the new can emerge from the heart of the past, creating processionary references that define a potential future.

Figure 6.11: Existential refrains (repetition of Figure 6.8 as a function of Figure 6.10)

By repeating the inversion of deterritorialization (Figure 6.8) through the lens of the diagrammatic refrain (Figure 6.10), this diagram illustrates the total machinic circuit required for the production of a subjective and existential territory.

Adding the territory of the refrain significantly alters the inversion of deterritorialization. In Figure 6.8, Guattari illustrates a general movement where deterritorialized forms of content and expression converge on a phase of attraction to create an existential territory. However, the introduction of the refrain in Figure 6.11 provides this process with a specific selector of choices or an option machine. The refrain functions as the clutch or governor of the machine by managing the "aleatory putting on hold" of the system’s heterogeneous components (SC, 147). It acts as the site where internal rhythms meet external structures, allowing the arrangement to lodge itself on a stratum while simultaneously seeking possible lines of flight. In its excited state, the refrain territory uses the δ (differentiation) to force the assemblage out of a dead, atonic autonomy and open it up to other enunciative possibilities.

Figure 6.11 contrasts two triangular wedges—the existential tensor and the modular tensor—which project from the refrain to define the territory. These two tensors are projected separately because an assemblage must always maintain a dual orientation. It requires a small plot of land or a home (the modular base) to prevent total dissolution, but it also requires lines of flight (the existential opening) to remain creative and processual.11 They are the necessary tension between self-conservation and becoming. The relationship between the virtual possibilistic attractor (φ) and the actual refrain is maintained through a cyclical loop between f(diag) and f(exp). This implies that a self-sustaining assemblage must constantly check in with its virtual possibilities. Without this loop, the refrain would collapse into an atonic state; a dead refrain that merely marks a territory without any power of mutation. This recursion ensures that the expressive a-signifying rupture continues to summon creative repetitions rather than deathly reiterations.

Throughout the diagrams in this chapter, we have seen different types of differentiation: δe (extrinsic), δ' (atonic/internal cracking), and δ'' (excited/possibilistic). In Figure 6.11, these are integrated into a single δ located within the refrain. This simplified δ is the point where all different modalities of differentiation are integrated into a singular pulsation or vibratory state of the arrangement. It is the differenciator of difference12 that allows the assemblage to maintain subjective consistency. By condensing these variations, the δ in the refrain confers a specific consistency on the instantiated flows, allowing the arrangement to acquire its own language and power of repetition. Thus, it acts as the engine of consistency, balancing the infinitely rapid speeds of the virtual with the absolute decelerations of territorial existence.

5. The Domain of Flows

Figure 5.1: Ontic and pathic operators

So the term ontic refers to the actual state of being or existence. This connection links the repertoires of the possible (Φ: Phyla/Proposition) to the actual physical, material, energetic, and signaletic Flows (F). I believe that the function of the ontic operators is likely to manage the relationship between the abstract organizational potential and material actuality. Flows are intensive fluctuation and primary matter. Φ are the abstract machinic phyla that organize these flows, transforming contingent fluxes into possible occurrences. The ontic operators thus describe how the possibles (Φ) are instantiated in the actual flows (F) and how the actual flows inform the repertoire of possibilities, given the bidirectional solid arrow connecting them. This linkage thus addresses the constitution of the systems of reality itself.

The term pathic relates to feeling, experience, or pathos. This connection links Existential Territories (T) to Universes of reference values (U: Dis-position). The pathic operators of self-reference are crucial for the production and resingularization of subjectivity. Territories are established through non-discursive, existential, and affective crystallization, while U (Universes) are systems of abstract value (such as music, love, or compassion). This relationship describes how an existence (T) finds its meaning or adherence to an incorporeal universe of endo-reference (U).

The function of these operators is to govern subjective self-references. They ensure the creation of consistency in subjectivity by transversalizing and reconfiguring various structural domains. This linkage is particularly concerned with auto-referentiality and auto-valorisation, enabling the continuous development of subjectivity. Since they are mediated by a dashed vertical line, this might be a relationship characterized by mediation, continuity, or perhaps the fragility of subjective construction, distinct from the rigid actual determination suggested by solid lines.

The mediation of Flows and Territories via modules suggests that the creation of a stable, existential territory from raw flows requires organizational units or standardized structures. In Hjemselv terms, Flows might be likened to expression-purports (material flows of phonation, scripture) which are channeled into Territories (expression-substance, such as bodies).1 The modules would be the mechanisms of form net projection onto expressive material, giving form and boundaries to the unformed material flows. This thus process capitalizes a memory of being (persistence) within the proto-enunciative substance of Territories. Modules thus function as the practical and structuring agents that convert energy and material into stable, identifiable components of existence.2

The solid bidirectional arrow—like the one for ontic operators—implies a strong, immediate, and reciprocal relationship. Flows influence the composition of Territories (Flow - Territory), and conversely, Territories organize, constrain, and structure the reception and circulation of Flows (Territory - Flow). This reciprocity reflects how expression-substance (Territories) receives an investment in the arrangement. The solid line suggests that this transformation is a close-to-equilibrium process of structural connection and material reality. It involves processes of stratification and encoding, ensuring the stable manifestation of bodies and territories.

Let’s see the abstract machine continuity by absolute acceleration. interesting last 2 words. Abstract machines deal with diagrammatic speed, proliferation, and revolutionary change. They are crucial for addressing contingent singularities and articulating systems of passage. Abstract machine continuity suggests that the transformation is guided by the underlying, self-organizing logic of these machines, providing the potential for novel ordination and anti-entropy. Absolute acceleration is a deterritorialization process reaching an extreme point, potentially infinite diagrammatic speed. This is a process of creation and radical break from conventional frameworks, moving beyond systems of redundancy. The “speed of light” is used axiomatically as the maximum speed for problems to move in special relativity.3 Absolute acceleration, therefore, pushes the limits of conceptual transformation, creating a rupture capable of causing a universe to emerge directly. This acceleration forces the possibilities (Φ) to crystallize into entirely new reference systems (U), such as a new world and people that do not yet exist.

The mutational filters enable this continuity by selecting and instituting these novel systems (U) from the repertoire of possibilities (Φ). Mutations are something of sudden turnarounds or qualitative jumps. The filters act as selective thresholds that register the fact that a new kind of flow of signs or instrumental purport has been invented, leading to a “total turnaround” and the creation of another universe. They are responsible for discerning a singularity and triggering far-from-equilibrium effects that radically change a problematic. Without these filters, the possibility of absolute acceleration might collapse into a black hole or a cancerous BwO (destructive deterritorialization). They function to guarantee the possibility of a rupture or creation that institutes novel stratified formations.

Finally, let’s see chaos. Chaos is the realm of unformed matter, synonymous with the primordial soup of redundancies. It is the background against which philosophy, art, and science cast planes to organize thought. Chaos is the totality that contains all complicated, divergent series simultaneously. The abstract machine itself is crucial for moving away from Chaos and creating consistency. The escape route labeled “return to the soup of Chaos” originates from Φ because Φ is the domain responsible for articulating the potential paths out of Chaos, determining the conditions for crossing thresholds of reality. When the abstract machine fails, the system of possibles collapses back into the ungrounded state. If the repertoire of possibilities (Φ) is unable to form connections, ground itself in reality (Flows), or institute a new Universe of value (U) through acceleration, the organizing structure dissolves. This regression shows that the differentiation necessary for existence or thought has failed, leading to an ungrounding. It is the potentiality (Φ) itself that—when unconstrained or misdirected—dissolves back into the infinite, undifferentiated, and overwhelming multiplicity of Chaos. This is the danger inherent in radical deterritorialization—it risks turning to destruction. If Φ fails, the primary achievement of conceptualization is negated, returning the entire problematic field to its primal, unformed state.

So to summarize here and finally move onto the excruciating analysis of the domain of flows, we can say that the Ontic and Pathic operators model describes a dynamic system where material reality (F) and conceptual possibility (Φ) interact horizontally to form existential domains (T) and vertical systems of value (U). The horizontal connections (ontic operators Φ-F and modules F-T) deal with the construction and manifestation of actual reality and territory, using reciprocal, solid arrows indicative of close-to-equilibrium processes. The vertical connections (mutational filters Φ-U and pathic operators T-U) deal with the creation and evaluation of meaning and subjectivity. The path from Φ to U via absolute acceleration is the revolutionary vector—the ligne de fuite aiming to create mutant universes of value[far-from-equilibrium]. The pathic operators T-U affirm the existential consistency of these creations, linking embodied experience to systems of reference. The unique escape-failure from Φ to Chaos highlights the inherent risk: the freedom to explore new possibilities (Φ) always harbors the potential for total dissolution if the abstract machine fails to achieve revolutionary transformation (U) or material realization (F and T).

Figure 5.2: The ‘soup’ of redundancies: m = 0

yoooo finally flows…wait this looks familiar…

The variable m here is a measure of the system’s consistency or memory/persistence. When discussing the emergence of flows and linear structures, Guattari denotes how the process leading to stable consistency is marked by different values of m:

• m=1 signifies the persistence of a filtering t, content unspecified [Figure 5.3].

• m>1 signifies stochastic linearization, where serial memory thickens and is weighed down with more ‘givens’.

But here the diagram is explicitly assigned the condition m=0, which indicates a state of zero consistency. This signifies that in the soup, the chaotic filter dissolves instantaneously in the Universe of virtuality, meaning there is no retention of memory or persistence within this state. Since there is no differentiation, formal relationship, or memory retained—only randomly arranged and indeterminate material—the elements, though physically present, are redundant in terms of organized information or meaningful structure. They are thus a primary material continuum that lacks the necessary mediating operators for position-retention that would capitalize a memory of being. i think this one is so hypercomplex, that it is very simple…

Figure 5.3: Persistence of a filtering t, content unspecified (m = 1)

First off, let’s emphasize the contrast between the chaotic m=0 state and the minimal consistency of m = 1. This is the crucial shift from undifferentiated chaos to the affirmation of existence, or “being-there” (being-in-itself or ontological autonomy)4. The condition m=1—measure of consistency is one—signifies that a minimal condition for consistency has been established. This consistency is the initiation of a minimal memory of being. The sequential line depicted here with its repeating pattern (…–) continuously linked by the t operator, demonstrates the boundary condition required for the sheer affirmation of being to take hold.

Our good friend t appears here. The persistence of this minimal measure of endo-consistency is established by the persistent application of the t operator, rather than the simple presence of the content[dots/dashes]. Let’s remember from chapter 4 that the operator t is explicitly labeled the “operator of existential self-reference” in diagram 4.5 (SC, 113). It is a pathic operator of self-consistency that capitalizes a “memory of being (persistence)” (SC, 75).5 t is located at the crossroads of Endo-consistency and Endo-reference [Figure 4.4]. Endo-consistency implies an internal principle of cohesion, meaning the persistence relies on its own affirmation, which is essential for establishing any discrete machinic nucleus. m=1 thus signifies the birth of an internal loop, separating minimal self-persistence from dissolution into chaos (m=0).

The operator t acts as a filter by establishing maximal and cold consistency through an infinitely decelerated speed [Figure 4.6]. This paradoxical relationship defines the nature of minimal existential affirmation. Null speed [–∞] characterizes the intensity of t, which establishes a stopping zone—a zone of the suspension of determinability. This extremely low velocity[stopping zone] prevents the internal segment (…–) from dissolving back into chaos or moving into high-speed machinic deterritorialization (which involves infinite acceleration, d+∞). Instead, the moment is stretched and affirmed continuously in an immanent relation to itself. The resulting consistency is maximal and cold.

The consistency is maximal because it is absolutely determined by itself. This affirmation, described as pure, sui generis, necessitation, rests on nothing external or tangible. It is a state of absolute self-containment, providing high consistency[–∞]. This cold form of self-reference bypasses interaction, causality, and production. It is fixed in its self-affirmation, unlike the hot intensities generated by processual becoming or diagrammatic flux. It describes the eternal return of representation where being is regrounded on itself, often resulting in nothingness or repetition.6 Guattari writes: “This unary linearization, the vital minimum of consistency, might recall the activity of an amnesiac saying his rosary: what it affirms through repetition is not the discursivized figure but only itself, as principle of repetition.” (SC, 120). This low-speed, endo-referred self-referential quality—the continuous downward-curving line connecting the repeating segments—creates the persistent, consistent boundary by imposing a minimal internal coherence. It is the foundation for an existential self-consistency, ensuring that even a minimal sequence—the dots and dash—holds itself together through sheer self-reference.

The content[the dots and dashes] is unspecified for t to function as a fundamental, minimal filter. This reflects a key theoretical principle for Guattari’s architectonics: the formal transcendental requirement for consistency must be established before specific, concrete determination can occur. For stochastic linearization to happen (m>1), there must already be a stable, persistent entity capable of holding a memory and registering these traits. m=1 provides this necessary foundational boundary (endo-consistency), allowing the entity to register its difference from others[alterity] in subsequent complexification. m=1 captures the minimal formal function of persistence, separated from any material or semantic inscription. If the content were specified (as in a thought, a quantity of energy), it would automatically entail greater degrees of striation and categorization, which belong to more complex systems of redundancy (like stochastic linearization, m>1). This diagram focuses purely on the act of filtering/self-reference t itself—the sheer capacity to persist—rather than what is persisting. The content is merely the flow of basic elements—dots/dashes—which serves as the raw, undifferentiated material being held in persistent relation by the operator t. This is why Guattari calls this an “empty form of existentialization, without, as a consequence, being the support of any content relation”.

Finally, the operator t is the proto-enunciative substance that gives rise to Territories. Territories are characterized by existential recursion and necessitation—a choice for finitude, an attachment to everything and to nothing with a view to constituting a world. The persistence of t (m=1) performs this exact function: it is the initial, minimal act of existential self-affirmation that asserts “I[?] exist” (a kind of cogito) and holds itself together internally (endo-consistency), regardless of external content. This stability, arising from the infinitely decelerated speed, fixes the initial parameters of what will become a self-referential Territory—a coherent, although rudimentary, sphere of existence capable of returning upon itself and defining its own internal laws. It is the minimal condition for a bounded existential space to resist the pull of chaos and become an existential territory.

Figure 5.4: Stochastic linearization: m > 1

Stochastic linearization describes the process through which probabilistic, measurable consistency (where the measure m>1) emerges from the primal chaotic soup of redundancies (m=0). The term ‘stochastic’ implies that the arrangement or outcome can be predicted using the calculus of probabilities. With stochastic linearization, the system passes to memories greater than zero. The filters involved in this process are no longer merely minimal memories of themselves; instead, they initiate the retention of formal relations of symmetry, homology, and disparity, which are termed by Guattari as durations of alterity. These filters stick to the most basal discursivity.

When m>1, the raw elements—dashes and circles—are organized temporally and numerically, moving beyond unary stochastic connectivity, which only slowed the reference iteration down. The grouping itself institutes a localized form of order, allowing the memory to register qualitative ruptures and the durations of alterity (the length of the group: 2, 2, 1, 5 elements). This number (3, 2, 1, 5) represents the specific Domain assigned to the newly formed temporal group, marking the successful instantiation of a quantifiable entity or serial segment.

The temporal groupings defined by the brackets and assigned Domains are the initial formation of a stabilized consistency. This grouped unit, characterized by its measured complexity (m), corresponds to an endo-consistency. The sequential movement between these stabilized groups, such as the transition from Domain 3 group to Domain 2 group, or from Domain 1 unit to Domain 5 group) involves a form of transistency. The marks x appear in the second row of Figure 5.4 at specific boundary moments (t2​,t4​,t6​). These moments immediately follow the completion of the Domain 3, Domain 2, and Domain 1 groupings. Given their boundary position, the x marks signify a moment of articulation or intervention related to the boundary conditions of the segment just completed. They appear for the overlay of a second stratum or process, suggesting the intervention of a second domain, likely related to the abstract machinic phylum (Φ) or the beginning of dissipation or even deterritorialization. But in all honestly, I am not sure.

Figure 5.5: Serial smoothing

In the earlier stage of stochastic linearization, initial filters were engaged, enabling the system to register minimal memories of itself, such as qualitative ruptures and durations of alterity. Serial smoothing builds upon this by engaging serial memory that thickens and becomes “weighed down with more and more ‘givens’” (SC, 122).

The serial filter (F1 to Fn) functions as a mechanism for iteration-memories and the persistence of the filtering of traits. The filters impose sequential order onto the initial flow. This process is sensible smoothing (or sub-position). Sensible smoothing ruptures with existential endo-reference and generates linearized discursive sequences. These sequences are calibrated based on a principle of immanence. The sequential operation of the filter ensures that inter-entitarian difference is not abolished, but rather consolidates its existence by sharing it with the serial operators of reference (f1, f2, fn…) that memorize it. The smoothing process is furnished with rhythms and refrains, which mobilize “more and more ‘heavy’ temporalities” in the register of discursivity.

The staging of paradigmatic series refers to the emergence of structured, sequenced units that stand in contrast to the continuous flow of chaos. The smoothing process is characterized paradigmatic coalescence. This operation involves stabilizing and grouping traits into a finite, iterable series. The staging of paradigmatic series is essential because, at this stage, memory is still closely attached to basal discursivity and is incapable of discerning higher-level figural constellations; it can only register ruptures and durations of alterity. The smoothing process establishes these basic numbered units of perception.

Figure 5.6: The serial coalescence and the heterogenesis of Flows

The initial parts of Figure 5.6 illustrate the historical sequence through which chaotic input is stabilized into recognizable Flows, moving from minimal memory to structured coalescence. This process is generally referred to as serial smoothing, resulting in the stable, discursive state F. Processionary linearization illustrates a simple, linear sequence (S1​,S2​,S3​,Sn​) with memory m=1. This is the absolute minimum level of consistency required to emerge from the soup of chaos. Paradigmatic coalescence, shown with memory m=5, signifies that the filters are implicated in an evaluation system arising from non-discursive enunciative intensities (T). This level involves “memories of memories,” which actively reproduce and re-engender regularities by making them come alive within their own paradigmatic stagings.

Now the central diagram shows the internal structure of the Flow/Phyla axis mapped onto the Universe/Territory axis, showing the serial coalescence and heterogenesis of Flows. Heterogenesis here means that inter-entitarian difference is consolidated and memorized by serial operators of reference. The structure depicts a crucial vertical stratification defined by a caesura of Flow, separating the molecular, deterritorialized processes of the upper strata from the molar, territorialized processes of the lower strata. This stratification highlights the dynamic tension between two opposing modes of consistency defined by reference speeds:

• The Bottom Coalescence (F → T): Territorialized Consistency.
  
  This section, involving Flows and Territories, is the realm of modular, serial and finite relations. It is ssociated with infinitely slow speed of reference [∞−]. This speed is also denoted as d−∞ (absolute deceleration of determinability). This movement is intrinsically territorializing. F and T have an endo-consistency and define the domain of discontinuity (d−∞ = discontinuity). It links serial states (s1′′​ to sm​) to territorial states (t1′′​ to tm​) resulting in Tm​ = ∑t′′. This modular structure results from the deceleration of existential ‘grasping’ (or self-referential agglutination). This involves negative determinability integrating positive determinability (d−∞∫d+∞) to territorialize a circumscription of positive traits.
  

• The Top Coalescence (Φ → U): Deterritorialized Consistency.
  
  This section, involving Phyla and Universes, is the realm of fractal, non-proximal and infinite relations. It is associated with infinitely fast speed of reference [∞+]. This speed is also denoted as d+∞ (absolutely accelerated speeds of reference of determinability). This movement is intrinsically deterritorialized or deterritorializing. Φ and U define the domain of continuity (d+∞ = continuity). The speed is synonymous with zero consistency and absolute lability of iteration. It links serial states (s1′​ to sn​) to territorial states (t1′​ to tn​) resulting in Tn ​= ∑t′. The infinite speeds transfer complexity and hyper-complexity between the domains Φ and U It involves the integration of negative determinability (d+∞∫d−∞) which defines the Phyla as a taking on of fractal-molecular consistency.

The vertical layering and the caesura of Flow are the essential differentiation in the composition of Flow’s consistency. The coherence of Flow is born when the halting of serial determination is reached (the flow comes up against a finite term sn or sm). This process of coalescence and heterogenesis is basically the halting of the process of serial determination, constituting Flow properly so-called as the product of a modular component of enunciation associating continuous references (d+∞) and discontinuous consistencies (d−∞). The process of determinability is suspended, deferred, and constrained to pass via the Phyla and deterritorialized Universes of the cycle of Assemblages, as we saw way back in chapter 3.

The continuous layer (f′) of infinitely fast reference and zero consistency'[Top Coalescence Φ → U] and the discontinuous layer (f′′) of infinitely slow reference and high consistency[Bottom Coalescence F → T] are simultaneously generated, yet define contradictory conditions. This paradox—that Flows are both referenced (by the serial operations) and operate at the high consistency of null speed ([−∞])—is resolved by viewing Flows as a modular component where the speed of determinability is decreased to create virtual consistency. The infinite speed of the Phyla and Universes (molecular dispersion, d+∞) is required to continually recharge the modular Flows and Territories (molar concretions, d−∞).

Figure 5.7: The two sequences of the striation of Flows

a) The module passive sequence

The top block (s1​ to sn​) and the Bottom Block (s7​ to sm​) are labeled d+∞ (infinitely fast speed of reference) and are positive divergence. These fast flows, the solid lines, are the source material—the referential series of infinite speeds (d+∞) that must be captured, decelerated, and segmented to produce finite, actualized existence. They accumulate to form the territorial endpoints tn​ and tm​.

The middle block (s4​ to sb​) is labeled d−∞Φ, indicating a state of suspension of determinability associated with the Machinic Phyla (Φ). The phase space ϕ[Φ] is the field of abstract machinic possibility[Rhizomes]. This block is the attractor ϕ with an indefinable contour which unifies potential series of determinations, functioning as something like a stopping zone of determinability. The operation occurring here is the integration of negative determinability (d+∞∫d−∞). The rapid flow (d+∞) comes up against this suspension zone. While the outer blocks are characterized by positive divergence (pure, energetic expansion), this internal block is where the inherent expansive movement is constrained. The dashed lines are segments where determination is infinitely deferred or slowed down, introducing discontinuity into the flow. Thus negative divergence refers to the process of convergence or agglutination—the necessary slowing and reversal of the chaotic tendency required to solidify consistency. This block mediates the abstract possibility of the Machinic Phyla with the actual, fragmented Flows.

The single, continuous, serpentine line running through the three blocks suggests the operation of an existential filter or a modular operator. This sequence is termed passive because it primarily performs a passive registration, folded back on itself, without external reference, unlike an active registering which is framed by a reference capable of prolonging it, thus operating by endo-ordination, where segmentary identification is finalized on the linear consistency of Flows. The passive module’s function is to ‘finitize’ or ‘contingence’ the flow’s determinability, creating the basis for the enrichment of possibility. This continuous, tracking line acts as the mechanism for molar aggregation, which involves a slow reduction in the relative speed of particles so they take on a relatively static form.

The resulting Territorial States (tn​ and tm​) are summed up into the final composition Tnm​. The summation implies that the flow has been stopped, reaching a finite term (sn​ or sm​). Let’s remember that the process of subjectivation is not fully fulfilled until an existential Territory is delimited. The production of T requires existential grasping (or self-referential agglutination), which is precisely characterized by the decelerated speed d−∞. The structure shown constitutes a Flow which is redefined as the product of a modular component of enunciation associating continuous references (d+∞) and discontinuous consistencies (d−∞). The resulting Tnm​ is thus the achieved consequence of modular striation.

b) The active processual sequence

The passive sequence is linked to modules (F↔T). This modular process deals with constitutive processes that are passive. The intrinsic traits of determinability (s4​,s5​,s6​,se​) characterize the passive modular sequence, which may become stuck in cycles or move toward black hole states.

The active sequence involves a non-linear line that transforms blocks of serial states (s) into T. The active line represents a process of singularization and machinic transistence. The action is considered active because it does not rely on mechanical determinism but rather on the creation, selection, and mobilization of potentialities. The active transformation agent is the active line of flight, which is catalyzed by the influence of Φ and U.

The Φ possibilistic attractor (dashed lines) functions as a field of potentiality that governs the movement towards new states. Φ is the possibilitistic pole of Phyla relating to Universes, thus the Phyla provide the structure of possibility for the virtual Universes to be actualized. The Φ attractor enables the active line of flight by offering a realm of continuity and possibility—or machinism in rhizomatic clusters—outside of the immediate contingent flow. For the active line of flight to restructure flows non-linearly, it must draw upon this field of fuzzy possibles7 which carries heterogeneous becomings. This entails the coexistence of an infinite fractal process (drawing on the virtual capacity of U) and a contingent determination that fixes or ‘ballasts’ it. The restructuring involves choices concerning the machinic phylum. Machinic phyla constitute an optional matter whose tendency is turned toward the possible and the actualization of mutant realities. The Φ attractor maps this realm of viable possibilities that the active line exploits.

The downward U vector is a crucial intervention of the incorporeal and virtual into the formation of the territorial state Tnmo. The influence of U drives the system towards the formation of the highly complex territorial consistency Tnmo​. This influence ensures that the resulting structure is imbued with existential consistency, reflecting the incorporeal universe of endo-reference. The process of traversing between dimensions is essential here, moving beyond merely psychological dimensions, in psychoanalytic circles, toward creative processes. U acts as a structural conditional—the virtual dimension that is always present—but the formation of Tnmo​ requires an active movement of actualization of U’s virtual resources. The downward vector suggests that U provides the potential—the infinite traits—which is then actualized or “plugged into” the flow determination. The entire ambition of this processual model is to grasp how tensions between tensors—like the Φ and U poles—make an event happen or not happen. The process is thus driven by the impulse to becoming and mutation drawn from U, which is why it is inseparable from creation.

The final state Tnmo​ (total territorial consistency) is the synthesized outcome of the active, non-linear intervention. The transition from serial states (s) to Tnmo​ involves active, non-linear sampling. We’ve just seen how this process selectively draws on certain components, moving beyond linear sequential determination. This active selection is driven by ethico-political options and a lust for life/creation. Tnmo​ is qualitatively different from the simpler Tnm​ of the passive sequence. This difference signifies the emergence of a new complex in-stance (T​), which is a process of existential singularization. The complex consistency of Tnmo​ reflects the articulation of individual practices into a collective diagram—a creative field, a rhizome—, which breaks free from systems of equilibrium and redundancy.

4. Reference and Consistency

Figure 4.1: The two states of chaos

We start the short chapter with Figure 4.1. It differentiates two major states of chaos based on their ontological nature (actual/virtual), their communicative mode (discursive/non-discursive), and their degree of complexity (complex/hypercomplex):

• Complex Actual Discursive States (F., Φ):
  
  F and Φ are located on the actual side of the metamodel. The actual world is defined as the given side, objective, quantitative, and abstract. These states are discursive. Discursivity is synonymous with sequential order that is exo-referenced to Energetico-Space-Time (EST) coordinates. They articulate discursive multiplicities of expression. This side is characterized by ordinary complexity, which is proper to real Flows (F) and possibilistic Phyla (Φ). This complexity allows for actual potentialities that can be listed and consolidated.
  

• Hypercomplex Virtual Non-discursive States (T., U.):
  
  T and U are located on the virtual side. The virtual is opposed not to the real, but to the actual, and is fully real insofar as it is virtual. The virtual side defines the giving aspect, relating to consistencies, subjective reality, and intensive qualities. These states are non-discursive. Non-discursivity concerns the incorporeal, affective, intensive dimension of the assemblage, not governed by ordinary space and time coordinates. Non-discursive reality relates to the pathic apprehension of being-in-the-world. This side is characterized by chaotic hyper-complexity. This hypercomplexity is virtual, non-discursive, and constantly on the way to dissolution.

The cycle of infinite speed connects the two states (Actual Discursive/Virtual Non-discursive) in a continuous, two-way loop. Chaos, which is the source of all determinability, is defined by an infinite speed of birth and disappearance. Configurations that outline themselves in chaos dissolve at infinite speed. This speed transgresses the limit set by the speed of light. The cycle is a continuous coming-and-going at an infinite speed between the two poles of chaos and complexity. This rapid oscillation occurs between a state of chaotic “grasping” (T, U) and the deployment of complexions anchored within worldly coordinates (F, Φ), and takes place prior to processes of spatialization and temporalization. The function of this infinite speed in the cycle is to enable the differentiation of entities into ontologically heterogeneous complexions and their simultaneous chaotization as they abolish their figural diversity. The system thus oscillates between zero consistency (pure chaos) and constructed consistency (F, Φ, T, U)—the infinite virtuality is loaded with finite speeds, which are necessary for the conversion of the virtual into the possible. Therefore, the infinite speed is the transfer of complexity and hyper-complexity between the possibilistic Phyla (Φ) and the incorporeal Universes (U).

The hypercomplex virtual non-discursive states (T., U.) are further designated as the loci of processual recomplexification. Let’s investigate this concept. This refers to the ability of the virtual domain to constantly introduce new complexity. The chaos of the plane of immanence is the primary matter of virtuality, serving as the inexhaustible reserve of infinite determinability, implying that a return to it always provides matter for the complexification of the state of things.

The hypercomplex virtual state (T, U) is crucial because it is the domain of virtualities that haunt the entropic tensions inherent to chaos:

• Universes (U) function as incorporeal ecosystems and self-generate instances of discursivization called filters. U allows for the creation of new fields of the possible.

• Territories (T) function as anchors, conferring autopoiesis and singularity on zones of subjectivation. They guarantee the possible recharging of the system with processual complexity.

Ultimately, the virtual side (T, U) is where new charges of complexity are acquired, creating the conditions for ontological bifurcations and the emergence of coefficients of processual creativity. This confirms the principle that the reality of the possible always has primacy over the possibility of the real.

Figure 4.2: Intersecting dimensions of reference and consistency

The two intersecting axes, Consistency (Vertical) and Reference (Horizontal), define the core ontological coordinates used for mapping assemblages:

• Reference: Referenced/Referring:
  
  Reference distinguishes whether the domain’s existence is contingent upon external coordinates or internal self-affirmation.

  • Referenced (Exo-reference): This side corresponds to the domains of Flows (F.) and Phyla (Φ). Exo-reference is the serial arrangement [l’arrangement sériel] that results from putting terms into discursive connection. It concerns elements whose truth or essence is defined as extrinsic to their existence, meaning they refer to external systems.

  • Referring (Endo-reference): This side corresponds to Territories (T.) and Universes (U.). Endo-reference is the intensive, non-discursive, proto-existential operator from which arrangements result. The singular element is its own reference and generates its own world of reference, affirming itself as self-referential.
    

• Consistency: null/high

  
  Consistency expresses the stability, coherence, and density of processes. Speed is the decisive factor defining the degree of consistency. Following the tradition of Spinoza, D&G argue that speed is an expression of ontological status. Flows and Phyla function in time (Chronos) based on finite speeds, while Universes and Territories engage with non-pulsed, Aeonic time and absolute speeds. The primordial slowing down, manifested in finite speeds, is necessary for processes to acquire physical existence or actuality.
  

  • Null Consistency of Infinite Speed (+ ∞): This pole aligns with the upper half (Φ. and U.), characterized by infinite speeds of transformation (+ ∞) that transgress the limit set by the speed of light. Infinite speed is synonymous with the absolute lability of iteration and, consequently, zero consistency. This pole relates to the hyper-complexity and infinite determinability of the chaotic Plane of Immanence.

  • High Consistency of Null Speed (- ∞): This pole aligns with the lower half (F. and T.), characterized by decelerated and quasi-null speed (- ∞). This slowing down (or reterritorialization) is synonymous with an intensification of consistency. When speeds fall to quasi-null speed [−∞], the sequencing of opening back up can become of a quasi-infinite length—maximal consistency. This pole pertains to structured, durational, and territorialized forms.

The four ontological functors are positioned at the extremes by combining a reference mode with a speed/consistency degree:

• Φ: Referenced / Null Consistency + ∞: Phyla are characterized by a discontinuous fractalization marked by phase spaces working at infinite speed (d+∞). They possess low ontological consistency but are necessary for mediating possibility, being the integration of negative determinability (d+∞ - d–∞).

• U: Referring / Null Consistency + ∞: Universes are incorrigible segregation and self-referential enunciative instances. They operate at a paradoxical speed (d±∞), being simultaneously infinitely rapid and infinitely slow, staying in a state of suspension (aerosol). They are the site of unlimited complexification and absolute determinability.

• F: Referenced / High Consistency -∞: Flows are bound to energetico-spatio-temporal discursivity. They are characterized by discontinuous striation and are associated with a state where hyper-slow speeds (d–∞) of determinability are suspended, forming modules of territorialization, possessing maximal, cold endo-consistency.

• T: Referring / High Consistency -∞: Territories constitute the second pole of deterritorialization characterized by the absolute slowing down of determinability (d–∞). They are anchors for existence—endo-consistency (maximal and cold), integrating positive determinability (d–∞ - d+∞) by freezing and selecting positive traits.

The association of Φ. and U. with null consistency of infinite speed (+∞) showing their closeness to the chaotic origin. Both fields belong to the plane of consistency’s upper half, which is less consistent in ontological terms and circulates at greater speed. This condition is the reserve of infinite potentiality: U is the unbound Constellation of determinability, and Φ is the unbounded network of abstract possibilities (Rhizomes).

The central region, labeled “range of consistencies of modulated speed,” describes the actual state of subjective and machinic arrangements far from the theoretical extremes of pure chaos or total stasis. This region defines the space of trans-consistency or transistence. This is the locus of processual recomplexification where entities gain coherence and stability. Assemblages of enunciation are generated within this central matrix-like configuration, requiring a complex set of intermediary factors and filters to operate. This meta-model operates by decelerated and modulated reference speeds,being defined by the process of filtering chaotic multiplicities into relatively homogeneous sets, which involves the mutual articulation of Flows and complexity at finite speeds. This modulation ensures that systems—though exposed to infinite virtuality—acquire the finite speeds necessary for the conversion of the virtual into the possible. The movement within this range involves constant switching between persistent virtual implosion and transistent actual expansion, a game of taking consistency. Furthermore, even the existence of the whole diagram depends on the striation of infinite reference speeds into heterogeneous components of consistency, allowing for local and contingent determination.

Thus, Figure 4.2 maps the irreducible ambivalence of the chaotic process—oscillating between the virtual (Giving, high speed) and the actual (Given, high consistency)—which requires both infinitely fast hyper-transversal1 (d+∞) and absolute territorialized slowing (d–∞) for subjective processes to gain consistency and irreversibility.

Figure 4.3: Matrix of the potential and virtual

This matrix positions F. and Φ under the category of Potential and T. and U. under the category of Virtual.

In the specific structure of Guattari’s later work (which employs actual and “virtual as coupled, complementary concepts), the Potential is mapped to the Actual. The Potential states are what is always-already given. They are the given, abstract, and assembled world. The components in this domain are generally discursive—or proto-discursive—and are associated with objective deterritorialization. On the other hand, the Virtual is generally opposed to the Actual (Potential). The Virtual states are the giving or creative dimensions, corresponding to what is non-discursive and intensive. Generally both in Deleuze/Guattari, the virtual is distinct from the possible in classical philosophy; the virtual is fully real insofar as it is virtual. The virtual domain is subjective and is where existential Territories and incorporeal Universes reside. The Virtual axis (U. and T.) is associated with subjective deterritorialization.

• Potential Column (Actual, Given): This column encompasses the raw material, abstract plans, and measurable coordinates of existence.

  proposition [Φ]: Φ are defined as operating via propositional discursivity (hence, proposition). The prefix ‘pro-’ (as in proposition/pro-positional) shows their nature as abstract lines of possibility that stand for or forward the process. Φ constitutes the deterritorialized machinic possibility and is the domain of the actual possible.

  
  dis-tance [Flows]: The term dis-stance suggests the extensive coordinates (space and time) that define these Flows; they’re energetic-spatio-temporal discursivity—the distance or separation necessary for flows to be contingenced and articulated. The prefix ‘dis-’ indicates separation, distribution, or segmentation necessary for measurement and existence within spatio-temporal coordinates.
  

• Virtual Column (Giving): This column is the results of creative activity: the emergence of subjective value systems and defined existential spaces.
  
  dis-position [U]: The term “dis-position” suggests the arranging or setting out of traits of determinability in a virtual, non-discursive way. The prefix ‘dis-’ (similar to Φ’s definition but applied to the virtual) refers to abstract possibilities and the re-arrangement of positions. U. functions as the catalyst for resingularization, shifting indeterminacy into determinability.
  
  in-stance [T]: The term “in-stance” (or in-stantiation) marks the moment when Flow reaches a threshold of existential consistency and is marked by difference. This is the process where Flows acquire a self-consistency or localizable habitat. The prefix ‘in-’ emphasizes the process of incarnation, existential grasping, and local definition, suggesting being “in” a certain state or locality (an in-stance). yeah

Figure 4.4: Matrix of reference/consistency crossover, in the context of an Assemblage

a thing here

The matrix uses the dimensions of reference and consistency to segment the plane of consistency into radically heterogeneous domains.

1. Reference (Horizontal Axis)

We know that reference is concerned with how entities relate to a given order or multiplicity.

• Exo-Reference (External Reference): This mode of reference involves the serial arrangement resulting from connecting n terms of a multiplicity in a discursive way. Exo-reference is attached to the materiality of the process and implies that the element’s truth or essence is external to its existence, as it relies on another element for its designation. The operations here generally take place within logics of discontinuous or continuous discursive sets (as seen in F. and Φ).

• Endo-Reference (Internal/Self-Reference): This is the intensive, non-discursive, proto-existential operator from which the serial arrangement originates. It is characteristic of existential pragmatics, where the singular element is its own reference and generates its own world of reference (auto-reference). Endo-reference confers the entity its complexity, singularity, and existential consistency. This mode of reference recedes in the face of deterritorialized constancy and consistency.

2. Consistency (Vertical Axis)

We’ve seen above that consistency expresses the stability, density, or precariousness of connective processes.

• Endo-Consistency (Internal/Maximal Consistency): Characterized as maximal and cold—a form of passive, territorialized connectivity. This mode of consistency is associated with elements that are continuous and durational, deriving its cohesion from the conjugation of processualities of intrinsic consistency. The real domains of Flows and Territories are considered endo-consistent.

• Exo-Consistency (External/Minimal Consistency): Characterized as null and hot—associated with discontinuous and momentous elements, linked to regularities, algorithms, and deterritorialized consistency. Exo-consistency expresses the capacity to open up new fields of possibility. The possible domains of Phyla and Universes are viewed as exo-consistent due to their characteristic openness.

Here Guattari positions the four functors based on their operationality within an assemblage:

1. Φ. (Phyla): Exo-Consistency / Exo-Reference: Φ is abstract machinic phyla, which are configurations of possibility. They are characterized by discontinuous or momentous states. Therefore, Φ is located on the axis of Exo-Consistency (null/hot, characteristic of openness and potentiality). Φ operate within logics of infinite continuous algorithmic discursive sets, meaning they rely on externally articulated, serial organization, thus positioning them in Exo-Reference.

2. U. (Universes): Exo-Consistency / Endo-Reference. U are incorporeal Universes, which are the non-discursive complexity and possibility. Like Φ , U. is characterized by Exo-Consistency due to its openness and discontinuous nature. U function as the non-discursive, self-consistent locus for the generation of singular existence. This focus on intensive self-affirmation aligns U. with Endo-Reference.

3. F. (Flows): Endo-Consistency / Exo-Reference: F stands for energetic-signaletic Flows, being the actual, real material/energetic base of the assemblage. Flows are characterized by continuous and durational states, placing them in Endo-Consistency (maximal/cold stability). Flows operate through serial arrangements put into discursive connection, aligning them with Exo-Reference.

4. T. (Territories): Endo-Consistency / Endo-Reference: T. are existential Territories, the concrete manifestation of the virtual-real. Territories are continuous and durational (Endo-Consistency). T. functions as a proto-existential operator where singular existence affirms itself (self-reference), aligning it with Endo-Reference.

The concepts located at the boundaries of the quadrants—synapses, modules, ontic operators, and pathic operators—are crucial as they mediate the necessary transformations—smoothings—between the heterogeneous domains. Let’s see them.

Synapses: located in Φ (Exo/Exo) and U. (Exo/Endo) (Top boundary): Synapses are mutational filters that operate at a deterritorialized level. As we saw way back in chapter 2, they relay the surplus value of possibility via Synapses of Effect (Se) and Synapses of Affect (Sa). They are critical for establishing the irreversibility of assemblage processes by marking an explicit break/cut that initiates a self-enunciative procedure and allows for the crystallization of a singularizing Constellation of a Universe of reference (∑U). They effectuate the passage from finite to infinite modal essence.

Modules: F. (Endo/Exo) and T. (Endo/Endo) (Bottom boundary): Modules are territorialized proto-enunciation and modular filters, associated with the Endo-Consistency domains, serving as operators of deceleration and guaranteeing persistantial consistency through memory and segmentary identification. They function as territorialized guarantors that anchor the assemblage to being-there.

Ontic operators: F. (Endo/Exo) and Φ (Exo/Exo) (Left boundary): Ontic operators are deterritorialized concrete machines located on the axis of objective deterritorialization. They hinge Flows and Phyla using exo-referenced coordinates. They relate to the materiality of the process and perform the irreversibilization/diagrammatic function, acting as a catalysis of selection and conversion (like the mould of a key as in diagram 15 of chapter 3).

Pathic operators: U. (Exo/Endo) and T. (Endo/Endo) (Right boundary): Pathic operators are self-referencing operators located on the axis of subjective deterritorialization. They relate to the pathic dimension—the immediate, intuitive, preconceptual apprehension of life (the felt rather than the perceived). Pathic operators of heterogenesis confer a pseudo-identity on energy sites and enable the heterogenesis—exploration of unknown virtuality—function.

Now Guattari’s integration works by transforming the binary oppositions of the previous models into an operational geometry that explains how the different domains interact and stabilize.

• Actual Expression (F., Φ ) is split along the Exo-Reference axis, thus the Actual Expression is defined by its reliance on Exo-Reference (discursive serialization). The actualization of expression happens externally via relations.

• Virtual Content (T., U.) is split along the endo-reference axis, thus The Virtual Content is defined by its reliance on Endo-Reference (intensive, non-discursive self-affirmation).

• Real (F., T.) is split along the endo-consistency axis, thus the Real side is stabilized by Endo-Consistency (durational, continuous, localized consistency). This is the regime of persistence.

• Possible (Φ, U) is split along the exo-consistency axis, thus the Possible side is characterized by Exo-Consistency (openness, discontinuous states, hyper-complexity). This is the regime of transistence.

The intersectionality at play here confirms that an Assemblage is never purely one or the other. For instance, Flows possess the serialization of Exo-reference but gain density and stability through Endo-Consistency (durational stability). Conversely, Universes require the intensive, self-affirming dimension of Endo-reference but are characterized by the unstable, possibility-generating dynamicity of Exo-Consistency.

Figure 4.5: Exo-reference and endo-reference

Exo-reference and Endo-reference define two radically distinct modes of establishing existential reference, particularly in relation to the functioning of systems and enunciation.

We’ve already defined exo-reference as the serial arrangement resulting from connecting n terms of a multiplicity through a discursive connection. In this mode, the existence or essence of an element is considered external to its existence, relying on another element for its designation. Showing Exo-reference by a nested set of curves or braces labeled “series of order n” illustrates its nature as an extrinsic system based on ordered, sequential relations. This domain operates within logics of discontinuous or continuous discursive sets. The series signifies that for an element to have meaning or position, it must be articulated in relation to others in a predefined sequence or system. Exo-reference is attached to the materiality of the process. The arrow originating from the center and pointing toward the series suggests that, here, the subject/system engages outward to establish its coordinates through external, serialized relations.

Endo-reference is the intensive, non-discursive, proto-existential operator from which serial arrangements originate. It is characteristic of existential pragmatics where the singular element is its own reference and generates its own world of reference (auto-reference). Showing Endo-reference by a single point labeled t signifies its singular, self-contained, and non-discursive nature. The label “operator of existential self-reference” highlights that this domain concerns existential affirmation or grasping of being, functioning as a focal point of existentialization that is autopoietic and self-productive of reference.

But we’ve already seen all of this above, let’s look further into the series of order n, which refers to the sequential, linear organization inherent in discursive systems. Exo-reference operates in the framework of logics of discursive sets. This mode of reference involves connecting n terms in a serialized, or linear, fashion. Maurizio Lazzarato, in Signs and Machines: Capitalism and the Production of Subjectivity, when discussing Guattari, discusses how, since the series relies on extrinsic coordinates and reciprocal determination, the essence or truth of the elements is external to them. For example, in linguistic analysis, an element is discursive relative to another element that is its referent, meaning the truth is external to its existence (SM, 207)2. All this is related to Sartre’s concept of seriality where entities in a series are united passively by being turned toward an exterior object or common interest, without necessarily having a common project or even being aware of one another.3 In The Machinic Unconscious, Guattari talks about how exo-reference relates to phenomena of formal resonance or interaction that precede the substance-form coupling (MU, 15), but it remains confined to the discursive and reversible domain.

The point t functions as the core of existential self-affirmation. Thee operator t initiates a process of self-organization or singularization, where the existential component continually comes back to itself to consolidate or dissolve its consistency. This is distinct from discursive logic, which is linear. Endo-reference confers the entity its complexity, singularity, and existential consistency. It is the locus where a proto-subjectivity is knotted together via a feedback loop that returns on itself. The entity is fully attached to its existence (its “topos”).

Finally, endo-reference recedes in the face of deterritorialized constancy and consistency. The movement toward high deterritorialization (Exo-Consistency) can destabilize the internal certainty of self-reference, leading to phenomena like infinite accelerated speeds of reference of determinability in Universes. Conversely, Endo-Consistency provides the necessary memory and territorialized anchor (T) for the emergence of the self-referencing subject.

Figure 4.6: Exo-consistency and endo-consistency

The matrix maps three levels of Consistency (vertical axis) onto two modes of Reference (horizontal axis): Exo-reference and Endo-reference.

We’ve seen that exo-consistency pertains to the highest state of deterritorialization and maximum velocity, characterized by raw, unformed matter, describing the primary level of molecular agitation and chaotic flux. It is associated with the pure potentiality of the BwO, which is intense, unformed, nonstratified matter defined by axes, vectors, gradients, and thresholds. Consistency, in this absolute sense, is neither totalizing nor structuring; rather, it is deterritorializing. Exo-consistency’s quality of nullity signifies the absence of established organization. It refers to the minimal definition of consistency—the state of things before formalization or stratification—where the memory of the system is effectively zero. Its quality of hotness denotes maximum intensity and speed (often absolute speed). It refers to the sheer processual capacity of chaotic multiplicities composing and decomposing complex arrangements at infinite speeds. This hot state is far from homeostatic equilibrium.

Processual transistency is the dynamic, transversal state where flows and forms achieve relative stability and organization through continuous variation from d∞+ [See footnote 1]. This is the level where machinic assemblages operate. It is the domain of transistence, or transition, where heterogeneous components are knotted together. This consistency is achieved by the constant, transversal interaction of elements. The processual nature of this level means it is defined by mixed and relative speeds. It is engaged in the imposition of striation upon smooth flows. The lines of deterritorialization are folded by lines of segmentarity and stratification to create measurable organization. Striation pertains to the internal complexity and operational closure of a consistency. These striations are themselves machinic, meaning they are actively produced and constantly changing.

Endo-consistency defines a state of maximal structural fixity, characterized by internalized redundancies and near-equilibrium, denoting the maximum level of stability and structural organization. It is achieved when a process of subjectivation stabilizes into an established Existential Territory (T), whoch implies a state of infinitely decelerated speed or effective stoppage. It characterizes systems that mimic the homeostasis of physical systems in equilibrium, minimizing flux and variation.

In the first row, endo-reference’s intensive operators of absolute speed in U refer to pure processes of deterritorialization transcending finite spatio-temporal (EST) coordinates. This is the speed of unlimited potentiality (d+∞), characteristic of the flow of incorporeal Universes. These are arranged in Constellations, whose entities operate at an absolute speed that cannot be related to EST coordinates. This absolute speed is linked to the infinite molecular-fractal chaosmos, where anything is determinable into any-machine-whatsoever. When singularity is self-affirming in the U-domain, its essence becomes the motor of existence—existential energy—operating at this absolute speed.

In the second row, the coupling between Incorporal Universes and Existential Territories signifies that processual transistency is where the subjective and objective poles of existence and value intersect dynamically. T is the embodied, territorialized context, while U. is the constellation of incorporeal values and virtual choices that guide the process. Subjectivation is fulfilled in the domain T, but the catalyst for resingularization often operates at the U-level. In this coupling, organization[striation] is actively produced and regulated by abstract machines. Machinic striations—unlike organic stratifications—are continuously subject to becoming and mutation, giving rise to systems of articulation and semiotic scaffolds. Relative and mixed speeds are here. They are mixed because they are composites resulting from the combination of different material and incorporeal flows (F and U), and relative because they are measured against the established parameters—the striation—that temporarily organizes them. The relative speeds are born from the necessity of organization (T) and the guiding of value (U). They are mixed because they result from combining heterogeneous elements, such as abstract machinic propositions (Φ) and sensible territories (T). For example, physical particles (in the F domain) must respect the law that their speeds are less than or equal to that of light (a measurable, relative speed). These mixed speeds are essential for the complex interactions of the machinic phyla and territorial existence. Φn refers to the abstract machines or Phyla. The index n suggests that the diagrammatic function—the blueprint of the assemblage—is captured within a specific order or structure.4 In the context of exo-reference, the abstract machine, which should ideally be purely deterritorializing, is harnessed to organize flux into formalized expressions and contents.

Our beloved operator t is distributed across the intersection from endo-reference from exo-reference in the third row. In highly stratified systems, maximal consistency is achieved through deceleration. T-time is subjective, related to the subjectivation process fulfilled in the T-domain. The rigid, maximal consistency of Row 3 implies a time that is fixed or infinitely decelerated (d-∞), relating to serialization and redundancy. Here, Infinitely decelerated speed (d∞-) is characterized by a maximal slowdown, leading to stratification5 and fixation, associated with negative determinability—the power of freezing. This slow speed is characteristic of endo-consistency, where the system is closed and highly stratified. This state is necessary for linearization and quantifiable movement, where singularity is fixed and defined by its external, territorialized coordinates. This corresponds to the process of forming stratified compositions and maximal determinability6. The series of order n implies a sequential, stratified arrangement required for linear representation and signifiance. Therefore, this series functions to regularize and formalize the components, enabling them to be understood within finite, discursive systems.

Figure 4.7: Levels of consistency

uhh ok?

let’s actually start from 3) endo-consistency of order n cuz it just makes more sense ok?

3. Endo-consistency of Order n and Order m

   
   The concept of endo-consistency describes a state defined by self-contained relations, specifically in the diagram as two nested series of order n (sn). Endo-consistency refers to an internal coherence, often characterizing subjective processes that are blocked or perpetually spinning round and round. This internal fixation or recursive loop prevents transformation and is often associated with the symptom formations that schizoanalysis aims to elucidate.7

   The difference between order n and order m signifies a change in the internal organization or complexity of the system. In the metamodel, changes in order often correspond to moving from basic initial coherence—like low memory or simple persistence—to a higher degree of consolidation—high memory or complex persistence—, possibly involving different temporalities and qualities. The shift from n to m is the result of a transformation (Transformation 1, pointing horizontally to tn and subsequently involves a transition process (the line Φnm). This movement implies that the initial endo-consistency (n) is subjected to a process that restructures its internal organization, resulting in a new stable internal state (m) capable of sustaining the ensuing ascension towards exo-consistency; molecular transmutation.

   
   Trans-consistency is consistency through transversal connections or passage between systems, distinct from mere linear or local causality. Because it is exo-referred, it must relate outward to the Plane of Consistency or the BwO, the destratified plane where absolute deterritorializations occur. Trans-consistency functions as an interface that structures the possibility of linkage between otherwise segregated domains (such as different Universes of reference, or specialized fields of competence).
   
   The mutational filter is integral to the transformation process, specifically filtering the passage during the ascension of Φnm. The filter enforces a selection or transformation of the initial elements. This suggests that only components capable of undergoing a fundamental mutation are carried to the next level (order m). This critical passage moves the system toward something of a liminal crisis between deterritorialization and potential reterritorializations. The concept of the mutational filter reflects the constructivist nature of schizoanalysis. It insists on defining conditions of change, especially for generating new practices and subjectivities that break free from established codes and the given. The filter is likely instrumental in defining what is retained or modified during the move from one stabilized internal order (n) to the next (m) on the path to external efficacy.8

   
   The Line Φnm of Exo-referred Trans-consistency is the ascension which originates in Φn. The Φnm therefore is the diagrammatic passage or the intensive trajectory of transformation that carries the consistency from organization n to m. The Φnm functions as a ligne de fuite[line of flight]. A ligne de fuite is characterized by its capacity to carry the assemblage over to the Plane of Immanence. This line is the processual vector that introduces discontinuity and rupture into the established coherence, allowing for the articulation of form directly onto matter. Being exo-referred implies that this line is directed towards the Outside, emphasizing that the consistency generated is relational to the exterior, challenging the internal closure of the initial endo-consistency. This directionality is critical for political pragmatism and micropolitics, as it seeks to activate singularities and move beyond existing structures.

1. ∑U^Φ Endo-referred Exo-consistency: The summation (∑) suggests that the final state involves a maximal opening to, or successful capture and articulation of, these diverse possible meaning structures, transcending the local context. ^Φ refers to the machinic Phylum in its most integrated or actualized state, indicating the success of the deterritorializing machinic process (the vertical ascension). This component ensures the connection to the flow of matter and expression. The synthesis ∑U^Φ is a consistency where the machinic material transformation (^Φ) is functionally articulated with a complex, diversified constellation of incorporeal meaning and potential (∑U).
   
   Its quality of exo-consistency implies that the resulting organization has achieved a coherence defined in relation to the exterior—the deterritorialized Plane of Consistency. This consistency is dynamic, open, and capable of perpetual renewal, having utilized the line of flight to reorganize itself machinally. It is a consistency oriented toward possibility and the outside. Its quality of endo-reference means that the consistency, while externally achieved (exo-), is oriented back towards the internal functioning and existence of the assemblage. The system is rooted in the individual or collective existential commitment. This internal reference is crucial because the process must be lived out and acted upon by the participating subjects, so to speak. The final state provides the subjective conditions for production, establishing a sense of reality and truth tied to the act itself, where the act secretes Existential Territories, ensuring that the consistency is tied to praxis and the creation of subjective territories. The simultaneous nature of endo-referred and exo-consistency thus describes a state where the system achieves external effectiveness (exo-consistency via ^Φ) anchored internally in a newly constituted subjective reality (∑U, endo-referred).

I believe that the process depicted in Figure 4.7 is essentially the schizoanalytic project: finding a way to transform a stable, open internal order (endo-consistency of order n) through a phase of radical opening (trans-consistency) enabled by the machinic Phyla (^Φ), which forces a reconstitution into an externally efficient, yet subjectively anchored, new consistency (∑U^Φ endo-referred exo-consistency). This entire process is about achieving coherence not by reducing complexity to simple codes, but by constructing a new system of articulation capable of generating creation and political efficacy.

Figure 4.8: Ontological exo-reference and pathic endo-reference

The two domains of the matrix—Ontological exo-reference and Pathic endo-reference—define two fundamentally distinct modes of operation or logics of the referent involved in the construction of reality and subjectivity. Ontological Exo-reference deals primarily with the material and machinic consistency of reality, focusing on the objective conditions of existence, encompassing the analysis of givens related to the economy of bodies, territories, and being-there. It refers to the processes, structures, and systems that exist outside or prior to subjective experience. This column focuses on how external reality is registered, analyzed, and structured, often through coding and decoding systems that define the sociological and material infrastructure. The structures involved here are highly concerned with persistence and objectivity. The Φnm state (in the Exo-consistent row) specifically denotes the convergence of Phyla.

Pathic endo-reference deals with the subjective, existential, and incorporeal consistency of perception and being, focusing on the internal, subjective experience of existence, the realm of affects, intensive continuums, and Universes of reference. The emphasis here is on how experience is structured through subjective perception and desire. The primary mode of accessing this domain is often described as atmospheric, pre-discursive, or an ensemble of affect [affect d’ensemble]9. The designation UΦ (in the Exo-consistent row) points to Constellations of Universes of reference that are catalyzed by deterritorializing ruptures.

The four mediating concepts—ontic operators, pathic operators, mutational filters, and modular filters—govern the movements (transitions) within the matrix, ensuring that the model captures dynamic processes rather than static categories. Operators mediate transitions between the different levels of consistency (vertical movement: Exo-consistent / Transistant / Endo-consistent). These mechanisms facilitate the movement across structural layers or planes of organization.

• Ontic Operators: These apply vertically within the Ontological exo-reference column. They manage the transition of material and machinic components (Φ) between different levels of structural organization. Since they operate on the ontological plane, they deal with how elements related to bodies, resources, and objective territoriality are stabilized, transformed, or dissolved across strata.

• Pathic Operators: These apply vertically within the Pathic endo-reference column. They manage the transition of affective and incorporeal components (U) between different consistency levels. They deal with the formation and modification of subjective territories, affects, and values, linking existential experience across structural strata.

Filters mediate the transformation between the two modes of reference (horizontal transformation: Ontological / Pathic) within a single consistency level. They are the necessary coupling or interchange for the system to function dynamically.

• Modular Filters (Endo-consistent Row): Modular implies structures that are definable, repetitive, or capable of being codified into standardized units. As the prompt specifies, they mediate the transformation between sn, sm (Ontological exo-reference) and tn, tm (Pathic endo-reference). This suggests they handle the structural articulation found at the stratified level, transforming external data (content variables s) into elements of expression (expression variables t). This mechanism ensures that content and expression, bound by a mutual solidarity (as per Hjelmslev’s warning), are coherently structured at the level of definable consistency.

• Mutational Filters (Exo-consistent Row): These filters mediate the transformation between the machinic phylum (Φnm) and the new universes (UΦ). Mutation suggests a radical, often unexpected, transformation or change. This type of filtering is crucial at the most external (Exo-consistent) and deterritorialized level, where the abstract machine constructs the BwO or diagrams lines of flight. So we’ve seen just above, the mutational filter thus links the material/machinic trajectory (Φnm) to the creation of new existential territories and possibilities (UΦ).

The variables placed within the matrix define the nature of the consistency level they inhabit and the reference mode they adhere to. Following A Thousand Plateaus, we can argue that the variables sn, sm and tn, t_m are linked to the process of double articulation which affects both expression and content on a stratum in the domain of the endo-consistent. They are defined by their mutual solidarity. These variables are the components of articulation found at the stratified level:

• sn, sm (Ontological exo-reference): These variables likely are the materials or substances of content, fitting the external/objective reference mode. They define what is materially present or codified.

• tn, tm (Pathic endo-reference): These variables are the materials or forms of expression, fitting the internal/subjective reference mode. They define how content is expressed or perceived.

The variables Φnm and UΦ deal with the macro-level consistency and potential for change:

• Φnm (Ontological exo-reference): The designation of this state as being under Ontological exo-reference implies that it is the objective, external machinic consistency or the material phylum. It captures the abstract technical or material reality of the assemblage, such as engineering flows, infrastructure design, axiomatic systems.

• UΦ (Pathic endo-reference): The designation of this state as being under Pathic endo-reference implies that it is the incorporeal consistency of subjective Universes of reference. It captures the subjective and affective experience arising from the interaction with the external system. This is the realm where non-segmented multiplicities, intensive continuums, and emissions of particle-signs occur on the BwO.

The transistant row is crucial as it is the processual or dynamic nature of the assemblage, mediating between structured consistency and pure deterritorialization. The transistant state highlights the inherent instability and transitionality of systems, capturing the moment when connections are forming or dissolving. It corresponds to the principle of becoming or movement with infinite speed, which operates towards a line of flight. It captures the complex phase where Diagrammatization occurs—the interchange between material and semiotic systems at the most deterritorialized level.

Figure 4.9: The smoothing and striation of Assemblages of enunciatio

this one looks familiar…

jinhkfnjkg

yeah lets just go ahead.

1. Smoothing of the sensible or sub-position: generates immanently to sensible, cognitive, and affective experientiations. It functions as a form of ontological conversion (passive). This process involves the transformation of aleatory chains of redundancy into linearized, smoothed, proto-machinic sequences, described as the endo-ordination of sensible smoothing. This mechanism calibrates and articulates sensible qualities.

2. Striation of modular instantiation: The striation of modular instantiation is the development of heterogeneity within the domain of Flows (F). It achieves a static instantiation of possibility. This striation is characterized by sequencing, digitalization, and binarization. It marks the shift from passive endo-ordination (sensible smoothing) to in-stantiation by trans-ordination, which marks specific differences. This fixation of modular, finite, discontinuous traits allows for quantifiable differences, though it resists full reduction to a digitalized message. It is situated at the junction of discursive smoothing (F-T) and deterritorializing smoothing (F-Φ).

3. Expressive smoothing (E.C.): The expressive smoothing is a form of machinic smoothing located between the Flow (F) and Phylum (Φ) domains. It breaks the uniquely proximal discursivity of Flows to introduce a caesura and an opening of possibilization. The E.C. (Expression-Content) function is the bipolar disposition that channels Flows into fields of Expression and Content, dynamizing the inherent heterogeneity capital of the flows. This smoothing is crucial for generating machinic surplus value. It is essentially a deterritorializing smoothing that allows the possible to ooze out of all the encysted modular forms. This process leads to the production of Machinic Propositions (Φpm), which are virtual and abstract. remember last chapter? yeah everything from that.

4. Abstract machinic striation (Pm): This phase is defined as rhizomatic striation or trans-position. It organizes possibility itself. This striation is the heterogeneity developed within the Φ domain. It involves the transition from expression (traits of extensity) to intensity (traits of intensity). Abstract machines (Φma) lose fixed identity and become trans-positional, exploring variations outside of testifiable temporality. The machinic striation acts as the operational integration of heterogeneous points of view, increasing its power of effect and reducing entropy. This phase confers a relative ontological autonomy on the corpus of abstract propositions.

5. Incorporeal smoothing: Incorporal smoothing is located between the Machinic Phyla and Incorporeal Universes (U). This is a smoothing of deterritorialized phase spaces. It is the process by which the incorporeal enunciators (U) sweep and smooth basins of virtual determinability. This transition moves the machinic organization from a state of effectiveness (Pm) to one of necessitation (U). Crucially, the difficulty in distinguishing Phyla from U implies that their smoothing and striation phases are rigorously synchronic and homothetic, meaning they are highly compossible and intimately mixed. This smoothing allows for the chaosmic Plane of Consistency to operate, promoting new modalities of spatial and intensive proximity.

6. Striation of virtual states (ΣU): This is the heterogeneity developed within the U domain. It results in singularized Constellations of Universes of reference. This process occurs through a synaptic dis-position which acts as an explicit break/cut. It constitutes the auto-affirming incorporeal enunciations, which confer an ontological necessity on the phyla of the possible. This striation sets up the irreversibility of the assemblage process, marking it with a singularizing figure or “proper name”.

7. Smoothing of self-reference: The necessary virtual entities (U) are linked back to the fundamental being-for-itself10 of existence (T), creating the subjective foundation. This smoothing occurs between the Universe (U) and Territory (T) domains. It is described as a pseudo-smoothing because it lacks the discursive, extrinsic relations found in other smoothings, translating the fact that there are no longer extrinsic relations between Universes and ‘unary’ existential Territories. It is the intensive, internal, pure affirmation of difference (being-for-itself or ontological autonomy). It relates to the Body without Organs (BwO). This self-affirmation is what the Territories utilize to generate heterogeneity and alterity from their own interior, providing crystals of ontological self-affirmation.

8. Existential striation (Striation of existential segmentarities): This striation occurs within the T domain (Territories). It involves the fixation of subjectivity, forming hard or supple segments. The existence of this segmentarity fixes the subjective territory. According to Guattari, who, according to Segovia, emphasizes the Territory domain (T), the process of subjectivation is only fully completed when an existential Territory is delimited. This striation converts older modular sensible Territories (Ts) into a new species of existential Territory (Te), resulting from an enrichment of potentialities.

9. Smoothing of the sensible or sub-position: The finalized subjective territory (T) is linked back to the flows of perception and material existence (F)…

A Situation is defined by its intense sensation and specific, singular occurrence, resisting reduction to pre-defined elements within a system, a lived intensity that escapes from the forced passivity of flatness, biopower, and spectacle, focusing on the rediscovery of presence, of life, where signs, following Baudrillard, operate as the real rather than mere repesentations, collapsing into affect. A Situation can be identified by affective indices—non-discursive markers of intense, lived experience and forces, serving as signals or manifestations of a burgeoning or active Situation.

Now what?

My research plan for the future development of affective accelerationism goes as follows:

• A close study of Reza Negarestani’s neorationalism in Intelligence and Spirit, already finished here. And of general neorationalist philosophy.

• A close study of Felix Guattari’s Schizoanalytic Cartographies, currently being done in this substack

• A close of Francois Laruelle’s Principes de la non-philosophie, which will be done here when I finish wthi Guattari.

• Engagement with the study of diagrammatics within Guattari, Deleuze, and Châtelet.

• Engagement with the study of quantum mechanics.

• A critical appropiation of the functive of vectors in mathematics and physics.

• A critical engagement of phenomenology, with a post-phenomenological[depth] reading of Deleuze through Kant, Husserl, Sartre, Merleau-Ponty, and Simondon, so as to dismiss flat and abysmal readings of Deleuze.

• A critical engagement with Inigo Wilkins’ study of noise in Irreversible Noise: The Rationalisation of Randomness and the Fetishisation of Indeterminacy.

• A critical revindication of Deleuzean epistemology and ontology in light of neorationalism.

The general goal here would be to sketch out a philosophical program that would be constructed through diagrammatizational practices, functioning as a matrix for non-standard philosophy, primarily the merging of Negarestani’s universalist neorationalism, Guattari’s constructivist metamodelizational schizoanalysis, and Laruelle’s non-philosophy.

Let’s hastily draw out some of our points:

• Negarestani's neorationalism is envisioned as a program for elaborating and constructing the theoretical and practical realizabilities of Geist. This endeavor is framed as developing a conception of philosophy that operates as a program for the elaboration and construction of the theoretical and practical realizabilities of geist, pushing thought toward prospects that are asymmetric to its past and present, advocating for the unboundedness of thought. This conceptualization of philosophy is a program for an artificializational-navegational vector that constructs an outside view of ourselves. Furthermore, Inigo Wilkins' study of noise highlights a movement upward toward the autonomy of reason and downward toward heteronormative causes, criticizing greedy naturalization. Wilkins' work frames its objective as providing a multi-level explanation that differentiates and co-articulates the scientific concepts of randomness and noise, maintaining a realist metaphysics compatible with contemporary science.

• Our philosophical pursuit will be characterized as the Expérience diagrammatique, where thought confronts chaos through inventing, tailoring, and warring concepts to grasp and construct the world beyond conventional social partitions and the given. For Deleuze, Guattari, and Châtelet, the diagram is recognized not merely as a tool or sign, but as the expression of the intensities of thought. Châtelet, in particular, emphasizes the physicomathématique dimension of the diagram. His work stresses the topological and spatial nature of the diagram, where diagrams are not fixed tools but mobile entities that must be inhabited to capture a certain gesture or mobility. The physico-mathematical diagram acts as a dispositif de capture (capture device) or stratagème (stratagem) that attraps a gesture (or graph) which cuts out pieces of the virtual. This gesture, related to the Greek root grbh- (to scratch or engrave), is an act of mutilation or scratching that breaks resemblance and defigures a representation, thus allowing for the production of non-representational presence or Figure. Conventionally, a diagram is often reduced to a sign (an icon of resemblance) or a tool for clarifying calculations. Deleuze and Guattari rupture this traditional view, insisting that the diagram does not represent the world, but traces it, re-opening the virtual dimension of representation extinguished by modern thought. This refusal to be confined to representation makes the diagram non-reductive to the subject/object partition, allowing it to think of a milieu instead.1 A diagram is a technique of worldbuilding-allusions. Unlike a metaphor, the diagram is not exhausted; it prolongs itself into an programmatic operation.

• Guattari's Schizoanalytic Cartographies uses the fourfold conceptual system (Flows, Phyla, Territories, Universes) as a meta-model. This meta-model is a diagrammatic relational constellation before becoming a technical apparatus, as it provides a simultaneously abstract and concrete rendering of a system, modeling processes from within ecological dynamics, rather than relying on a transcendental viewpoint. This method is inherently constructivist, seeking to synthesize abstract qualities and contingent contextualization. Guattari defines being as a permanent modulation of consistency, exploring the speeds of determinability achieved through the interplay of functors on a constructed plane of consistency. This constructivism requires reconciling order within disorder, and disorder within order.

• For Laruelle, the concept of decisionality is identified as the invariant structure of philosophy itself. Here, every traditional philosophical system involves a decision—a decaedere or cutting off from the Real—in order to explain or represent the Real exclusively through its chosen method. To leave decisionality means abandoning the fundamental philosophical gesture of staking a transcendent claim to capture reality. Non-philosophy attempts to achieve this by moving toward a non-standard thought that refuses the hierarchical and exclusionary nature of the philosophical decision. And we’ve seen that the diagram is a non-representational abstract machine or a diagrammatic relational constellation. These machines feature lignes de fuite and deterritorialization, functioning through what may be called a operation of mutilation or extraction, which articulates the Real itself. This process strips away the clichés and representations (doxa), which philosophy must renounce to engage in genuine thought.

• Diagrams are intrinsically linked to tackling problems and undecidable propositions. Philosophy's task, in a diagrammatic/constructivist sense, is not to answer a question—which would presuppose a solution—, but to adapt to corresponding elements in the process of being determined. If philosophy is conceptualized as a program, its purpose is operational, determined by what it does and the realizabilities (possible operational effects) it constructs, rather than its truth claims or referents (what the data stands for). The diagram facilitates this shift by enabling thought to explore what might be—the space of possibilities—rather than being shackled to what is (givenness). This framework aligns with Laruelle's contention that the axioms of non-philosophy (which incorporate the philosophical decision) are under-determined by radical immanence. The act of diagrammatization, by dealing with the actuality/virtuality and the movement of becoming, allows for a position of renegade indifference2 or indivision—the non-relational thought of the One—which escapes the relational duality (immanence/transcendence) that fuels the vector of philosophical decisionality. In sum, by working diagrammatically, philosophy is re-engineered into an operational program that explores emergent possibilities and internal consistency through non-representational processes, moving thought away from the authoritative, exclusive, and transcendent act of decision toward an immanent exploration of the Real's potential (the "abstract without abstraction") into how thought can realize its own ends.

These ideas may be subject to change as they’re just a sketch.

3. The Cycle of Assemblages

Figure 3.1: Matrix of four modelling and meta-modelling entities

The matrix is structured around two intersecting axes that categorize the four functors: Discursive vs. Non-discursive. The horizontal axis distinguishes between Discursive (left side) and Non-discursive (right side). Discursive domains are associated with actualization on the plane of expression and include Fluxes and Machinic Phyla. They relate to discursive ensembles that determine relationships between fluxes and machinic systems. Non-discursive domains are associated with virtualization on the content plane and include Existential Territories and Incorporeal Universes. These domains involve non-discursive BwOs that determine relations between existential territories and incorporeal universes. Non-discursivity is described as pathic apprehension of being-in-the-world, which is not primarily spatio-temporally located or describable as such, but secondarily discursive.

The vertical axis distinguishes between continuous (top row) and discontinuous (bottom row). Continuous entities include Machinic Phyla and Incorporeal Universes. Machinic Phyla, for instance, operate in the framework of logics of infinite continuous algorithmic discursive sets. This continuity can imply a hyper-continuous character. Discontinuous entities include Fluxes and Existential Territories. The exo-reference of Fluxes, for example, operates within logics of finite discontinuous discursive sets. This discontinuity can introduce breaks between different strata and within each stratum.

Based on these distinctions, each quadrant is a specific combination of these properties and houses one of the four functors:

• The discursive/continuous quadrant (Φ): Abstract Machinic Phyla.

  Machinic Phyla are abstract entities that preside over objective laws and changes, comprising evolution, abstract machines, blueprints, plans, diagrams, rules, and cybernetic control mechanisms. They act as sources or roots of expressions like machinic propositions of logic or computer code. They are described as multipolar, proliferating in every direction and dimension, overlapping in Rhizomes, and forming knots of effectiveness.

• The non-discursive/continuous quadrant (U): Incorporeal Universes.
  Incorporeal Universes are the virtual possibilities and values that escape the energetic, legal, evolutionary, and existential coordinates of the other three domains. They involve individuations that model experience through the incorporeality of intensive movements.

• The discursive/discontinuous quadrant (F): Energetic-Signaletic Flows.
  Flows encompass material and physical signals, subject to the coordinates of energetic quanta, space, and time. They are the actual and real aspects of the world. Flows are often described as having a high degree of consistency, but in the context of this figure, they are characterized by discontinuity along the vertical axis.

• The non-discursive/discontinuous quadrant (T): Existential Territories.
  Existential Territories relate to subjective identity, the sense of self, and existential apprehension. They are formed by the combination of Flows, Phyla, and Universes. Territories model experience through the corporeal grasping of a spatialized milieu or world.

The matrix also introduces two concepts at the bottom of the columns:

• Exo-referred modelling: This concept applies to the left column, encompassing Fluxes and Machinic Phyla. Exo-referred indicates that these domains deal with the given, abstract world, often without perceiving entities. Flows and Phyla are without concrete forms and indifferent. Exo-reference is defined as the serial arrangement resulting from the discursive connection of multiple terms. Modelling here refers to systems that organize and structure, but often with the risk of reductionism. This side concerns the Given.

• Endo-referred meta-modelling: This concept applies to the right column, comprising Existential Territories and Incorporeal Universes. Endo-referred signifies that these domains are formed and formal, being the concrete and giving field of sensible Territories and existential Universes. Endo-reference is described as an intensive, non-discursive, proto-existential operator. Meta-modelling refers to a more complex and enabling alternative to prevailing social and psychic models. It involves developing possible openings onto the virtual and creative processuality, aiming to decipher modeling systems and ensure transversal passages between different problems. This side concerns the Giving.

Figure 3.2: Deep structures Φl and synaptic opening

The arrow signifies a difficult but crucial leap in Guattari’s philosophy. It illustrates the transformation from the register of multiplicity of possibilities (Φ) to the powers of virtual affect and enunciative virtualization (U). This is a processual activation or transferential apprehension that leads to the actualization of an Effect and the virtualization of an Affect. It highlights the capacity of machinic deep structures to open into dynamic, creative, and self-organizing enunciative processes, bypassing traditional notions of a predefined subject or referent.

Inter-Machinic1 propositions are non-hierarchical and trans-semiotic, meaning they do not start from simple elements and build to complex ones, and they cut across different semiotic strata. They are the dynamic elements that make a machine function concretely, similar to neurological connections. Within the deep structures (Φ), these propositions are the bearers of molecular and infinitesimal—deterritorialized—charges of energy. They’re an "operational integration of heterogeneous points of view" and "proliferate in every direction and in all dimensions," overlapping in rhizomes and budding into "knots of effectiveness" (SC, 92). Their role is to catalyze connections between systems and allow the transfer of machinic processes to extralinguistic domains. They function directly with machinic sign-points and create surplus value of code, enabling a machinic proliferation when organized with far-from-equilibrium machinics. They directly participate in the process of engendering objects and realities.

The diagram depicts a synaptic opening of enunciating modifications within U as the crucial outcome. This synaptic opening is a deterritorialized release of enunciation, a generative rupture that produces new affects and subjectivities. It's a very complex and difficult leap that transforms abstract possibilities into virtual affect and actualized effects, leading to enunciative surplus-value and irreversible processes. These incorporeal Universes, once activated, become self-referential and actively produce new references, rather than simply reflecting existing ones.

The placement of F and T at the base and U at the apex, with Φ being deep structures that inform U, illustrates how Φ and U are a more abstract, deterritorialized, and virtual dimension compared to the more concrete and territorialized F and T. The principle of exclusion in Guattari's broader model specifies that there are no direct tensorial relations between F and U, or T and Φ, indicating that different mediations are required for their connection (SC, 58). This diagram highlights one such mediation—the synaptic opening.

Figure 3.3: Matrix of the Possible, Real, Actual and Virtual

The matrix's columns and rows establish two conceptual distinctions. The distinction between discursive actualization and enunciative virtualization and possible ocurrences and contingenced (real) occurrences. Discursive actualization corresponds to a domain that involves actualization on the plane of expression. It is generally associated with what is given, objective, quantitative, extensive, and abstract, leading to coherent, formal expressions. Discursivity often implies linear causalities and regulated successions of forms. Enunciative virtualization corresponds to a domain that involves virtualization on the plane of content. It is associated with the giving, the subjective, qualitative, intensive, and concrete, often involving non-discursive or pathic apprehension of being-in-the-world. It tends towards unary, discontinuous elements and mixtures.

Possible occurrences are fields of potentiality and virtuality. These are associated with phenomena that have a low degree of consistency and are often discontinuous, like aerosols. They encompass what is abstract and potential, not yet fully realized in a fixed, tangible form. Phyla and Universes are examples of possible occurrences. Contingenced (real) occurrences are actual, tangible manifestations and concrete realities. These occurrences tend to have a high degree of consistency and are continuous. They refer to states that are present and often bound by specific spatio-temporal coordinates. Flows and Territories are examples of contingent (real) occurrences.

Based on these distinctions, the matrix positions four fundamental entities:

• The Discursive Actualization / Possible quadrant (Φ):

Phyla are described as the Phylum of actual possibility or actual possible. Phyla are involved in discursive actualization and preside over objective laws and changes, capable of generating subjective mutations through new combinations of material potentials. They operate within "infinite continuous algorithmic discursive sets" (SC, 72)

• The Enunciative Virtualization / Possible quadrant (U):

Universes are defined as the Universe of virtual possibility or virtual possible. Incorporal Universes escape the energetic, legal, evolutionary, and existential coordinates of the other domains, existing as hypercomplex virtual non-discursive states with low consistency and discontinuity.

• The Discursive Actualization / Contingenced (Real) quadrant (F):

Flows are the Flux of actual real or actual real. They are material and energetic components, actual and extensive, operating through energetico-spatio-temporal[EST] discursivity. Flows have a high degree of consistency and are given in a continuous mode, referring to the actuality of material relations within finite physical systems.

• The Enunciative Virtualization / Contingenced (Real) quadrant (T): Territories are the Territories of virtual real or virtual real. They relate to subjective identity, the sense of self, and existential apprehension. While virtual, they are concrete and operate as continuous movements that embody experience through a "corporeal grasping of a spatialized milieu" (WG, 52). They possess a high degree of consistency despite their virtual nature.

The horizontal axis (Discursive Actualization / Enunciative Virtualization) maps processes of semiotization and expression, indicating how elements are brought into being through (a-)signifying means. The vertical axis (Possible occurrences / Contingenced (real) occurrences) differentiates between potential states and their concrete manifestations, highlighting how the virtual informs the actual and how abstract potentials become real through specific contingencializations.

Figure 3.4: Matter, substance, form

This model can be understood as a matter-substance-form triangulation.

• m (primary matter): This is primary matter or purport (sens), which Guattari, following Hjelmslev, describes as unformed, amorphous, or formless. It is a matter-movement bearing singularities or haecceities, qualities, and operations. In this context, it is the initial unformed state of redundancies, a primary material continuum that can be energetico-spatio-temporal—EST—or signaletic. It is akin to semantic and physical reality, encompassing non-semiotized meaning—matter of expression—and continuums of material flows.

• f (proto-machinic form): This vertex is a proto-machinic form, indicating an initial or emergent state of form. Forms generally imply a code, modes of coding and decoding. Unlike the unformed matter, this is a formed state of redundancies. Guattari links form closely to abstract machines, seeing them as a formless form that precedes full semiotic formation and has no substance of its own. The diagram labels it proto-machinic to highlight its initial, possibly unactualized, yet structured potential within the system.

• s (proto-enunciative substance): Generally, substances are nothing other than formed matters. They are semiotically formed when a form is projected onto matter or meaning, effectively manifesting form in matter. The term proto-enunciative suggests an initial stage of substance that will become involved in processes of enunciation or expression. The difference between materials and substantial elements involves a change in organization.

We see some solid lines with the center labeled discursive relation (connecting m to f): It suggests that primary matter is organized or structured into a proto-machinic form through a process of discursivity. Discursivity is often associated with the actual and structured aspects of assemblages and can be seen as an ordering principle. This relation highlights how the amorphous gives way to a preliminary organization.

The dashed lines labeled F (connecting f to s, and s to m): The dashed arrows, labeled Flows, indicate a more dynamic, fluid, and processual type of relation. The arrow from f (proto-machinic form) to s (proto-enunciative substance) shows that Flows are instrumental in transforming form into substance. The arrow from s (proto-enunciative substance) back to m (primary matter) suggests a cycle where flows are also involved in the potential return or dissolution of substance back into primary matter.

Essentially we have:

1. From Matter to Form: The process begins with primary matter (m), which is inherently unformed but possesses intense potential. Through a discursive relation, this matter is given a preliminary structure, becoming a proto-machinic form (f). This step involves an ordering and shaping, moving from pure potentiality to an initial, coded configuration.

2. Form to Substance via Flows: The proto-machinic form (f), influenced by Flows (F), is then actualized into a proto-enunciative substance (s). This Flow (F) is the energetic and signaletic processes that mediate the transformation. Substance, in this view, is formed matter, implying that the abstract form finds a tangible, albeit proto-enunciative," manifestation through these dynamic flows.

3. Substance to Matter via Flows: The model then completes a cycle by showing proto-enunciative substance (s) reverting to primary matter (m), also mediated by Flows (F). This cyclical aspect, driven by Flows, indicates that the process is not necessarily linear or permanent. The matter-substance-form triangulation does not adhere to a classical dialectic, where elements are fully subsumed or negated; instead, elements like matter subsist as residues that can re-affirm new potentialities. This highlights the reversibility and continuous transformation within the system, where formed elements can dissolve back into the unformed flux, or become the raw material for other-new formations.

The unnamed diagrams

In the table of contents, the small diagrams in page 76-77 are cited.

In the context of the autistic closure, Guattari writes that "form continually falls back onto primary matter" (SC, 76), which is shown by the s to m (Flow) arrow. This shows substance, derived from form, returning to primary matter, rather than progressing to new, differentiated states. The absence of a direct, productive flow from m to s (or s to f leading to a new 'f') within a generative cycle (beyond the m -> f -> s -> m loop) is crucial here. The diagram itself, by not showing interaction beyond this specific cycle, visually implies the closure and the lack of external engagement or novel creation.

On another hand, dialectical exhaustion describes a dynamic and generative process that yields expressive surplus value (ΔF.). It involves the "putting into relation of the diverse forms". This interaction[exhaustion], creates effects not included in any of the smoothings of Flow, leading to a "bipolar regrouping of smooth components" and "chains of expressions of machinic Phyla" (SC, 77). The process leads to the creation of something new and unexpected—a surplus value or existential supplement. It is a second stasis of deterritorialization, expressive deterritorialization, but one that is creative and open. It is a process of singularization and heterogenesis.

Basically, the autistic closure model illustrates a failure of the system to generate new possibilities, resulting in empty repetition and a lack of true deterritorialization. The dialectical exhaustion model, however, shows how the active putting into relation of diverse forms can overcome such stasis, producing a novel "expressive surplus value" and pushing the system towards new configurations and possibilities. While the former is a closed system, the latter exemplifies a processual opening and mutational specificity[singular-ity].

Figure 3.5: The bipolar arrangement of an expressive deterritorialization (with seven Flow components)

The diagram is centered on a horizontal axis connecting two main conceptual poles: Φ. (Machinic Phyla) on the left and Te (Existential Territories) on the right. The double-headed arrow connecting Φ. and Te signifies a reciprocal and dynamic relationship between these two poles. The diagram shows two columns of components labeled F. (Flows) and T. (Territories), each with seven numbered elements (F.1-F.7 and T.1-T.7). Then, the diagram shows two arrows pointing away from the main axis, labeled ΔFc and ΔFe. These, as we can just now, are the expressive surplus value or existential supplement (ΔF.) that results from the process of dialectical exhaustion.

Guattari furthermore states that "this dialectical exhaustion leads to a bipolar regrouping of smooth components around a function of Content (ΔFc) and a function of expression (ΔFe)".

• ΔFc refer to the new, emergent value or possibilities generated in the realm of content. Following Hjelmslev, Content refers to the unformed matters or intensities and formed matters into substances. It operates parallel to dominant semiotics. This surplus reflects novel configurations or organizations of material and conceptual aspects.

• ΔFe refers to the new, emergent value or possibilities generated in the realm of expression. Expression involves units of expression, nonformal functions or tensors, and semiotic fluxes. Expression has a degree of independence and can react upon contents. This surplus reflects novel semiotic, functional, or aesthetic possibilities. The distinction highlights the fundamental double articulation of content and expression within the generated novelty, indicating that creativity manifests simultaneously in what is expressed (content) and how it is expressed (form of expression).

Therefore, Figure 3.5 illustrates expressive deterritorialization as a dynamic, generative process that arises from the active putting into relation of diverse proto-machinic figures and their associated flows and territories. It contrasts sharply with autistic closure by producing novelty and opening up new possibilities, introducing ΔFc and ΔFe.

Figure 3.6: The three modalities of fluctuation

We have quite a thing here so let’s go piece by piece. The first section, labeled 1) sensible smoothing, is the initial stage in which chaotic or aleatory chains of redundancies—often referred to as the primitive soup—are transformed into more controlled, proto-machinic sequences. This process is a first relation of territorialized discursivity or substantial deterritorialization, aiming to bring a measure of order and retention to otherwise undifferentiated flows. Flows are the primary material continuum, such as energetic-spatio-temporal matter or signaletic matter. T. (Territories) acts as a mediative operator for the retention of these proto-machinic forms, capitalizing a memory of being or proto-enunciative substance. The line and arrow leading from F. to T.[sensible territorialization] signify a process of existential homogenization or grasping. This is akin to a "mechanical smoothing that removes asperities from a material surface" (GDT, 131), where raw material flows are given a basic, localized consistency and proto-machinic form. The process results in a repetition of divisible and smoothed forms, bringing the erratic flows under a preliminary form of control and establishing a nascent territoriality.

The second section, 2) intrinsic striation of Flows, marks a significant shift from the first stage by introducing heterogeneity and differentiation within the smoothed flows. While sensible smoothing creates a preliminary, homogenized consistency, intrinsic striation works within that consistency to instantiate or mark differences. It is no longer about simple calibration but about a differential pinpointing and an instantiation—the marking of difference. This process opens up "to a logic that generates molecular intervals, amplifications, bifurcations, and infinite fractalization (incorporeal heterogenesis)" (SC, 124). The numbered F. components (F.1, F.2, F.3, F.4) are individual flows that are now subject to "numerical difference bearing on binary sequences of signs" (SC, 82) (See Figure 3.5). These are no longer undifferentiated but possess distinct—though often quantifiable—characteristics. The horizontal lines connecting these components conceptually illustrate the heterogeneity of Flows. This heterogeneity involves "sensible and abstract qualities that are both fundamentally resistant to being reduced in the form of a ‘digitalized’ message". It indicates that within the initial smoothed flow, distinct pathways or segments are formed, reflecting an internal differentiation and a trans-ordination that moves beyond simple internal calibration.

The third section, 3) E.C. bipolarization of Flows illustrates a regrouping and organization of the differentiated flows around two fundamental functions: Expression (E) and Content (C). The large bracket labeled E and C shows that the striated flows (F.1-F.4) from the previous stage are now organized or bipolarized2 into these two functions. This E.C. function results from machinic smoothing selecting specific interactions among the flows. This stage signifies a change of state from a passive registration of heterogeneity to an active one, implying the "beginning of a reference to energy" (SC, 88). It is here that "proto-energetic taking consistency of the differential interval" occurs (SC, 87).

The overarching concept of Φ. = machinic smoothing (deterritorialized reference) frames this entire process as a movement toward deterritorialized machinic Phyla. Φ. (Machinic Phyla) is abstract machinic possibility and reservoirs of potential effectuation. Machinic smoothing refers to the function of opening up possibilities from encysted modular forms.

Figure 3.7: Cycle of the Assemblages of enunciation

Love it when Guattari maps out the entire chapter in one diagram…

The diagram outlines eight distinct phases in the cycle of assemblages of enunciation, moving through energetic-spatio-temporal flows, machinic phyla, incorporeal universes, and existential territories.

1. Sensible smoothing (modular): This is the starting point, characterized by the "Brownian dispersion of redundancies of entity" (SC, 119). It involves an initial linearization where a persistent rhythm allows for a preliminary filtering of elements. This process calibrates and articulates sensible qualities and establishes endo-ordination where segmentary identification and memory are finalized on the linear consistency of Flows. The output of this stage is described as Flow with relative ordinates (For) and substantial—or sensible—Territory (Ts).

2. F'. striation of the instantiation of Flows: Following sensible smoothing, which produces Flow with relative ordinates (For), this stage is a trans-ordination where evaluation crosses a threshold of existential consistency. It involves the marking of difference or in-stantiation. The striation of Flows integrates positive determinability (d+∞) with negative determinability (d–∞) within modules of territorialization. This process generates molecular intervals, amplifications, bifurcations, and infinite fractalization.

3. Machinic smoothing Fmc: This stage is where machines and machinic fields are engendered on the basis of the striated flows from the previous stage. It involves a regrouping and a bipolar disposition characterized as Expression-Content (EC) relations, where specific interactions are selected. This is a proto-energetic taking consistency of the differential interval, marking a change from a passive to an active registration of heterogeneity, which implies an energy charge. The label Fmc here explicitly refers to Concrete machines.

4. Rhizomatic striation Φma: Following machinic smoothing, this stage involves a caesura that shifts from expressive traits to intensive traits, and from extensity to intensity. It is the operational integration of heterogeneous points of view, where the idea of an external point of view disappears. Machinic Propositions (Φpm), which were earlier forms, are here requalified as abstract machines (Φma), losing some of their original identity characteristics and proliferating in rhizomes in every direction and dimension. This is defined as the integration of negative determinability (d–∞) by positive determinability (d+∞).

5. Smoothing of incorporeal Universes: This stage involves the fitting together of incorporeal Universes of possibilities through the hyper-continuous character of machinic phyla from the previous stage. Universes are described as enunciative instances of phase surfaces of possibility (φ). They are both distinct and indistinct, relating to one another at infinitely rapid (d+∞) and infinitely slow (d–∞) speeds (d±∞), being a vibratory state of a process. This is where the virtual dimension becomes central.

6. Striation of Constellations of Universes ΣU: This is the process that gives consistency to incorporeal Universes. It is characterized by the crystallization of a singular-singularizing Constellation (ΣU) within them. This stage involves an ontological sliding from a paradigm of object-reference to one of aesthetic consistency. It is associated with singularization, necessitation, heterogenesis, and irreversibilization.

7. Existential smoothing: This stage involves the "coiling back of Expression onto Existence" (SC, 144). It is characterized by an existential dis-position that is influenced by semiotic potentials from Phyla and Universes. Here, faciality traits, emblems, and signatures function as existential refrains. The virtual enunciation, singularized by a Constellation of a Universe, confers ontological necessity on the Phyla of possible. Existential Territories (Te) are formed, acting as sites for self-organization.

8. Striation of existential segmentarities: This final stage involves the formation of existential crystallizations. It is described as a soft topology that shifts from molar to molecular composition. Existential Territories are cut-out from complexions, and Constellations are constructed in Rhizomes. This stage grounds sensation in experience and roots it in bodily, spatio-temporal continuities. The cycle then loops back to sensible smoothing (stage 1), indicating a continuous and recursive process.

The cycle continuously alternates between smoothing" and striation, which are fundamental conceptual differences in the process of arrangement-formation:

• Smoothing is primarily a function of ontological conversion. It operates to create trans-quadrant homogeneity from a heterogeneity of register, or to homogenize and subsume diversity. It often involves a passive registration of a state resulting from an ontological mutation, equalizing and capitalizing on it. Examples include the mechanical smoothing of surfaces or statistical approximation in communication engineering.

• Striation, conversely, is about the enrichment of the possible and the virtual. It develops heterogeneity within the same quadrant or register. Striation stuffs the system with new potentialities, processualizes, and intensifies it. It actively marks differences, generates molecular intervals, amplifications, bifurcations, and infinite fractalization. Note: Stratification and striation are in no way equal nor similar concepts.

The E.C. relation stands for Expression-Content and is central to machinic smoothing (box 3). Self-reference is explicitly linked to the Body without Organs and is a crucial aspect of existential smoothing (box 7). In this stage, "dispositional enunciation has no other basis than itself," relating to other Universes in a non-causal, non-interactive mode (SC, 182). It is produced as quantities of intensity through concrete machines. The relationship between boxes 3 and 7 suggests that the machinic processes of content and expression are intertwined with the formation and constitution of existential self-reference. The expressive function (f(exp)) leads to the existential function (f(exi)), mediated by a diagrammatic function (f(diag)), demonstrating the profound connection between the two, but we’ll get to the specific functions when their respective diagrams come.

The horizontal double headed arrows connect the abstract machinic Phyla (Φ) (rhizomatic striation, box 4) and striation of Constellations of Universes, box 6) with incorporeal Universes (U) (smoothing of incorporeal Universes, box 5). The thingies U Φ and ΦU signify the dynamic and reciprocal relationships between these domains:

• ΦU. (from box 5 to 4): This is the process where machinic propositions (Φpm/Φma) contribute to the construction or valuation (V) of incorporeal Universes (U). The abstract machines (Φma) proliferate in rhizomes, enabling the "fitting together of incorporeal Universes of possibilities" (SC, 92).

• UΦ. (from box 5 to 6): This indicates the direct relationship between Universes (U) and their Constellations (ΣU). Phyla and Universes relations of compossibility, meaning their smoothing and striation phases are synchronic and homothetic. These arrows highlight the active interplay between abstract machinic possibilities and the virtual, incorporeal realms they help constitute.

Now let’s see the particular elements or processes that characterize the transitions and states within the cycle:

1. Ts (Sensible Territories): The initial outcome of the striation of existential segmentarities, which involves the taking on of consistency in substantial or sensible territories—thus allowing for the cycle to really start with the smoothing of flows.3

2. For (Flow with relative ordinates): This is the "end state of smoothing of Flows" (stage 1), is a state where memorized and controlled states of discursivity are associated with "virgin states of 'matter'" (SC, 82).

3. Fest (Flows of Expression/Energetico-Spatio-Temporal): In machinic smoothing (stage 3), Flows of Expression "extract themselves from sensible fluctuations" (SC, 80). This is the expressive function that capitalizes on heterogeneity.

4. Φpm (Machinic Propositions): These are generated on the basis of striated flows (feeding into stage 3 and leading to stage 4) and are bearers of the "symmetric-fractal and deterritorialized representation of the ruptures of contingency" (SC, 163).

5. ΦU: This notation, is the movement from Phyla to Universes, highlights the compossibility between incorporeal Universes (U) and possibilistic Phyla (Φ), meaning they are not easily distinguished and fundamentally relate to each other.

6. UΦ: UΦ denotes a directional relationship, often implying a recessive inversion in the cycle of assemblages, moving from Universes (U) towards Phyla (Φ) and Territories (T). This signifies a requalification process where Universes influence Phyla. Similar to ΦU, UΦ describes a relationship of enunciation of a referent, which is understood as auto-referential. Generally, with machinic striation (affecting Phyla), the concept of an external point of view dissipates, and deterritorialized machinic Phyla proliferate in a multipolar fashion, overlapping in rhizomes and fitting together with incorporeal Universes, therefore[maybe] we get UΦ & ΦU.

7. UV (Virtual Universes): The striation of virtual Universes fundamentally constitutes incorporeal Universes. It describes something that repeats, affirms itself, is neither localized, finite, nor discursive, but is singular or, more precisely, irreversibly singularizing. This process is what grants Universes their essence to exist. What provides Universes with their consistency and what striates them is the crystallization within them of a singular-singularizing Constellation (∑U). Guattari often cites artworks as the best illustrations of this crystallization.

8. Te (Existential Territories): These are cutouts that result from existential smoothing (stage 7). They are involved in the existential requalification and form crystals of self-organization during heterogenesis.

To summarize, the cycle begins4 with the stage of sensible smoothing (1), transforming chaotic dispersion into initial, albeit limited, consistencies through the establishment of sensible territories. This leads to the striation of Flows (2), differentiating and instantiating elements through processes of trans-ordination and fractalization. From this, machinic smoothing (3) emerges, bipolarizing Flows into Expression and Content (E.C.) and engaging with concrete machines, imbuing them with an energetic charge. This machinic activity then results in rhizomatic striation (4), where machinic propositions are requalified as abstract machines, proliferating in rhizomes and integrating diverse points of view. These abstract machines contributed[contribute] by[to] the smoothing of incorporeal Universes (5),forming hyper-continuous virtual spaces characterized by infinite speeds. This virtuality is then structured through the striation of Constellations of Universes (6), where singular constellations crystallize, leading to processes of singularization and necessitation. This leads to existential smoothing (7), where expression coils back onto existence, constituting self-referential territories through existential refrains. Finally, the cycle moves to the striation of existential segmentarities (8), where intensive traits date and eventalize facts, grounding sensation in lived experience, before looping back to inform and transform new sensible flows.

Figure 3.8: Expansion of the fields of the Possible

This diagram, although looking simple, depicts a continuous expansion of deterritorializations and reterritorializations, demonstrating how new possibilities are constantly generated and how they interact with existing forms of manifestation. The diagram's arrows indicate a dynamic and reciprocal relationship between the fields of possibility and domains of manifestation.

The flow from domains of manifestation upward into fields of possibility and then horizontally is the movement of deterritorialization and possibilization. It involves the fractalization and smoothing of actual Flows into abstract machinic Phyla. This process breaks up measurable volumes into measurable networks, atomizing the fluid world into aerosolic networks that are countable and measurable. The expressive function f(exp) is key here, generating a expressive surplus value [Figure 3.5] and creating Phyla as a field of machinic propositions [Figure 3.6]. This shift is genetic and allows the discontinuous to be more powerful than the continuous, fostering the birth of abstract machines. It transforms existing material and signaletic flows into potential, abstract forms, moving from the "being-there" to the "integral of its possible dis-positions" (SC, 84). So the horizontal movement within the fields of possibility indicates the exploration, proliferation, and systematic management of these newly generated possibilities.

The flow from fields of possibility downward into domains of manifestation and then horizontally is actualization and territorialization, where abstract possibilities are concretized and find existential consistency. It is mediated by the diagrammatic function f(diag), which acts as "the reverse side of the expressive function" (SC, 145) The diagrammatic function ensures the reduction of machinic propositions (from the fields of possibility) to the construction of existential refrains in subjective Territories (within the domains of manifestation). This brings a "surplus value of possibility δ to the sensible surface," creating sensible and then existential territories. This process involves a "coiling back of Expression onto Existence," shifting from a fractal-molecular register to a molar-modular one. Thus, the horizontal movement within the domains of manifestation indicates the stabilization, iteration, and complexification of these concrete entities, allowing them to carve out habitats and develop existential modules.

Therefore, we can say that this diagram shows how Flows and Territories in the concrete world undergo processes of deterritorialization and abstraction—via expressive fractalization—to generate vast "fields of possibility" (Phyla and Universes). This involves taking into account their "integral of its possible dis-positions, before, after, next to and beyond its actual manifestations" (SC, 84). These abstract fields of possibility, in turn, are selectively actualized and territorialized—via the diagrammatic function—back into concrete manifestations, giving rise to new existential territories and singularized entities.

This unnamed diagram is the process of the linearization of redundancies. The diagram is composed of two primary elements: the character o and the hyphen - (which, along with spaces, acts as a separator or a void). In the first line, there's a frequent, yet irregular, repetition of os and clusters of os, interspaced by hyphens and varying numbers of blank spaces. Examples include o-ooo-oo-, oo- -oooo-, o-o-o-o-. This creates a sense of redundancy—the elements o and - reappear consistently, but without a strictly rigid or immediately discernible pattern. This irregular repetition, akin to a "Brownian dispersion" or "primitive soup" (SC, 81), embodies Guattari's concept of redundancy/Deleuzean difference without concept as the unused capacity of a given code or the presence of more information than is strictly necessary for basic transmission, but which is nonetheless present in a chaotic or unorganized state.

Visually, the first line is significantly longer and appears more diffuse, with greater variability in the spacing and grouping of os and -s. It is a state of high variability and less control. The second line is notably shorter and presents a more compact and seemingly organized sequence (oo-oo- -o- -oo). The progression from the first line to the second, if interpreted as a conceptual movement, suggests a process of ordering, compression, and control. It moves from more scattered, "aleatory chains" to "smoothed, proto-machinic sequences that have been brought under control". This linearization involves mechanisms of segmentation, identification, and memory retention of these basic operations, moving from a state of systematic forgetting to a rudimentary, observable order. It's about establishing a unary linearization, which constitutes a vital minimum of consistency.

Thus, Figure 3.8 is the continuous expansion of deterritorializations and reterritorializations that “leads to the constant grafting of new loops in the domains of manifestation and fields of possibility" (SC, 80). The linearization of redundancies is the fundamental starting point or initial phase of this larger Expansion of the fields of the Possible. It is the primordial transformation of chaotic entity redundancies into the elementary, smoothed, and controllable proto-machinic sequences. This initial ordering, which introduces a vital minimum of consistency and allows for the emergence of regularities, is indispensable for the more elaborate continuous expansion and the grafting of new loops that Figure 3.8 is. Without the linearization of its constituent flows, the field of the possible would remain an undifferentiated soup of redundancies, lacking the discernible elements and relationships necessary for any meaningful expansion or differentiation to occur.

Figure 3.9: Module of the sensible smoothing of Flows

The arrows pointing from Fm (material Flow) to Ff (Flow-form) towards Ts (substantial—or sensible—Territory) is the active processing of raw, unformed material and its emergent forms by the non-discursive operator. This convergence illustrates that the chaotic, unorganized redundancies (Fm) and their rudimentary formations (Ff) are taken into account and filtered by Ts, as it functions as a module of territorialization. This further shows the initial work of imposing order and consistency begins, moving from a state of systematic forgetting to one where a vital minimum of consistency is achieved, as in Figure 3.8.

The arrow leading away from this process to Fro (Flow with relative ordinates) is the "end state of smoothing of Flows". Fro is the result of the interaction, demonstrating that the initial irregular redundancies have been subjected to "segmentation, identification... [and] retention in memory" (SC 81). The term relative ordinates indicates that a rudimentary, calibrated order has been established, associating "memorized and controlled states of discursivity with virgin states of 'matter'", showing that while some structure is imposed, the matter itself retains its potential for further reconfigurations.

Figure 3.10: Pseudo-synthesis of the sub-position of Flows (endo-ordination)

The three numbered slots in the bracket (1, 2, and 3) are three simultaneous series of operations that are fundamental to the sensible smoothing process. These operations are:

• Segmentation: The breaking down of continuous data into discrete parts.

• Identification of the segment generated: Recognizing and categorizing these discrete parts.

• Retention in memory of the two preceding operations: Storing the segmented and identified information to allow for its potential reproduction. This sequence of operations introduces a "supplementary threshold of consistency of manifestation (persistantial consistency)" (SC, 81).

The bracketed section labeled calibration of relative ordinates is the process by which a rudimentary order is imposed on the previously unformed or aleatory flows. This calibration is crucial for segmentary identification and for organizing information that can then be retained in memory. Relative ordinates imply that the individual 'O' elements, originally without fixed positions or values, are assigned a contextual place in relation to one another. This move establishes a basic framework for identifying and reproducing patterns within the flow. The calibration process, as a series of segmenting, identifying, and memorizing operations (1, 2, 3), takes the "material Flow" (Fm and Fm′′) as its input. The lines of 'O's (Fm and Fm'') is the raw, unformed redundancies that are being analyzed. The single 'O' appearing within the calibration bracket might be a discrete unit or point of identification that emerges from the larger stream of redundancies, serving as a reference point for the relative ordinates. The process essentially filters and organizes these unformed elements, giving them a minimal, localized consistency through endo-ordination. This endo-ordination is the identification and memory are finalized on the consistency of the flows themselves, rather than leading to a more expansive transformation.

It is described by Guattari as pseudo because, despite the ordering and initial consistency achieved, the process "does not abolish the unformed character of the input Flows (Fm)". This implies that the initial raw potentiality of the flows is retained, making the synthesis a provisional and partial one, rather than a definitive, fully integrated transformation. Therefore, the endo-ordination emphasizes an internal ordering that remains somewhat parasitic on the segmentary processes, lacking a full "take-off" into more profound existential consistency.

Figure 3.11: The in-stantiation of Flows

The bracket labeled Fi on the left is the singular, continuous input flow that is subject to the in-stantiation process. The entire horizontal structure on the right, comprising For1 and For2, illustrates the outcome of this process: the original, single flow (Fi) has been broken down and differentiated into two distinct sub-flows. This movement signifies a transition from a more undifferentiated state to one where specific, discernible differences are marked within the flow.

In the context of Figures 3.9 and 3.10, the o-o-o-o-o-o patterns initially is unformed, chaotic data. However, when they appear as For (Flow with relative ordinates), they have undergone a calibration process [Figure 3.10], meaning they now possess memorized and controlled states of discursivity and are organized in relation to a system of relative ordinates. They are no longer purely chaotic but have achieved a minimal consistency. The diagram shows two distinct such patterns—For1 and For2—emerging from the single Fi. This is where the in-stantiation aspect comes into play: Fi, as the raw instantiated flow, is further differentiated into these distinct, ordered sub-flows, each with its own relative ordinates. The key difference from a raw, unformed Fi is the introduction of internal distinction and ordering within the flow.

I believe that the specific labeling For1 and For2, along with their distinct horizontal lines of 'O's, is the bifurcation or division of the original flow into multiple, separate instances. This is not merely a repetition but a marking of difference. Each sub-flow (For1, For2) is a distinct, segmentary identification within the overall flow. This arrangement highlights the generation of heterogeneity from a potentially homogeneous input, moving beyond simple linear consistency to a more complex, differentiated structure. The distinction between these sub-flows might even relate to "numerical difference bearing on binary sequences of signs," (SC, 82) though the diagram visually presents them as separate streams rather than binary digits.

Pretty much, while Figure 3.10 showed a pseudo-synthesis that smoothed flows and gave them relative ordinates, this next step, in-stantiation, introduces a more profound segmentation and differentiation, allowing for heterogeneity to emerge within the flow itself.

Figure 3.12: Double articulation of machinic smoothing: the EC function (repeated from Figure 3.5)

The diagram demonstrates a double articulation by dividing the machinic smoothing process into two distinct, yet reciprocally presupposing, functions: E and C. This bipolar disposition is selected from the interactions within raw flows and serves to manifest "a principle of the expression or extraction of traits of machinic effectiveness (machinic propositions composed of sign-particles)" (SC, 85).

• E function (Expression): The E function is the "expression or extraction of traits of machinic effectiveness". It is generated by the deterritorialized fractal process and is essentially correlated to a deterritorialized and fractal smoothing of the set of striations of Flows. Its role is to enable the "possible [to] ooze out of all the encysted modular forms that harbour it" (SC, 138) by decompartmentalizing and spreading it across immaterial, atopographical, and unlocalizable fields. The sub-flows labeled F1i, F2i, and F3i (instantiated Flows) relate to the E function by being given a specific consistency that allows them "to acquire a language that is proper to them" (SC, 85). This involves the endless repetition, deformation, and miniaturization of sensible module formulae, and their reframing within an expressive surplus value.

• C function (Content): The C function is the Content pole of this bipolar disposition. While the diagram shows it interacting with sub-flows F4i through F7i, Guattari describes Content as originating from "immaterial, atopographical, unlocalizable fields of possibility" (SC, 138). It operates in reciprocal presupposition with Expression, meaning that "signs are at work in things themselves just as things extend into or are deployed through signs" (ATP, 87). The C function's role is to organize and give consistency to the possibilities unleashed by the E function, often by engaging with modular stratifications of the everyday world. This is evident in examples where an abstract idea or dream (like Leonardo da Vinci's flying machines) gains consistency through collective enunciation, proliferating algorithms, and diagrams, eventually becoming concretized in vital societal drives. This shows that Content is where the machinic propositions derived from Expression are actualized and integrated into tangible, albeit dynamic, formations.

The E and C functions work together in a relationship of reciprocal presupposition, meaning that they are mutually defining and constantly interweaving rather than being separate entities. The E function performs a fractal proliferation, endlessly deforming and miniaturizing forms and generating a surplus value of code by exploring the "phase space of possibility" (SC, 134). Concurrently, the C function, as the other pole, takes these possibilities and works to organize and stabilize them, integrating them into modular stratifications of the world. This active interplay moves beyond mere representation, creating a productive act that transforms input flows into Flows of Sign-particles, which are then charged with power.

The ultimate result of this double articulation of machinic smoothing is a dynamic movement from manifest being-there (territorialized, finite, discontinuous Flows) to an integral of its possible dis-positions (deterritorialized, transfinite, continuous Phyla and Universes). This process is a headlong flight leading to a "continuous expansion of discursive domains, of fields of potentiality and of Universes of virtuality" (SC, 86). By converting signaletic Flows into Flows of Sign-particles, charged with power and capable of multilocal exploration—the machinic smoothing generates a crystal of heterogeneity. This, in turn, increases the abstract machine's power of effect by reinforcing the potentiality for singularization and reducing entropy within the system. This transformation is essential for opening up to a "logic that generates molecular intervals, amplifications, bifurcations and infinite fractalization (incorporeal heterogenesis)" (SC, 124), setting the stage for more complex machinic operations and the emergence of new realities.

Figure 3.13: The three modes of substantiation

yep, one of those…

This diagram is about focuses on how different forms of smoothing contribute to the substantiation of various entities. Substantiation refers to the transformation of states of non-formed matter (m) into formed states (f) through a process of substantializing mediation (s). This diagram expands upon the previous discussion of machinic smoothing by situating it within a broader model that includes sensible smoothing and the double smoothing of Universes.

Smoothing in this context is a function of ontological conversion, passively registering states and then equalizing, legalizing, or capitalizing them. It refers to transformations between neighboring quadrants, creating a new homogeneity.

• Sensible Smoothing (Bottom-Left Quadrant, related to F and T):

  “We have already noted that sensible smoothing ruptured with existential endo-reference and that it ‘secreted’ linearized

  discursive sequences, the calibration of which was based on a principle of immanence.” (SC, 86).

Sensible smoothing is a territorialized smoothing that operates between the domain of Flows and existential Territories. It functions by modules of the linearization of redundancies, transforming aleatory chains... into smoothed, proto-machinic sequences that have been brought under control [Figure 3.8-11]. This process establishes a sensible, cognitive, affective, territorialized existential homogenization, which Guattari also characterizes as 'grasping', manifestation, or 'putting into being'. It is an instantiation of Flows that ultimately produces a module of sensible territorialization and involves discursive smoothing along the axis FT, calibrating and articulating sensible qualities. It is the most grounded of the smoothings, dealing with the concrete organization of matter.

• Machinic Smoothing (Top-Left Quadrant, related to F and Φ):

  “For its part, machinic smoothing, carried out by the EC function, breaks with the uniquely proximal type of discursivity specific to Flows, so as to introduce a caesura, a completely new opening of ‘possibilization’ and to authorize pragmatics (machinics) that are creative of temporalization and spatialization, energy conversions, putting to work of encodings and diverse modes of semiotization.”

Machinic smoothing is described by Genosko as an "energetic conversion of static molar Flows to dynamic molecular possibility" (GAI, 214). It involves an "Expression–Content polarization" and a "caesura that engenders the machinic pro-positions[sic] Φpm" (SC, 92). This process moves from the expressive register to the intensive, transforming traits of extensity—the signaletic part of sign-particles—to traits of intensity. Φpm (machinic propositions) are deterritorialized machinic Phyla that proliferate in every direction and in all dimensions [Figure 3.7]. Machinic smoothing "requalifies machinic Propositions Φpm as abstract machines Φma", indicating a transformation towards a more abstract, operational integration of heterogeneous points of view where the idea of an external point of view disappears.

• Double Smoothing of Universe (Top-Right Quadrant, related to Φ and U):

  “Further on, with the smoothing of Universes, we will see a generalized and infinite opening appear, escaping radically from discursive coordinates, whatever their nature might be, preparing the promotion of monads of substantial self referencing of the type matter-substance-form (m.s.f.).” (SC, 86).

This process is a generalized and infinite opening that "escapes radically from discursive coordinates" (SC, 86). It prepares the "promotion of monads of substantial self-referencing of the type matter-substance-form (m.s.f.)". Unlike machinic smoothing which deals with deterritorialized phyla and their propositions, the double smoothing of Universes concerns the enunciative instances of the phase surfaces of possibility (φ). These "phase surfaces constitute objects that no longer respond to the criteria of an actualized distinctiveness," being "distinct and indistinct at the same time" (SC, 151). It is a process that works "flush with the enunciative, deterritorialized, non-discursive and virtual matters" (SC, 158), indicating a high degree of abstraction and openness.

• Pseudo-smoothing BwO (Bottom-Left Quadrant, related to U and T)

This is explicitly designated as "pseudo" because, unlike the other three modes of substantiation, it "translates the fact that there are no longer any extrinsic relations, which arise from the logic of discursive sets, between the Universes of incorporeal multiplicities and the ‘unary’ existential Territories" (SC, 87). This distinction implies that the other three types of smoothing—Sensible, Machinic, Double Universe—involve an active process of substantializing mediation (s) through which matter (m) is transformed into formed substance (s) and form (f). The presence of the m.s.f. triangles in these other sections, and its absence in the pseudo-smoothing BwO, shows that the BwO, in this context, describes a state where such discrete, extrinsic, and formative transformations do not occur.

The three active smoothings work together in a processual cycle, where the output of one can feed into the other, driving a continuous expansion of discursive domains, of fields of potentiality and of Universes of virtuality. Each striation—processes within a domain that enrich possibility—acts as a "junction-operator between two smoothings, ensuring that the system is constantly being enriched and intensified.

Figure 3.14: Abstract Machines

The diagram illustrates the hierarchical composition of Φma by showing its internal derivation from Phyla of machinic propositions (Φpm), which themselves are structured into three distinct levels (Φ′, Φ′′, Φ′′′):

• Φ′ (Initial Propositions): This likely is machinic propositions in their more nascent form, still carrying traits of extensity and possibly operating with an extrinsic ordering inherited from material and signaletic flows. These are propositions beginning to deterritorialize but might still be relatively tied to specific contextual Expression and Content poles.

• Φ′′ (Intermediate Striation/Requalification): This stage signifies the process of machinic striation or requalification where propositions move towards deeper intensive traits and undergo an "operational integration of heterogeneous points of view." (SC, 92). At this level, the idea of an external point of view disappears, and propositions begin to shed a certain model of identity and of identification. They become more hyper-continuous, preparing for further abstraction.

• Φ′′′ (Advanced Deterritorialization): These are the propositions that have undergone significant transformation, approaching the threshold of becoming an abstract machine. They are now trans-positional, capable of leaping from one phylum to another, exploring and working "variations-derivations-integrations proper to the fields of possibility" (SC, 93) outside of testifiable temporality. They no longer respond to arborescent logic but embody a "systematic management of possibility" and an "increase in its power of effect".

Therefore, the abstract machine (Φma) is not an elementary given but rather a product of a hierarchical and developmental process rooted in the Phylum of machinic propositions (Φpm). This phylum, in turn, encompasses various degrees of abstraction and deterritorialization, enacted by the three levels of propositions (Φ′, Φ′′, Φ′′′). The curly brackets and connecting lines denote a compositional unity and a processual flow. They emphasize that Φpm is comprised of Φ′, Φ′′, Φ′′′, and that Φma arises from or is constituted by Φpm as it undergoes further requalification. This arrangement demonstrates that Φma is an emergent entity, achieving its abstract, deterritorialized, and creative power through the progressive transformation and integration of machinic propositions. The process involves moving from more localized and externally referenced qualities towards a generalized, intensive, and internally coherent management of possibilities, ultimately defining the abstract machine's capacity to construct new realities.

Figure 3.15: The band of continuous variation of the lock and key machine

This diagram illustrates a conceptual model of an abstract machine through the seemingly simple interaction of a lock and a key.

The Continuum Φ is the possibilistic forms of the lock and key system, functioning as a band of continuous variation. Conceptually, it is the set of all possible profiles that a key could have to effectively operate a corresponding lock. This continuum is limited, as indicated by points A and B, but its nature is infinite due to its "continuist texture" (SC, 95). It operates in deterritorialized coordinates and belongs to an incorporeal Universe of virtual alterity. In a broader sense, this continuum can be understood as unformed, amorphous, or formless matter, which is crucial because abstract machines operate by "matter, not by substance; by function, not by form" (ATP, 141). For the machine to operate on a continuous band means that its functionality is tied to a dynamic range of variations. This continuous variation allows for infinite topological deformations and deterritorialization into a molecular register, fostering a proliferating contiguity of possibilities beyond specific, fixed instances.

The diagram shows two key components: F.k (profile of key) and F.l (profile of lock).

• F.k ("profile of key") signifies a contingent, concrete, discrete form of a particular key. It is a specific, material profile, embodying a singularity.

• F.l ("profile of lock") signifies the contingent, concrete, discrete form of a particular lock. Like the key, it is a specific, singularity profile.

Now the thing is that while F.k and F.l are distinct material forms and never quite coincide perfectly, their variations must remain within a separation-type limit for the system to function. Their interaction is described as a biunivocal relationship, where a deterritorialized machinic form synchronically ‘inhabits’ both manifest positions (key and lock). The machinic effect or successful operation occurs when these concrete forms are understood as belonging to the broader Continuum Φ of possible forms. The actual conjunction between the concrete forms—F.k, F.l—and the possibilistic forms—Continuum Φ—is what enables the machine to exist and function[connect].

The diagram also shows Limits A and B. These are crucial limit-profiles that define the thresholds of tolerable error for the operation of the lock and key. Beyond these limits, the opening effect ceases. The conceptual function of these limits is to delineate the zone of effectiveness within the continuum where the key and lock can successfully interact. They establish the boundaries for reproducible forms at an ontogenetic level and allow for evolutionary variations at a phylogenetic level. Despite defining boundaries, the continuum within these limits retains its infinite character due to its continuous, rather than discrete, nature.

This diagram shows that the "soul of code, of the sign, language, catalysis, the imprint, the image, the tracing, the plane, the programme of concrete machines" is their diagrammatic function, which associates exo-referred (materiality of process) with endo-referred (complexity, singularity, existential consistency) modalities of evaluation. This continuous variation allows the machine to be a "junction, a knot of Flows” that facilitates reproducibility and evolutionary possibilities, constantly negotiating between manifest heterogeneity and possibilistic heterogeneity.

Figure 3.16: Ontological requalifications of the four primary stase

love when brother Felix lays out half of the entire model in a diagram

First let’s see the distinction at heart here between Flows and Phyla. This is crucial because it highlights the two fundamental sides of reality that Guattari seeks to articulate: the raw, continuous, given material-energetic movements (Flows) and the discontinuous, abstract, organizing principles or connections (Phyla) that process these movements and open up possibilities. Arrangements operate by continually articulating these two dimensions, mediating between the “given” and the giving aspects of the world. Without this distinction, the complex, processual nature of existence, which is always in a state of "unfolding" between these modalities, would be reduced to a singular, undifferentiated continuum.

The four primary stases are the key stages or processes, we’ve seen within the continuous cycle of transformation between Flows and Phyla.

• Sensible smoothing of Flows [Figure 3.6-7-9-10-13]: This process describes the initial territorialization and homogenization of raw, energetic, and material flows. It occurs between the domain of Flows and that of existential Territories. It is characterized as a grasping, manifestation, or putting into being, creating a sort of existential homogenization through modular experientiations (sensible, cognitive, affective…). This smoothing "passively takes note of the state resulting from an ontological mutation/caesura" and "equalizes-legalizes-capitalizes this state" (SC, 98). It finalizes "segmentary identification and its memory on the linear taking consistency of Flows" (SC, 82).
  
  Entity For: Refers to the initial stage of Flows undergoing endo-ordination, which is the calibration of internal ordination. This is when Flows are passively smoothed and segmented, taking on an initial consistency.
  
  Topos sub-position: This term denotes an underlying, fixed, or initial spatial arrangement or layering. The sensible smoothing of Flows occurs at the sub-positionality level. The conceptual link is that the internal, foundational ordering of Flows (For) results in their occupying a basic, underlying sub-position within the assemblage.
  
  Enunciation: Endo-ordination: This refers to the process of internal calibration and organization of flows, "where segmentary identification and its memory were finalized on the linear taking consistency of Flows" (SC, 82). It's about establishing consistency within the flow itself.
  
  Operators: Modules of territorialization: These are specific organizational units that grasp or finitize flows, creating stable, bounded territories. They agglomerate referential series into a finite bundle. These modules facilitate the internal ordering characteristic of endo-ordination.
  
  Ontological Modalizations: Substantiation: This refers to the process by which non-formed matter takes on formed states, acquiring a stable material or signaletic form. "Substance is the manifestation of form in matter" (SC, 271). For the sensible smoothing of Flows, the outcome is that the raw, continuous matter of Flows gains a specific, albeit passively determined, material or signaletic substance, becoming a formed state with initial consistency.
  

• Striation of instantiation of Flows [Figure 3.6-7-11]: This stage occurs when the smoothed flows are marked by differentiation and the emergence of new potentialities. The "striation of Flows is at the junction of two previous smoothings,"—the point of transition and diversification (SC, 117). It is a marking of difference or in-stantiation, where flows acquire a bounded intrinsic memory. Unlike mere passive smoothing, striation develops, stuffs with new potentialities, and intensifies the flow. This involves an "agglomeration in a finite bundle" (SC, 124) of referential series and the emergence of "an attractor...which unify potential series of determinations". It opens flows to a "logic that generates molecular intervals, amplifications, bifurcations and infinite fractalization (incorporeal heterogenesis)".
  
  Entity Fi: Instantiated Flows, which emerge from in-stantiation by trans-ordination. This is where flows are marked by differential pinpointing or marking of difference.
  
  Topos dis-position: This implies a dynamic arrangement, configuration, or active setting out. Existential dis-position is a state of active arrangement. The differentiation and marking of Flows (Fi) actively re-arrange their configuration, leading to a dynamic dis-position that is open to future possibilities.
  
  Enunciation: Exo-ordination: this enunciation signifies a move beyond purely internal ordering. It corresponds to the differential pinpointing or marking of difference that occurs when flows are striated, opening them to new possibilities.
  
  Operators: Concrete [traits of molar extensity]: Here, the operators involve a blend of components. The traits of molar extensity refer to the formed, extensive aspects of the flow.
  
  Ontological Modalizations: Manifestation: This describes the "coming-into-being" of a "field of density" or "crystal orders from a stochastic chaos" (SE, 143). It is about how entities grasp or put into being. Through the striation and instantiation of Flows, a particular configuration or set of differentiations becomes manifest, acquiring a discernible presence and a more active, though still bounded, form of existence with specific enunciative consistency or invariant values.

• Machinic smoothing of Phyla [Figure 3.5-…-7-12—…-15]: This process describes the opening of flows to the realm of the possible and the abstract machinic. It is a "form of smoothing that opens onto the possible" and "subsumes the diversity and heterogeneity of entitarian compositions" (SC, 117). The goal is to move "from the proto-machinic smoothing of Flows to the deterritorialized machinic Phyla" (SC, 78). This involves a caesura that shifts from the expressive register to the intensive, transforming traits of extensity to traits of intensity, effectively deterritorializing the machinic. Thus, the shift towards deterritorialized reference.
  
  Entity Φpm: Machinic Propositions, which are the potentialities or relatable sets of existing diagrammatic connections that Flows intersect with. They are a Capital of possibility.

  Topos pro-position: This directly relates to the concept of pro-posing or setting forth possibilities. The nature of Phyla as abstract connections and potentialities (Φpm) means they are fundamentally engaged in pro-position–formulating or offering blueprints for what could be.
  
  Enunciation: Coordination: This refers to the "expressive coordination of machinic smoothing". It's about organizing the abstract qualities inherent to machinic propositions, shifting from extensive to intensive traits.
  
  Operators: Concrete [sign-particles]: the emphasis is specifically on sign-particles, as they provide the infinitesimal, energetic, and deterritorialized impulses necessary to transform rigid, territorialized Flows into dynamic, possibility-rich Phyla. In The Machinic Unconscious, Guattari writes that sign-particles are the "irreducible nuclei of the abstract machinic possible" that define the potentiality within these Phyla (MU, 49)5.
  

  Ontological Modalizations: Possibilization: This concept relates to the "birth of the possible from a real world of Flows," which "entails the birth of abstract machines". It involves processes that open up new fields of possibility. The machinic smoothing of Phyla leads to the generation and proliferation of abstract possibilities. Phyla function as "reservoirs of potential effectuation" (SC, 102), thus the outcome is an expansion of the possible within the assemblage.
  

• Rhizomatic striation of Phyla [Figure 3.7-14]: This stage involves the complex organization and proliferation of abstract machinic possibilities. This "striation confers on them a hyper-continuous character" and allows them to be established through the fitting together of incorporeal Universes of possibilities (SC, 92). It operates "at the junction of two smoothings," specifically between "deterritorialized-fractal-expressive smoothing" and the "smoothing of incorporeal Universes of reference" (SC, 149). This involves the infinite topological deformations and deterritorialization of forms, leading to an infinitesimal molecular register and establishing extrinsic contiguity between molar and molecular levels. Thus, the enrichment of the possible and virtual within the Phyla.

  
  Entity Φma: Abstract Machines, which are the requalification of machinic Propositions Φpm. They are pragmatic operators that traverse various levels of reality and establish and demolish stratifications.
  
  Topos trans-position: This denotes movement across, transformation, or translation between different levels or registers. Abstract Machines (Φma) are the active forces of deterritorialization and transformation, capable of absolute translateability, which enables the trans-position of elements and the creation of new connections across heterogeneous domains.
  
  Enunciation: Trans-ordination: This is a logic of translation and connection across domains, opening to continuous and transfinite evaluation. It is characterized by the ability to establish extrinsic contiguity between disparate levels.

  Operators: Concrete [traits of molecular intensity]: At this stage, the operators, primarily through abstract machinisms (which are everywhere and nowhere), are at their most active and deterritorialized. They effectuate infinite topological deformations and deterritorialization, constantly generating and connecting possibilities through sign-particles and traits of intensity to form rhizomes.
  
  Ontological Modalization: Effectuation: This describes how abstract machines are "embodied and thus actualized in and enveloped by territorialized entities" (SE, 188). It is the process by which "machinic assemblages effectuate the abstract machine" (ATP, 71). The rhizomatic striation of Phyla culminates in the actualization or concretization of these abstract possibilities. It is the active implementation of abstract machines, leading to the creation of existential Territories and Universes of reference through a rich interplay of qualitative openings and energetic charges. This process gives the assemblage its full capacity for singularization and heterogenesis.

Figure 3.17: The concrete machine of the extensity/intensity transformatio

the final one…

This diagram shows a three-stage process by which a concrete machine transforms an initial Instantiated Flow into a Rhizome of abstract machines, fundamentally shifting from a state of extensity to one of intensity.

Stage 1 begins with an Instantiated Flow (Fi) that is transformed into energetico-spatio-temporal Flows (Fest). This initial transformation is driven by the bipolarization of Expression (E) and Content (C), forming the EC function. The EC function shows the role between expression and content as variables of the arrangement in perpetual interaction. This stage involves the striation of Flows which occurs at the junction of two smoothings and branches into antagonistic directions within an Assemblage of enunciation. Striation here implies breaking up unmeasurable volumes into measurable networks, analogous to fractalization, transforming fluid, amorphous flows into aerosolic quasi-Flows with distinguishable elements. The EC function, through machinic smoothing, selects and bipolarizes interactions into Expression and Content, signifying that heterogeneity is actively registered and becomes productive of Effects rather than passively observed. This process implies the charging of signaletic or encoding indices with energy, leading to a requalification of neutral Flows.

Stage 2 moves from the energetico-spatio-temporal Flows (Fest) to a Phylum of machinic propositions (Φpm). This process is the dynamic management and capitalization of the heterogeneity generated in the first stage, making it bear fruit beyond elementary operations. It marks the shift from the extensive register to the intensive or from traits of extensity to traits of intensity. This propositional smoothing process involves the "molecular secretion of Universes of reference 'parallel' to the molar worlds of manifest Flows" (SC, 92). The outcome is a Phylum of machinic propositions (Φpm), which is characterized by its multipolar nature, proliferation in all directions, and overlapping in rhizomes, leading to knots of effectiveness. A machinic phylum is a "constellation of singularities, prolongable by certain operations," converging on assignable traits of expression, becoming a continuous flow of matter-movement (ATP, 406).

The final stage transforms the Phylum of machinic propositions (Φpm) into a Rhizome of abstract machines (Φma). Transpositional striation is the process by which the "traits of intensity constitutive of abstract machines cease to be pro-positional so as to become trans-positional" (SC, 93). These traits "sweep across their paradigmatic Phylum of origin and can, at any moment, leap from one Phylum to another," demonstrating their fluid and dynamic nature. This striation integrates heterogeneous points of view and eliminates any external point of view, as abstract machines operate by their own internal logic. The Rhizome of abstract machines (Φma) is the product because these machines are multipolar, proliferate in every direction and in all dimensions, overlap in rhizomes, and bud in knots of effectiveness.

Chapter Discussion

Let’s now see the various arguments posed here by Guattari that weren’t covered by the diagrams.

Guattari starts the chapter by starting with a very pertinent question: Why Start from Four Entities? Guattari argues against axiomatic models with two terms (like Being/Nothingness)6 which he sees as leading to depotentialized representations and an inaccessible "grund" (foundation). Similarly, he suggests that dialectics with three terms result in pyramidal or arborescent determinations. Instead, Guattari proposes that it is only with "3 + n entities" that a trans-entitarian—matricial—generativity can be established without prioritizing one essence over another (infrastructure over superstructure). This multi-entity approach also enables a principle of self-affirmation, auto-retroaction, and an auto-poietic—self-founding—basis. Then we might ask ourselves: how is that Carlos A. Segovia in his, otherwise very precise and pertinent, study of Guattari argues that Guattari’s philosophical project is dyadic? Segovia argues that Guattari's dyadism refers to an underlying relational logic or a mode of structuralist thinking that apprehends the world through mutually defining and reciprocally differentiating pairs of concepts, which are then integrated, unfolded, and complicated within his broader multi-entity—four-functor—frameworks to generate complex, singular, and autopoietic processes. This allows for the simultaneous affirmation of both chaos and order, and the exploration of transitions from indeterminate to determined possibilities. Segovia emphasizes that this dyadism is a "constructivist principle that allows 'monadic' or qualitative forms to take shape on a single plane of consistency" (GBD, 25). It is not a reduction but a framework for understanding how multiple, heterogeneous elements interact and produce consistency. The dyadic relationships, such as inverse proportionality (A = 1/B), mean that terms do not simply add up to a totality, keeping the structure open from within and without.

Continuing with the chapter, for exo-referred modelling systems, two notions suffice: Flows (F) for discontinuous discursivity and Phyla (Φ) for continuous 'intercalary' discursivity. However, endo-referred meta-models demand a heterogeneous multiplicity of categories that can account for specific processes of heterogenesis and singularization. Guattari highlights that the unary discontinuity of contingency (T) cannot be simply linked to intensive incorporeal—non-discursive—multiplicities (U), requiring heterogeneous synaptic operators from machinic relations (Φ) to intercalate them. This quadripartition is illustrated in Figure 3.1, which presents a "Matrix of four modelling and meta-modelling entities" for Discursive (Φ, F) and Non-discursive (U, T) categories, distinguishing between exo-referred and endo-referred modes. Importantly, Level I, comprising Phyla (Φ) and Universes (U), is considered the deterritorialized integral of the territorialized Flows (F) and Territories (T) of Level II.

Guattari then describes continuous discursivity (Φ) as marking the infinite multiplicity of a state of fact or things, which appears only in 'contingenced' (territorialized) Assemblages. Discursivity is seen as a sequential order exo-referred to Energetico-Spatio-Temporal (EST) coordinates. This order manifests in two modalities:

1. Rhizomatic (Φr): An organization with knots and crossroads, implying a networked machinic consistency.

2. Parallel linear chains (Φl): An organization that separates machinic clusters and agglomerations, leading to heterogenization and necessitating changes of level and crossings of deterritorialization thresholds.7

Trans-deterritorializational operators emerge from this, leading to Constellations of Universes of reference (TU), which relate to the logic of bodies without organs. Figure 3.2, "Deep structures Φl and synaptic opening," illustrates the machinic—intermachinic—propositions and synaptic openings associated with enunciating modifications.

Then Guattari distinguishes between discursive actualization and enunciative virtualization. Possible occurrences are linked to Φ and U, while contingenced (real) occurrences are linked to F and T. This is depicted in Figure 3.3, "Matrix of the Possible, the Real, the Actual and the Virtual". The exo-reference of Flows operates within finite, discontinuous discursive sets, whereas Phyla (Φ) function within infinite, continuous algorithmic discursive sets, shifting the framework from Figure/Ground relations to Machinic knots/continuous systemic Ground.

Furthermore, Φ expresses all possible pro-positions and trans-positions concerning 'contingenced' states of Flow. The consistency of machinic regions stems from both extrinsic determination and a transistential self-consistency at deterritorialized levels. The machinic Plane of consistency (Φ) is therefore complemented by a Plane of immanence (U), or Plane of self-reference, which is a locus for the generation (heterogenesis) of singular positions of existence, rather than a universal frame. Guattari critically notes that Thomas Kuhn's paradigms are understood to exist only within Phyla, lacking connections to Constellations of Universes. He suggests that problems, like living beings, move through different coordinates: extrinsic EST coordinates and intrinsic intensive coordinates. The first generation of desiring machines aimed to bridge signaletic matters with deterritorialized subjective operations, necessitating abstract machines that traverse these orders. Process—as a line of deterritorialization—became the category of desire, now reframed as problematics of the production of enunciation.

Flows are described as intensive fluctuations that characterize the world. They are:

• Smooth: exhibiting 'identitarianizing' repetition of forms, leading to linearization.

• Cut into discrete figures.

• Given in a finite approach that delimits them in EST coordinates.

• Bearers of feedback and a memory of smoothing, calling for proto-machinism. A first relation of territorialized discursivity is defined by three characteristics: a primary material continuum—EST or signaletic matter—, the repetition of divisible and smoothed forms—proto-machinic form—, and mediative operators for position-retention that capitalize memory or proto-enunciative substance (T). Figure 3.4 visually shows the interplay of Matter, substance, form in this context. This relation of discursivity corresponds to the first stasis of deterritorialization: substantial deterritorialization.

A second stasis, expressive deterritorialization, emerges from the bipolar concatenation of fluctuations, having two modalities: an 'autistic' closure of proto-machinic figures—formal reiteration—or a dialectical exhaustion resulting in expressive surplus value or existential supplement (∆F). This leads to a bipolar regrouping around a function of Content (∆Fc) and a function of Expression (∆Fe), articulated via chains of expressions of machinic Phyla (Φ) and new existential Territories (Te). Figure 3.5 illustrates this bipolar arrangement of an expressive deterritorialization with seven Flow components. Figure 3.6 presents the three modalities of fluctuation, including machinic smoothing and the EC bipolarization of Flows.

The transition from proto-machinic smoothing of Flows to deterritorialized machinic Phyla involves general functions of smoothing and striation. Striation refers to heterogeneity within an entitarian register, while smoothing refers to inter-entitarian transformation between two registers, leading to new homogeneity. For instance, concatenating Flows (F) creates a striation—heterogeneization—of the sensible world, while bipolarizing Flows into semiotic and EST Flows involves smooth machinic Phyla (Φ). Figure 3.7 presents the "Cycle of the Assemblages of enunciation," where each striation functions as a junction-operator for vertical (deterritorialization) and horizontal (discursivization) smoothings. The cycle, though presented as closed in Figure 3.7, implies a continuous expansion of deterritorializations and reterritorializations. Figure 3.8 shows this "Expansion of the fields of the Possible".

Finally, a concrete machine, while appearing defined, is arbitrarily delimited, with its essence lying in a machinic functionality that traverses segmentary stratas and is inseparable from signaletic systems. Figure 3.15—"The band of continuous variation of the lock and key machine"—demonstrates how contingent, concrete forms interact with possibilistic forms in a continuous variation, expressing processual singularization. This involves a move from exo-referential coordinates to endo-referential traits. Enunciation is requalified as non-discursive self-enunciation, and intensive ordinates introduce irreversibility. Concrete machines, through "refrainized" spatio-temporal sequences, bear qualifying traits that open up to possibilistic Phyla and virtual Universes. The negentropic reasons of Phyla function as reservoirs of potential effectuation, whose intensive power is the richness of Constellations of Universes of reference. Traits like deterritorialization and self-consistency enable transversal establishment across heterogeneous strata, known as traits of inherence. Figure 3.16 provides a provisional summary of "Ontological requalifications of the four primary stases," while Figure 3.17 illustrates "The concrete machine or the extensity/intensity transformation". And boom we done good night.

2. Semiotic Energetics

Figure 2.1: The axes of deterritorialization and relative discursivity

The vertical axis of deterritorialization is the movement away from a territory or the opening of an arrangement to other possibilities. The top of this axis signifies infinite values of deterritorialization. This corresponds to absolute deterritorialization, a state where coordinates are absent or abolished, and the system is far from equilibrium. Abstract machines operate at this level.

The bottom signifies finite values of deterritorialization. This often corresponds to relative deterritorialization, where the movement away from a territory is constrained by compensatory reterritorializations, segmentation, or black holes. This dimension characterizes the stratified aspects of arrangements, where deterritorialization is more limited.

The horizontal axis of discursivity is the sequential order of phenomena—Energetic-Spatio-Temporal (EST) coordinates. The left side is the plural discursivity. It is characterized by continuous, fusional complexions of Flows and rhizomes of Phyla—the given aspects of existence. This side relates to objective and actual components. It encompasses modelization and ordinary complexity.

The right side is unary discursivity. It is characterized by discontinuous, mixed divisions of Territories and constellations of Universes—the giving or creative aspects. This side relates to subjective and virtual components. It encompasses metamodelization and hypercomplex states.

Figure 2.2: The layering of the four levels of intensive quantification

This is one of the really good ones.

The components within Flows are:

• Mc (Matter of content): This refers to unformed, amorphous matter or purport, which is redefined as semantic and physical reality, including non-semiotized meaning and a continuum of material flows.

• Diag (Diagrams): Within the context of F, "Diag" refers to elements or processes that can be diagrammatic. Diagrammatic components are a-signifying and produce rather than represent, operating outside language in fields like mathematics or computer code. The diagrammatic function works on traits of expression within F.

The components within Phyla are:

• Rm (Machinic rhizomes): This term emphasizes the non-linear, interconnected, and multi-directional nature of these abstract machinic processes, akin to a rhizome.

• Pm (Machinic propositions): These are bearers of symmetric-fractal and deterritorialized representation of ruptures of contingency. They’re the operational integration of heterogeneous points of view and proliferate in every direction.

The components within Universes are:

• ΣU (Constellations of Universes): This denotes the collective arrangements of these incorporeal references and values.

• N (Noemata): Noemata—Noemas—are sites of sense entities related to Universes.

The components within Territories are:

• Ts (Sensible territories): These are specific existential territories, often described as surfaces of sensation or existential modules that can be stabilized by recursive iterations.

• Me (Existential matrix): This implies a structured arrangement of existential conditions or a point of self-referential engagement within a territory.

The diagram shows the relationships between the functors through its arrows.

• The arrows from Flows to Machinic Phyla generally signify integration and fractalization. Phyla are the integrals of Flows, meaning Flows are structured and organized into rhizomatic networks. This transformation involves a machinic smoothing that breaks the proximal discursivity of Flows, introducing possibilization and abstract machines, often linked to the secretion of code.

• The arrows from Phyla to Univierses show the transformation from abstract machinic possibilities to incorporeal universes of reference. The components of Phyla (Rm, Pm) feed into the Universes (ΣU, N). This is part of what Guattari calls noematic processes.

• The arrow from Universes to Territories indicates the incarnation of virtual possibilities into concrete existential territories. Pathic operators of heterogenesis bring an entropic dimension, conferring a pseudo-identity without fixed contours. Singularizing constellations of Universes help block fractalization of expression to processualize arrangements of enunciation toward the dissymmetries of Universes.

• The arrow from Territories to Flows completes the cycle—necessitation or the existential function that binds territories back to the material and signaletic flows. This is the process where a choice for finitude and an attachment to constituting a world is found at the heart of enunciation, grounding it in a tangible reality.

The arrow from Me (Existential matrix), a component of T, to ΣU (Constellations of Universes), a component of U, signifies that existential matrices can contribute to or relate to the formation of constellations of universes. This is a "synaptic disposition" where a constellation of a Universe of reference is crystallized. Synaptic tensors of affect (Sa) are also noted between ΣU and Ts, indicating connections related to subjective affects.

The looping arrow within the Flows quadrant, involving Mc (Matter of content), denotes an internal, self-referential dynamic or process within the domain of Flows itself. This looping arrow suggests that the matter of content undergoes internal processes of transformation, differentiation, or calibration. This internal dynamic—striation of Flows—related to numerical differences in binary sequences of signs and sensible/abstract qualities, highlights how the raw, unformed material of reality is continuously being reconfigured within the F domain, often resisting direct digitalization. It underscores that flows actively process their own content, even at a proto-semiotic level.

This metamodel is circular and iterative, with arrows demonstrating how each domain feeds into and transforms the others.Phyla integrate Flows, Universes emerge from these integrations and connect to Territories, which then inform Flows, and so on.

Figure 2.3: The relations of presupposition between the three unconscious levels

Components:

• Level I (Intrinsic Reference): This level is the primary unconscious. It is characterized by Systems and Structures and deals with non-separability. Its tensors of intrinsic reference are bijective—two-way—and continuous, making it a domain that schizoanalysis, when confronted indirectly, "has to surrender" to (SC, 62) It doesn't presuppose any other level.

• Level II (Semiotic): This level is the secondary unconscious. It is associated with separation and involves Semiotic Tensors which are projective vectors—one-way—and continuous. These semiotic entities bear a surplus value of possibility that can be actualized at the pragmatic level. This level presupposes Level I. Schizoanalysis actively works on the components of semiotization at this level, engaging in multiplication or reduction, enhanced discernibilization, or globalization of operations.

• Level III (Pragmatic and Subjective): This is the tertiary unconscious. It is defined by quantification and is essentially constituted by pragmatic synapses (Se) and subjective synapses (Sa)—which are described as Persistence and Transistence. They actualize Effects and virtualize Affects, linked to "contingent, singular character of the Assemblages" (SC, 65). This level presupposes both Level I and Level II.

The arrows in the diagram shows a principle of presupposition. This means that the functioning and existence of a higher level depend on and build upon the lower levels. The arrow from I to II signifies that the Semiotic (Level II) presupposes the Primary Unconscious (Level I). This implies that the ways in which meanings are separated and articulated in Level II are conditioned by the fundamental systems and structures of intrinsic reference established in Level I. The arrow from II to III indicates that the Pragmatic and Subjective (Level III) presupposes the Semiotic (Level II). This means that the pragmatic and subjective actions and processes of Level III are built upon the semiotic concatenations and possibilities generated at Level II.

The diagram shows an arrow from Level I back to Level III. This arrow, along with the sequential presuppositions, completes a cyclical flow of influence and integration. Level III's function is to adjust the quantum configurations of all three types (non-separability, separation, and quantification). It achieves this by capitalizing the past potentialities of the Systems and Structures from Level I and the surplus values of possibility from the semiotic concatenations of Level II, bringing them into the present and activating them. This implies that pragmatic and subjective activity (Level III) doesn't just arise from the lower levels; it actively re-engages with and transforms the foundational intrinsic references (Level I) and semiotic possibilities (Level II). It creates a continuous feedback loop where action and experience re-shape the underlying conditions of the unconscious. We could say Level I is the past, Level II is the future, and Level III is the present.

Figure 2.4: Map of entities and tensors

Another one of the good ones.

The numbered entities (1-10) and major concepts within the diagram shows specific aspects and manifestations of the four functors:

• Entities of Intrinsic Reference: These are the fundamental, primary level of the unconscious, where intensive entities acquire a weight of intrinsic reference, a systemic or structural truth.

  1. Mc (Matters of content): This refers to Energetic-signaletic Flows (F), which are the raw material and signaletic movements of reality. They are given, continuous, actual, and real movements, encompassing everything from flows of lava and libido to money and tears. They constitute the primary matter of any process of subjectivation.

  2. Rm (Machinic rhizomes): This refers to Abstract machinic Phyla (Φ), which encompass evolutionary processes, Guattari's deterritorializing abstract machines, and the blueprints, plans, diagrams, rules, and cybernetic control mechanisms. Phyla are analogous to rhizomes, forming discontinuous networks of actual and possible elements, such as atoms, musical notes, or people.

  3. Me (Existential matrices): This refers to Existential Territories (T), which embody subjective identity, the sense of self, and existential apprehension. Territories are continuous movements that are giving, virtual, and concrete, defining affective relations and are considered Cutouts from the world.

  4. ∑U (Constellations of Universes): This refers to Incorporeal Universes (U), which consist of values, non-discursive references, and virtual possibilities. These Universes are seen as Constellations and are described as virtual and possible.

     • Codes and Systems are aligned with the left side (Given) of the diagram [Mc, Rm].

     • Ordination and Structures are aligned with the right side (Giving) of the diagram [Me, ∑U].

• Semiotic Entities: These are entities that bear a surplus value of possibility and are susceptible to actualization at a pragmatic level. Schizoanalysis works on these components of semiotization.

  5. Diag (Diagrams): These encompass an a-signifying mode of semiotization. Diagrams actively produce and create new entities and types of reality. They directly engage with matter and involve the conjunction of deterritorialized signs and objects.

  6. Pm (Machinic propositions): These emerge from machinic striation and embody the operational integration of heterogeneous points of view. They are described as an integral of refrains and embody the symmetric-fractal and deterritorialized representation of the ruptures of contingency.

  7. Ts (Sensible Territories): These are specific kinds of existential territories. They are cut-out from diverse flows by iconic components and are characterized as surfaces of sensation that develop into existential modules through semiotic dynamics.

  8. N (Noema): This entity is associated with incorporeal Universes (U). Noematic tensors, within this framework, virtualize noematic contents within Universes.

     • Expression in Figure 2.4 corresponds to Machinic Propositions (Pm) and Noema (N), mediated by Machinic tensors and Noematic tensors respectively. Machinic Propositions (Pm) are entities within the domain of Machinic Phyla, and Noema are entities within the domain of Incorporeal Universes (U).

     • Content in Figure 2.4 corresponds to Matter of Content (Mc) (within the domain of Energetic-signaletic Flows, F) and Sensible Territories (Ts) (within the domain of Existential Territories, T), mediated by Systemic tensors and Sensible tensors respectively.

• Entities of Pragmatic Manifestation: These are where interactions and taking consistency become pertinent, involving action and reaction.

  9. Se (Synapses of effect): These are synaptic tensors that relay surplus value of possibility of Universes/Territories and risks towards systemic sites. They are associated with a systemically open effect, indicative of systems far from equilibrium.

  10. Sa (Synapses of affect): These are also synaptic tensors that relay surplus value of possibility of Flows/Phyla and risks towards structural sites. They are associated with a structurally closed affect (ego, superego functions) or a structurally open affect (becoming-animal, becoming-cosmos).

The tensors are crucial, acting as multi-dimensional vectors that describe inter-entity relations and facilitate transformations across different levels of consistency.

• Systemic Tensors (1-2 E1): Presented by continuous lines between (Mc)F (1) and (Rm)Φ (2) on the diagram's left side. They are bijective couples and are established on the side of the Given. They articulate material and energetic Flows on abstract machinic rhizomes.

• Structural Tensors (3-4 E): By continuous lines between (Me)T (3) and (ΣU)U (4) on the diagram's right side. They are also bijective couples and are established on the side of the Giving. They crystallize heterogeneous incorporeal Universes.

• Sensible Tensors (1-7 "2): By projective vectors from Systems towards Structures (from F to T). They virtualize sensible contents within the domain of Territories. Discursivity passes from energetico-signaletic Complexions (F) to existential Cutouts (T), charged with possibility-potential and dependent on a duration without subject or object.

• Diagrammatic Tensors (3-5 "): Presented by projective vectors from Structures to Systems (from T to F). They actualize a diagrammatic Expression within the domain of Flows. Discursivity actualizes diagrammatic expression from existential Cutouts (T) to energetico-signaletic Complexions (F), charged with potential for possibilities and respecting physical laws of particle speeds.

• Noematic Tensors (2-4 E): These tensors are shown from (Rm)Φ (2) to (ΣU)U (4), and are responsible for virtualizing noematic contents within Universes.

• Machinic Tensors (42 E): These tensors are shown from (ΣU)U (4) to (Rm)Φ (2), and are responsible for actualizing abstract propositional expressions in rhizomic Phyla.

• Synaptic Tensors of Effect/Affect (9 Se, 10 Sa): These are crucial intermediaries. They transfer the surplus value of possibility from semiotic entities (Diagrams, Machinic propositions, Sensible territories, and Noemas) towards the entity sites polarized into Systems and Structures (Flows, Phyla, Territories, Universes).

The arrows and lines within the diagram illustrate the dynamic processes and interrelationships between entities, rather than static representations.

• Double-headed Arrows (Bijective Couples / Tensors of Intrinsic Reference): The continuous lines between (Mc)F (1) and (Rm)Φ (2), and between (Me)T (3) and (ΣU)U (4), show intrinsic reference or reciprocal presupposition.

• Dashed Lines (Axes of Deterritorialization and Discursivity): The diagram is divided by two intersecting dashed axes of deterritorialization and discursivity (See Figure 2.1):

  • Horizontal Axis (Discursivity/Detotalization): This axis (abscissae) divides the diagram into a Given side (left, associated with Codes and Systems, Energetic Discursivity) and a Giving side (right, associated with Ordination and Structures, Propositional Discursivity, and subjective processes of deterritorialization).

  • Vertical Axis (Deterritorialization): This axis (ordinates) divides the diagram into an objective domain (top, associated with Machinic Phyla and Universes) and a subjective domain (bottom, associated with Flows and Territories).

Figure 2.5: Intersection of the Given and the Giving

The diagram is composed of four circles, each being a conceptual field:

• Rsy (Systemic Referent of the Given): This circle is the Given, specifically as an intrinsic systemic Referent. The Given refers to what is presented or exists, and its systemic referent denotes a structured, inherent reality that is intra-coded and supported by its own consistency.

• C (Content): This circle is Content, which, alongside Expression, functions as a functive of Hjelmslev's semiotic function (or Solidarity). Content is a variable of the arrangement, able to engender a content-substance and content-form.

• E (Expression): This circle is Expression, also a functive of Hjelmslev's semiotic function (or Solidarity). Expression is a variable of the arrangement, capable of engendering expression-substance and expression-form.

• Rst (Structural Referent of the Giving): This circle is the Giving, specifically as an intrinsic structural Referent. The Giving is what confers consistency onto expression and acts as a respondent of expression, linked to Universes.

The diagram shows interconnections between these circles, highlighting reciprocal relationships and the formation of the semiotic function. The double-headed arrows generally present in the diagram between these categories signify a mutual presupposition and continuous interaction.

• At point F., the Systemic Referent of the Given (Rsy) intersects with Content (C). This intersection implies a direct, reciprocal relationship where the inherent reality of the Given (Rsy) is engaged with and shaped by its Content (C), and vice-versa. The reciprocal connection between Rsy and C signifies that the Given is not a passive entity but is intrinsically linked to and articulated through its Content. This interaction is a fundamental part of the semiotic function.

• At point T., Expression (E) intersects with the Structural Referent of the Giving (Rst). This intersection points to a dynamic, reciprocal relationship where the Giving (Rst), which provides consistency to expression, is directly intertwined with and actualized through Expression (E).

This diagram fundamentally illustrates the concept of semiotic function or Solidarity as described by Hjelmslev, where Content (C) and Expression (E) are not to be opposed but are interdependent functives. Guattari utilizes this model to move beyond Saussurean linguistics, where signifier and signified—often conflated with expression and content—are seen as distinct. thus, signifying a dynamic, non-hierarchical process where existence (the Given and Giving) and semiotic articulation (Content and Expression) are in constant reciprocal presupposition and interaction.

I’m pretty sure that I don’t have to explain the tables…

Chapter Discussion

Guattari begins by examining the disabling effects of importing thermodynamic notions into the human and social sciences. He critiques the concept of an entropic Superego which forces the interpretation of all movement, transformation, or experiencable alteration through a singular energy economy, founded on the two principles of thermodynamics. This approach postulates a radical separation between the production of subjectivity and semiotic effectiveness, reducing them to a "cult of information or of the signifier" (SC, 49). This, in turn, leads to an impasse in understanding the dimensions of singularity, irreversibility, and bifurcation within cognitive Assemblages and the interdependence between systemic givens and expressive structures. Guattari argues that such monotheisms of energy are favoured by Integrated World Capitalism, which seeks to normalize and control modes of expression and valorization.

Guattari acknowledges Freud's initial attempt to establish a scientific foundation for psychology by introducing abstract quantities, leading to a deterritorialization of the psyche onto an unconscious scene unlocalizable in ordinary phenomenological coordinates.3 Freud's theoretical edifices interlaced energy components and mental representation. Freud's early model proposed the unconscious as a dynamic of repressed representations linked to a unique drive. This drive had a somatic level (biochemical energy from erogenous zones, aiming for constancy/homeostasis) and a psychic level (articulating language, object representations, phantasms, inter-subjective relations). Freud aimed to create "passages between the sexual libido and effects of sense" (SC, 50). With Freud's shift to the Id-Ego-Superego triad, energy metaphors became more anthropomorphic. Lacan later sought the "quasi-total 'liquidation'" of libidinal energy, reducing it to the signifying chain and denying its character as a flow. However, Lacan still conceded a "sacrosanct energy status" to this "organ of the incorporeal," though he described its quantification as useless.

Instead of an economy of drive quantities, schizoanalysis proposes a transformational modeling where "Territories of the Self, Universes of alterity, Complexions of material Flows, machines of desire, semiotic, iconic Assemblages, Assemblages of intellection, etc. can engender one another" (SC, 52). This moves from the form of instances to the "transmutations, the transductions of their substance".4 Its psychophysics refuses a univocal energetic and material substrate, instead working with transformations "straddling the most heterogeneous of domains conceivable". This involves transversality between Flows, Phyla, Territories, and Incorporeal Universes (escaping the coordinates of the first three). The mapping of Effects and Affects uses a quantification different from traditional physics and logic. It focuses on arrangements that can undergo radical transformations, schizzes or relinkages, rather than univocally characterized sets. The semiotics here is an "encyclopedic science of the phenomena of expression," a "phaneroscopy," (SC, 53) drawing categories from Hjelmslev's glossematics.

Guattari's model of the Unconscious is based on three types of energetico-semiotic quantum configurations:

• Non-separability: Refers to synchronic correlations at a distance that ensure compossibility between diverse entity states, independent of semiotic localization. These Tensors of non-separability are inscribed on the general Plane of Consistency along an axis of deterritorialization [Figure 2.1]. Refers to Level I of the unconscious

• Separation: Describes diachronic inter-entitarian transformations that establish semiotization components, indicating the propensity of entities to "exit, discursivize, delocalize or detotalize themselves" (SC, 55). It introduces dimensions of time and becoming and is inscribed on the Plane of Consistency by vectorized tensors along an axis of discursivity or detotalization [Figure 2.1]. There are two sorts:

  • Semiotic tensors: Engender "sites of sense entities" (Territories, Diagrams, Noemas, machinic Propositions).

  • Tensors of surplus value of the possible: Relay these sense entities toward pragmatic Effects and subjective Affects. [Figure 2.4]

• Quantification: Inter-entitarian relations established between non-separability and separation. It's the establishment of entity sites where energetic instances—thermodynamic, physico-chemical, biological—can be grafted. Interactions become pertinent only when Assemblages of enunciation are constructed to produce quantification, acting as a sectorial 'point of view' or energy charge. Quantification retroactively and prospectively projects quanta of deterritorialization and discursivity onto the Plane of Consistency.

Furthermore, themodel of the Unconscious faces contradictory demands: autonomous levels whose entities constantly presuppose and transform one another. To manage this, three constraints are imposed:

• Principle of Exclusion: Forbids direct tensorial relations between F and U, and between T and Φ.

• Principle of Dyschrony: Differentiates tensorial relations by axes of deterritorialization (bijective-synchronic) or discursivity (projective-diachronic), defining Level I—intrinsic Reference—and Level II—Semiotic—of the Unconscious.

• Principle of Presupposition: Level I (intrinsic Reference) does not presuppose other levels. Level II (Semiotic) presupposes Level I. Level III (Pragmatic and Subjective) presupposes Levels I and II [Figure 2.3].

The segmentation of the Plane of Consistency—from which the four functors emanate—rests on two arguments:

• For discursivity: An ontological argument: "there is the Given, thus there is the Giving" (SC, 58). This leads to:

  • Unary values: Corresponding to the Giving, introducing discontinuity and ontological appropriation—Cutout for T, Constellation for U—, operating by an economy of mixture.

  • Plural values: Corresponding to the Given, introducing continuity and ontological composition—Complexion for F, Rhizome for Φ—, operating by an economy of composition.

• For deterritorialization: A cosmological argument postulating two domains of intrinsic reference without immediate intersection: a systemic Referent for the Given (Rsy) and a structural Referent for the Giving (Rst) [Figure 2.5]. The axis is divided into:

  • Finite values: For reversible deterritorialization around an equilibrium point.

  • Infinite values: For irreversible deterritorialization drifting outside equilibrium.

Finally, the synapses of the Persistence and Transistence of the tertiary unconscious can be bivalent (conjunction of two afferent tensors, leading to extrinsic coding Effects (FΦ) or extrinsic ordering Affects (TU)). Trivalent synapses involve two afferent and one efferent synaptic tensor, leading to systemically closed/open Effects (F, Φ) or structurally closed/open Affects (T, U). And, synapses Sa and Se are coupled: persistence (Se -> Sa) virtualizes an Affect, and transistence (Sa -> Se) actualizes an Effect. This process of "taking consistency" suggests a "dream logic" or "logic of archaic intensities" (SC, 67).

I will be using the citation format of (SC, [page number]) to signify a direct textual citation of the book from the Bloomsbury edition from 2013, translated by Andrew Goffey. Further sources that will be cited in-text will follow the format of ([Title Initials], [page number]) with a footnote—when used for the first time—utilizing APA citation format.

Let the reader be warned that this book is one of the most complex philosophical treatises ever written, utilizing diagrammatizations as mirrors of the textual arguments brought forth. But, we’ll get through this, together. To follow the experimental nature of Schizoanalytic Cartographies, our method of study will consist of discussing the diagrammatizations of each chapter with the written arguments, completely disregarding linearity, that is to say we’ll give presentational primacy to the diagrams.

Goffey’s Introduction: The Artifice of Jargon. On Guattari’s Style

Before we formally start, let’s look into Goffey’s introduction to Schizoanalytic Cartographies as it discusses Guattari’s style, which is something every study of Guattari should start with, as it is his, perhaps, the most uncompromising aspect of this entire enterprise.

Schizoanalytic Cartographies is noted by Goffey as one of the last major French "theory" books to be translated into English, and it was not a significant success upon its initial French publication. Despite Gilles Deleuze's later tribute to its "marvellous four-headed system," it initially "fell deadborn from the press," akin to David Hume's Treatise of Human Nature. This lack of immediate resonance means the text retains much of its "singular experimental charge" for new readers, unburdened by extensive secondary criticism (SC, xv). Guattari's writing is characterized by a "peculiar –and peculiarly inventive– jargon," which is inseparable from his mode of theorizing. His vocabulary is highly idiosyncratic, ranging from "unusual" to "nigh on untranslatable" terms like "existential 'cutouts'," "Constellations of Universes of reference," "déclinaisons logicielles," and "ritornellization" (SC, xvi).

Goffey draws a distinction between Guattari's and Deleuze's writing styles, citing Deleuze's own comments. Deleuze described his own writing as flying off "in all directions" while simultaneously closing in on itself "like an egg" (SC, xvii). In contrast, Guattari's writing has a "schizoid flow carrying along all sorts of things," often bearing marks of its circumstantial origin and a "partially unfinished quality". Guattari was not a "professional philosopher" and playfully referred to himself as the "Douanier Rousseau of philosophy". This non-professional status allowed him to avoid "thinking in grooves" and to challenge conventional judgments about status and ability, as "jargons don't have authors".

Guattari's style is deeply connected to his pragmatic understanding of concepts, emphasizing their transformational role. He believed that theory gains its "greatest contact with the real through its very artifice" (SC, xxi). His "insouciance" regarding linguistic norms is a deliberate choice to prioritize actions that generate "machinic sense 'flush with the real'" over conventional clarity or consensus. His "jargon machine" takes off with terms like "power-signs, Plane of Consistency, machinic Propositions, micro-redundancies, anti-black hole," which are "prospective, prospecting devices" operating within an "experimental understanding of theory". His style, with its heterogenesis, aims to explore language "far from equilibrium" and generate "non-linguistic visions and auditions" (SC, xxii). Goffey states that translating Guattari presents significant challenges due to his "untranslatable idiosyncrasies of language use," which provide "indices of a writer's (or indeed, a culture's) movements of thought" (SC, xvi). Translators thus often face the task of re-establishing stabilized meaning where the original is more decoded, abrupt or jarring.

Therefore, Guattari’s work often requires an experimental use rather than a conventional scholarly analysis. As Tom Roberts rightfully says, this means readers are tasked with "maintaining an unfamiliar machine" and getting the "Guattarian machine up and running" (WG, 45)1.

Preliminary

Now, let’s see Guattari own preliminary.

Guattari starts by stating that the current era is characterized by a "curious mixture of enrichment and impoverishment" that manifests in several paradoxical ways (SC, 1). This blend affects various aspects of human existence, from access to knowledge and cultural dynamics to technological advancement and moral climate. One prominent aspect of this mixture is an apparent democratization of access to data and knowledge, which is paradoxically coupled with a segregative closing down of the means for their elaboration. While there is a growing universality of scientific signifiers and advancements in scholarship are shared globally, leading to a conceivable single super-information-machine accessible to vast numbers of researchers, this widespread access does not equate to a democratization of the means of production and elaboration of knowledge. Information technology is often controlled by states, and there's a tendency for power to disseminate secrets to discourage amateur involvement, prioritizing a hierarchy of differential growth over craftsmen's secrets. Capitalist systems, through scientific axtiomatization, limit knowledge politics in favor of a politics of flow. Elites possess the cultural capital and legitimate decision-making power, while subjugated classes are largely left behind. The mass media contributes to a desingularizing and infantilizing effect, and Integrated World Capitalism (IWC) aims to normalize and instrumentalize all modes of expression and valorization for its own benefit.

Additionally, there is a multiplication of anthropological perspectives and a global stirring up of cultures, occurring simultaneously with a growth in particularisms and racisms. Globalization involves extreme deterritorializations, disrupting existing social arrangements, and allowing for the emergence of new transcultural, transnational, and transversal value systems and earths. Unprecedented arrangements are forming where plants, animals, humans, and machines interact. However, this global stirring and universality of cultural contact frequently correlates with a heightened need for national and regional distinctness. Recourse to archaisms and traditional references can become a hallmark of racism, especially when political failures hinder the development of new modes of subjectification for a truly transcultural society. Figures like Donald Trump and the persistence of child labor are cited as examples of social ecological disasters arising from these dynamics (Guattari indeed had discussed the disaster that Trump already was in the 90s)2. Nationalist and fundamentalist movements—while resisting standardized capitalist subjectivities—can also represent socially conservative and even xenophobic returns to tradition. This results in a blur of languages and a mixed-up history, rather than a coherent system. Moreover, the expansion of capitalist influence has led to a narrowing of perspectives, fostering linguistic, regional, and ethnic issues rather than broad territorial entities.

Finally, an immense extension of techno-scientific and aesthetic fields of investigation is unfolding within a moral context of greyness and disenchantment. There has been a fantastic expansion of machinic phylums and continuous production of new artistic, scientific, and technical possibilities. Advances in information processing, telematics, robotics, and genetic engineering have brought forth immense potential. Computer-aided design can create unprecedented "plastic-Universes" and solve previously unimaginable mathematical problems. Aesthetic-machines are presented as advanced models for creating blocs of sensation and resisting the steamroller of capitalistic subjectivity, offering a paradigm for liberation and leading to the "creation and composition of mutant percepts and affects" (CEAP, 91)3. However, despite this technological and creative explosion, there's a pervasive sense of moral greyness and disenchantment. Human modes of life are deteriorating, with kinship networks reducing, domestic life being "poisoned by the gangrene of mass-media consumption," and neighborhood relations being minimal (TE, 1). The contemporary world struggles to absorb techno-scientific mutations in a way compatible with humanity's interests, seemingly locked in a race towards ruin. Traditional human territorialities are exploding, and the young are often disconnected from ancestral lands, living under precarious representations and programmed socio-professional trajectories.

Guattari now discusses the three series of voices/pathways,which serves to understand the fundamental ways in which apparatuses produce voices/pathways that form the basis of subjectification processes in contemporary Western societies. The three series of voices/pathways are distinguished as follows:

1. Voices/pathways of power: These circumscribe and circumvent human groups from the outside. This can occur either through direct coercion and a panoptic hold on bodies, or by the seizure of the soul through the imaginary.

2. Voices/pathways of knowledge: These are articulated to techno-scientific and economic pragmatics from inside subjectivity.

3. Voices/pathways of self-reference: These develop a processual subjectivity that founds its own coordinates and is self-consistent. This pathway establishes itself transversally to social and mental stratifications. It is described as both the most singular and contingent—anchoring human realities in finitude—and the most universal—richest in virtual Universes and lines of processuality—, opening the horizon of a processuality as the continuous emergence of creativity, akin to the Body without Organs.

Before going on the different instantiations of voices/pathways in the medieval, industrial and post-industrial social formations, Guattari writes how, in the schizoanalytic view, understanding the subject means moving beyond traditional methods like dialectics or structuralism, as well as Freudian and Lacanian psychoanalysis. These older approaches are critiqued for their reductionism, emphasis on language, and reliance on fixed, universal models of the psyche and subjectivity, such as the Oedipal triangle or the signifier. Instead, schizoanalysis is defined as metamodeling and cartography, a process of actively creating and producing the unconscious and subjectivity. It uses all modelling systems—whether theoretical, experiential, or aesthetic—to map out an individual's specific, temporary existential territories of feelings, thoughts, and experiences. These territories are unique, idiosyncratic, sensible, and finite worlds, encompassing cognitive, affective, and aesthetic dimensions. The goal is to engender these territories and open up possibilities for their transformation. Subjectivity isn't based on a fixed reality or classical logic; it's a process of singularization that is fundamentally open and auto-producing. It is built from traits of singularization—unique, event-like moments or existential stamps that provide a local persistence to existence. These traits simultaneously create a transistency or transversalist consistency, allowing for connections and movements across diverse domains. This dynamic and heterogeneous process cannot be fully grasped by conventional rational knowledge, which schizoanalysis argue ignores these virtual, uncertain, and vague aspects of being. Traditional scientific paradigms are seen as limited because they bracket off the essential dimensions of subjectivity, such as unique modes of valorization and singular processes, in their pursuit of universal laws and objective descriptions. They tend to simplify the complex, reducing the richness and heterogeneity of subjective experiences to a "generalized equivalence of affects and representations," (SC, 45) and often remain fixated on the past rather than embracing future possibilities. Schizoanalysis, in contrast, aligns itself with ethico-aesthetic paradigms, prioritizing creation and affect over strict scientific objectivity.

Guattari now distinguishes three zones of historical fracture or fundamental capitalistic components that have emerged over the last millennium, each marked by unique conceptions of power, knowledge, and subjectivity:

• The Age of European Christianity:

This era, arising from the ruins of the Late Roman and Carolingian Empires, established a new form of subjectivity. It was characterized by a double articulation: relatively autonomous territorial entities—feudal segmentarity—and the deterritorialized power of the Catholic Church, symbolized by a deterritorialized Christ. Unlike previous imperial powers, the central power was not directly totalitarian over basic territories and subjectivity, which allowed for a "schismatic vitality" (SC, 7) in religious thought and an explosion of aesthetic creativity. Guattari enumerates factors like a flexible monotheism, the development of religious institutions—parish schools, guilds, monasteries as "data banks"—, early machinism—iron, mills—and subjective integration mechanisms like clocks and written religious music. This age fostered early commercial and technological takeoffs while maintaining a balance among aristocratic, religious, and peasant subjectification.

• The Age of the Capitalistic Deterritorialization of Knowledges and Techniques:

Beginning in the 18th century, this age marked a growing imbalance between humanity and machines, leading to the disruption of established social territorialities and bodily reference points. Capital became the central semiotic mode of reterritorialization, establishing generalized equivalence for all forms of valorization, including economic and technological knowledge. This system maintained consistency through "perpetual racing ahead" (SC, 9) and constant relaunching of stakes, sweeping away existing cultures and territorialities. Despite referencing universalizing perspectives, it paradoxically led to reterritorializations based on nationalism, class, racism, and paternalism. The Age of Enlightenment was accompanied by a "hopeless fetishisation of profit" and an "irrational and archaicizing hold over unconscious subjectivity," (SC, 10-11) manifesting in hyper-individualized culpabilization, akin to a Kafkaesque universe. Consistency factors included the printed text, steam machines, steel, manipulation of time—chronometry[KANT], monetary credit—, and the biological revolution.

• The Age of Planetary Computerization:

This contemporary age, characterized by computational and telematic revolutions, introduces the potential for a creative and singularizing processuality to become a new basic reference, moving towards a postmedia era. However, Guattari notes that these immense potentials have so far often reinforced existing alienation systems, leading to oppressive mass-mediatization and "infantilizing consensual politics" (SC, 12). This era is fundamentally linked to Integrated World Capitalism (IWC), which increasingly shifts its power from producing goods and services to producing signs, syntax, and subjectivity, particularly through media, advertising, and opinion polls. It involves a new form of machinic enslavement, where surplus value becomes machinic, and society itself becomes the framework for capital's operations, aiming to normalize and control modes of expression and valorization. Its consistency factors include media, telecommunications, custom-made materials—plastic—, microprocessors altering temporality, and biological engineering.

Guattari's triad in this preliminary thus serves as a speculative cartography to understand contemporary mutations in subjectivity, particularly the rise of neoconservative ideologies and other archaisms, which often arise as reactions to capitalism's deterritorializing effects and the destruction of collective identities. He emphasizes the need to rethink these three interwoven voices/pathways to foster new social and aesthetic practices.

But before we start with the first chapter, I believe it is important to discuss post-media, as it is the other face of Guattari’s late work, and provides a lot of aesthetico-political context for the conceptualizations in Schizoanalytic Cartographies.

Guattari's concept of the post-media era represents a vision for a transformed media landscape that moves beyond the homogenizing and alienating effects of mass media, aiming instead for the singularization of subjectivity and the production of new modes of collective existence. This concept is linked with Schizoanalytic Cartographies, which provides the comprehensive conceptual framework for understanding how such a transformation might occur. Guattari's reflections on the post-media era arose from his critique of the "mass-mediatic pollution of collective subjectivity" and the "desingularizing and infantilizing leveling of the capitalist production of signifiers" (SE, 119)4, which we’ve also just seen now in the preliminary. He saw the prevailing media environment as contributing to an impoverishment of the very idea of subjectivity and a growing passivity. For Guattari, this was part of Integrated World Capitalism, which shifts productive structures from goods and services to signs and subjectivity, exercised through media, surveys, and advertising. Despite this critique, Guattari did not advocate for a rejection of technology but rather its reappropriation and transformation. He believed that new developments in media, such as the junction of television, telematics, and informatics, harbored the potential for deterritorializations that could lead to a "post-media era of collective-individual reappropriation and an interactive use of machines of information, communication, intelligence, art and culture" (SS, 279)5.

Thus we can say that, Schizoanalytic Cartographies provides the sophisticated theoretical apparatus—the meta-model of the four functors and the emphasis on constructing new existential territories and universes of reference—that underpins Guattari's vision for a post-media world. It's in this work that he painstakingly details how subjectivity can be resingularized and how new collective arrangements of enunciation can be built to counter the homogenizing forces of IWC and current media practices.

1. Analytic Cartographies

The four diagrams from Analytic Cartographies (Figure 1.1, Figure 1.2, Figure 1.3, and Figure 1.4) are the central construction points of Guattari's exploration of subjectivity and its production, fundamentally organized around four ontological functors: Flows (F), machinic Phyla (Φ), existential Territories (T), and incorporeal Universes (U). These functors are understood as meta-modelling categories that are not fixed identities but rather processual and constantly changing their state and status based on their overall arrangement.

Figure 1.1: Discursivity and Deterritorialization

This diagram (Figure 1.1) illustrates Guattari's framework for mapping the configurations of subjectivity, desire, drive energy, and modalities of discourse and consciousness. It deploys four domains (F, Φ, T, U) based on two sets of coordinates: This diagram plots the four ontological functors (F, Φ, T, U) across two axes: Discursivity (horizontal) and Deterritorialization (vertical). The four functors are positioned within these axes:

• F (Flows): Material and signaletic flows, such as libido, capital, or work. Flows are considered actual and real. They possess a high degree of consistency and are understood as continuous. They are characterized by energetic-spatio-temporal discursivity. Flows are often described as having an endo-consistency—meaning without an outside—and are arranged in Complexions.

• Φ (Machinic Phyla): Abstract machinic phyla, which are relatable sets of existing diagrammatic connections, blueprints, plans, or rules. Phyla are actual and possible. They have a low degree of consistency and are considered discontinuous. They are characterized by abstract machinic discursivity. Phyla are exo-consistent—open to outside influence—and are organized into Rhizomes. They emerge through the fractalization of Flows, breaking up continuous volumes into measurable networks.

• T (Existential Territories): Subjective identity, the sense of self, and existential apprehension. Territories are virtual and real. They possess a high degree of consistency and are continuous. They are endo-consistent and are structured as Cutouts. They represent a "lived and lived-in space" where an individual "feels at home" (SE, 60).

• U (Incorporeal Universes): Values, non-discursive references, and virtual possibilities. Universes are virtual and possible. They have a low degree of consistency and are discontinuous. They "escape the energetic, legal, evolutionary, and existential coordinates of the three preceding domains" (GDT, 99)6. They are exo-consistent and are organized into Constellations.

Figure 1.2: The matrix of cross-relations of the four categories

This matrix specifically maps the four functors against the Actual/Virtual and Real/Possible axes. It visually demonstrates how each functor occupies a unique position based on these cross-relations:

• F (Flows) are positioned as Actual Real

• Φ (Machinic Phyla) are positioned as Actual Possibility

• T (Existential Territories) are positioned as Virtual Real

• U (Incorporeal Universes) are positioned as Virtual Possibility

The figure highlights Guattari's argument that the "reality of the possible always has primacy over the possibility of the real" (SC, 28). This implies a dynamic where creative possibilities (Φ, U) can transform existing realities (F, T), challenging fixed, static conceptions of being.

Figure 1.3: The integration of the four categories

This figure illustrates the conceptual relationship where the Phyla envelop and subsume Flows, and Universes envelop and subsume Territories. It signifies that the more deterritorialized categories (Φ and U) act as integrals of the more territorialized ones (F and T). This suggests a hierarchical, yet transformative, relationship where the abstract and possible (Phyla, Universes) offer a broader, more encompassing perspective or potentiality for the concrete and real (Flows, Territories).

Figure 1.4: The optional matter libido-unconscious

This is a crucial figure for understanding Guattari's critique and reformulation of the psychoanalytic unconscious. It maps the concepts of libido and the unconscious onto the four-functor grid, presenting a clear micropolitical choice between two paths:

• The Reterritorialized Option (bottom of the graph):

This path represents the traditional psychoanalytic approach. Here, the libido is stratified into psychogenetic stages and dualisms—Eros/Thanatos—of Flows. The unconscious "takes refuge in the Territories of the repressed" (GAI, 205)7. Guattari argues that this option, favored by much Freudian and Lacanian psychoanalysis, leads to homeostasis and neurotic syndromes. He contends that Freud's followers ultimately reified the psyche's singularities into generic functions, reducing complexity. This represents a dictatorial conception of the unconscious leading to "impasses, blockages, incipient taproots" (ATP, 13)8.

• The Deterritorialized Option (top of the graph):

This path represents Guattari's schizoanalytic alternative, which aims to open up new possibilities for the libido and the unconscious. When the libido is located in the Phyla, it becomes a process-related energy that pushes dynamic relations into far-from-equilibrium conditions necessary for transformation and creation. This corresponds to the actual possible, discursive yet deterritorialized realm. When the unconscious is elevated to the incorporeal Universes of reference, it is understood as "the set of lines of alterity, virtual possibilities, and unheard-of becomings" (SC, 30). This challenges the idea of the unconscious being structured like a language or fixed by archetypes and mathemes. This option highlights how schizoanalysis allows for processes of singularization and the production of new subjectivities, emphasizing the heterogeneity of its components and its multiform productivity. It seeks to render operative/existentialistic desire and affects, rather than merely interpreting them.

Chapter Discussion

Now that we’ve presented the diagrams and explained them, let’s discuss some of the points in the first chapter that we’ve skipped over.

Guattari starts the chapter by discussing how schizoanalysis is conceived as a meta-model or übermodel designed to decipher and map various modelling systems across diverse domains, rather than being a general, foundational model itself, for fields like biology, cybernetics, ethnography, and psychiatry. This meta-modeling approach implies a constant "displacement of the analytic problematic," (SC, 17) moving away from preformed subjective structures towards Assemblages of enunciation that forge new interpretive coordinates. Guattari notes that any subjectivity is, in a sense, an activity of meta-modeling, involving the "transfer of modelling" and "transversal passages between problems of different kinds". Instead of reducing subjectivity to drives or affects, it focuses on the "impact of Assemblages of enunciation on semiotic and subjective productions" (SC, 18).

An assemblage of enunciation is defined as a collection of heterogeneous components that create subjectivations and engage in various semiotic and machinic processes of enunciation. These components are initially indifferent, meaning they can be material and/or semiotic, individual and/or collective, actively machinic and/or passively fluctuating. This concept moves beyond the thinking monad of the individual mind and aims to "de-centre the subject in favour of the social as such" (GBD, 54)9. Schizoanalysis is interested in "Assemblages that promote the concatenation of affects of sense and pragmatic effects" (SC, 19).

Unlike classical psychoanalysis, schizoanalysis does not adhere to fixed rules or normalized protocols. It embraces an anti-rule rule, demanding a constant questioning and re-evaluation of its own analytical tools and frameworks based on their feedback effects. This aligns with its pragmatic and experimental nature, prioritizing experimentation over hermeneutics. Guattari suggests that the effect of analysis is as an a-signifying mutation of a 'Universe-context', which is a Constellation of registers. Furthermore, schizoanalysis views a totalizing consciousness as a "founding myth of capitalist subjectivity" (SC, 26). Instead, it posits the existence of diversified processes of conscientialization that result from the deterritorialization of existential Territories. It recognizes that conscious and unconscious states are relative to the specific arrangements that enable their "composite assembly, superpositions, slidings and disjunctions" (SC, 23). The approach emphasizes that even unconscious processes can adapt to the existence of consciential components, rejecting a rigid, binary opposition between conscious and unconscious.

Guattari now critiques psychoanalysis for its attempts to mimic science, which is seen as a "scientistic mythology of shrinks" (SC, 33). This mimicry is categorized into three problematic ways:

• Asceticism (Trying to be an Exact Science): This pathway involves specialists striving to adopt the position of exact scientists, seeking perfectly defined objects and endeavoring to establish correlations and laws, as exemplified by psychophysics and behaviorism in the late 19th and early 20th centuries. However, this approach quickly led to disillusionment because it proved impossible to invent algorithms coherent enough for continuous scientific development. Guattari argues that this viewpoint is "fundamentally illusory and pernicious" (SC, 34) because scientific methods, by design, systematically bracket off the essential dimensions of subjectivity, such as enunciation, idiosyncratic modes of valorization, and irreducibly singular processes, which are central to understanding the psyche. Guattari's schizoanalysis, in contrast, aims to discard all scientific references in its mapping of subjectivity to avoid reductionism.

• Hysterical Identification ("Bluffing" at Scientific Methods): This refers to a "mimetic appropriation of scientificity" (SC, 33) that disregards reproducible experimental procedures or testable and falsifiable theories. Psychoanalysis is presented as the most significant example of this scientific bluffing. As it became institutionalized, psychoanalysis began to assert that its doctrinal claims could only be understood by a caste of initiates who had undergone a didactic cure, effectively detaching itself from common-sense scientificity.

• Propping (Using Scientific Concepts Metaphorically): This involves the lateral use of science where scientific statements or concepts are employed metaphorically or retain an exteriority to the discipline being considered, offering no real substantial help. Examples include Freud's seriously revised reference to Carnot’s Principle to justify his drive dualism of Eros and Thanatos, or Lacanian theorists plundering structural linguistics or mathematical topology for conceptual support. For Guattari, such metaphorical uses are ultimately unhelpful and should be avoided in schizoanalytic cartographies.

Guattari views postmodernism as a form of capitulation and a regrettable conclusion to the bankruptcy of a certain conception of progress and modernity. Guattari contends that intellectual and artistic milieus, especially those embracing postmodernism, have given up on "collective projectuality of any scale" (SC, 39). Instead, they advocate for a "tend to our garden" mentality, focusing on individual, ephemeral vogues and trends rather than concerted social action or large-scale societal change. Postmodernism is described as a "final twitch of modernism," not genuinely distinguishable from the "formalist and reductionist abuses" it reacts against (SC, 37). Guattari states that postmodern philosophers reduce the socius to "facts of language" and "binarisable, 'digitisable' signifying chains," continuing a very modernist tradition of structuralism influenced by early cybernetics and information theory (SC, 39). This philosophical stance is dismissed as not one, but merely an "ambient state of mind" that derives its "truths from the trends of the day" and lacks "serious speculative support" (SC, 40).

Guattari furthermore discusses that all forms of human thought and experience, including scientific paradigms and logical-mathematical rationality, arise from a shared fabric of underlying components. These shared components include: Perceptual schemes, affects, imaginary activities, and representations. The crucial difference, according to Guattari, lies in how these components are assembled and the intensity with which they operate within different arrangements. He asserts that the "subjectivity at work within the most elaborate scientific paradigms still functions in part in terms of animism and transcendental abstractionism" (SC, 35). All scientific approaches establish themselves on this same fabric, with only the specific arrangements and the intensity of the components varying. From this perspective, Guattari critiques the traditional scientific ideal that often prevails in psy- domains, which he views as a collective Superego. Instead, he advocates for an approach to schizoanalysis that finds its foundation in aesthetic disciplines, drawing on their modes of valorization, types of truth, and logic. He even expresses an openness to the "magic dimension" as a valid way of mapping "psychic Assemblages," (SC, 32) contrasting it with what he sees as sterile and reductionist scientific approaches.

To move beyond traditional, reductionist frameworks, Guattari introduces the concept of ontological pragmatics. This is a novel approach that departs from traditional logic and representation, which he believes often fall short in accounting for complex subjective formations. The primary purpose of ontological pragmatics is to perform a function of existentialization, which involves deploying and putting into intensive concatenation specific existential qualities. This means giving things a singular, unique existence that is not reducible to pre-established categories or universal principles, setting into existence new realities, rather than merely describing or interpreting pre-existing ones. This practice is akin to artistic creation, which Guattari sees as a model for generating new forms of existence. Utilizing intensive indices and diagrammatic operators that are not universal distinguishes schizoanalytic concepts like existential singularities or points of bifurcation from traditional psychoanalytic partial-objects or objet petit a, which he views as fixed and universal. Instead, these are described as "crystals of singularization, points of bifurcation outside the dominant coordinates, on the basis of which mutant universes of reference can spring up" (SC, 36). The function of existentialization operates with optional matters of subjectivity, which are domains of decisionality enacted by collective and/or individual Assemblages of enunciation. Unlike signaletic matters that are tied to extrinsic coordinates, optional matters engage "traits of existential intensities" that resist the axioms of set theories and are "ontologically ambiguous" (SC, 40). This pragmatics of setting into existence is not limited to language but extends to all other semiotic components and encoding procedures, whether natural or machinic.

Guattari ends the chapter with a critique of psychoanalysis that mirrors the arguments in Anti-Oedipus.10 Psychoanalysis and monotheistic religions are described as sharing the goal of gripping subjectivity in ethical axes that conform to the requirements of capitalistic logics. These capitalistic logics involve systems of judgment based on generalized equivalence, the suppression of animist intensities, the conversion of singular trajectories, and the reiteration and circulation of formal entities on deterritorialized markets (economic, moral, artistic). While religions act through direct suggestion and the imprint of standardized representations, psychoanalysis initially allows for individual expression but then takes it over to submit it to stereotypical and even more tyrannical forms. It is seen as a "religion in the second degree," (SC, 43) a religion of pure form where sacred texts (Freud's "Old Testament," Lacan's "New Testament") serve to fix an extrinsic armature to ritual practices largely emptied of content. The "original and insidious character" of psychoanalysis lies in its ability to conduct a "minimal lifting of the constraints" on discourse, creating the illusion that singularities of desire, especially in sexuality, might gain expression. However, this "enunciative license" is rarely fully utilized, as "any slight impulse to free up the ‘analysand’ running into the apparatus of the cure" is swiftly channeled by "pitiless semiotic remote control" (SC, 44). This process reinforces the patient's guilt and alienation, leading to a "masochistic passion on an inglorious Way of the Cross". The "gentle alienation and exploitation" (SC, 45) that results from this process is tied to the dynamic of deterritorialization and reterritorialization. Capitalist subjectivity is constantly pulled between being expelled from its native lands and undergoing an existential reterritorialization that is deeply intertwined with the system's functionality. Schizoanalysis thus redefines psychoanalysis as an "activity for the meta-modelling of pragmatic models of submission to the modern systems of ‘gentle’ alienation and and exploitation". This means psychoanalysis, particularly through its promotion of the Oedipus complex, functions to integrate individuals into the existing capitalist system and its values, ensuring their docility and conformity. It is seen as a means to cause beliefs to survive even after repudiation and to reconstitute a private territory for individuals.

“I don't wanna lose control but
I can't cramp my space to grow”

-Stonefruit, Armand Hammer

I am part of a reading group for Reza Negarestani’s Intelligence and Spirit, and these are my notes from the last chapter.

For citations of Intelligence and Spirit, the format will be (IS, x), therein x is equal to the page in which the cited text can be in the Urbanomic edition of the book. For other books, the specific edition and book will be noted down in a footnote. I’ve also taken from the various lectures given by Reza in The New Centre Research & Practice.

Diagrammatization

Here is a simplified version of the diagram

0. The Program of Intelligence

Now that we’ve gone through our thought experiment, Reza outlines the central thesis that philosophy, at its deepest level, is a program. It is understood as a collection of action-principles and practices-or-operations that involve realizabilities, which are defined as what can possibly be brought about by specific categories of properties or forms. Instead of asking "What is philosophy trying to say, what does it really mean, what is its application, does it have any relevance?" (IS, 407) this programmatic approach suggests asking "What sort of program is philosophy, how does it function, what are its operational effects, what realizabilities, specific to which forms, does it elaborate, and finally, as a program, what kinds of experimentation does it involve?"—essentially what we have here, is a functionalist definition of philosophy. Also, Reza frames Plato’s philosophy as a rebellious and "sacrilegious" endeavor that "topples the given order of things" (IS, 407), which we’ll unfold below.

According to Negarestani, philosophy begins with the universal thesis that all minds are equal, provided they satisfy the basic conditions of possibility for having mind. This equality is not inherent but is a task to be achieved through ongoing struggle against exploitation, by elaborating the fundamental idea that thinking is possible. In this context, philosophy is conceptualized as a mêtis, or a craft, that aims to cultivate intelligence and expand the horizon of what is intelligible. This crafting of intelligence is not limited to Homo sapiens, extending to anything that can meet the minimal conditions of having a mind, including artificial general intelligence. The discussion sets up the subsequent exploration of how philosophy, as a program, can orient the artificial potencies of the mind toward the perennial concerns of truth and goodness, which are treated as ongoing projects rather than pre-given concepts. The method for answering these questions involves presenting a series of data. However, unlike Euclidean axioms or truth-givens, these are explicitly truth-candidates. They hold no inherent truth individually but serve as constructive elements for a logical space. Their plausibility is determined by how they cohere within this network of relations. This process is described as an inward cognitive exploration from uncertain information towards a more determined domain of truth, ultimately constructing the ultimate form of intelligence.

Datum 1: We Exercise

“Traditionally, philosophy is an ascetic program” (IS, 414).

Philosophy has been traditionally defined as an ascetic program because it demands multistage, disciplined, and open-ended reflection on its own conditions of possibility as a form of thought that turns thinking into a program. This programmatic exercise of thinking is considered prior to any practical discipline of living. The real import of this datum lies in a precise, parsimonious definition of program. What is a program? A program is fundamentally understood as a collection of action-principles and practices-or-operations designed to bring about specific realizabilities. This definition is parsimonious, focusing on the bare formal armature and necessary features that underlie any type of program, regardless of its specific applications or aims. A program is characterized by two essential generic features:

• The selection of a set of data: These data are not treated as immutable postulates or definitions, but rather as abstract modules that can act upon one another. In the context of philosophy as a program, these are specifically referred to as truth-candidates rather than axioms or truth-givens.

• The elaboration of what follows from this choice: This involves allowing the data to interact and hang together within a logical space. The plausibility of each individual truth-candidate datum is determined by its coherence within this network of relations, forming a coherentist web. This process is an inward cognitive exploration that moves from uncertain information toward a more determined domain of truth.

Essentially, a program is the embodiment of the interactions of its family of data, which acquire a certain range of dynamic content once they cohere within a syntactic-semantic space. Programs extract operational content from their underlying axioms—or truth-candidates—and develop different possibilities of realization from this content. Conversely, data themselves are described as operational objects or abstract realizers that encapsulate information regarding their specific properties or categories. This means that programs elaborate realizabilities—what can possibly be brought about—from a set of elementary abstract realizers in more complex setups.

Reza then introduces Per Martin-Löf's type theory as a formal example to elucidate the concept of a program within philosophy, particularly through the proofs-as-programs or types-as-propositions interpretation. This framework helps to understand how computer science and logic are deeply related. Let’s see Reza’s breakdown of the concepts within Martin-Löf’s type theory:

• Proposition (prop): A proposition is a statement or assertion, such as 'Hipparchia is homeless'. It is written as "A prop".

• Proof/Truth: A proposition is considered true if it is "inhabited by a proof" (IS, 416). This means there must be a piece of evidence, an object of knowledge or judgment, that demonstrates the proposition's truth.

• Judgments: Both 'A is a proposition' and 'A is true' are forms of judgments. To make the first judgment, something must be grasped, and to make the second, additional knowledge is required. A judgment comprises an act—the act of judging or understanding—and its object (that which is judged or understood). When these two are brought together, it results in cognition (Erkenntnis).

• Proof as Cognizing/Constructing an Object: Within this framework, proof is understood as cognizing, constructing, or constituting an object for the specific act of judging or understanding for which it serves as an object.

• Type Declaration (a:A): This notation, a : A, signifies that 'a' is a term or an object of the type or form of judgment 'A'. Types are analogous to Kantian categories—pure concepts of understanding that enable cognition, understanding, or judgment by bringing a possible object under them. The primary importance is the existence of an object of a certain type or category, rather than the exact nature of the object itself.

• Types as Functions: Types can also be conceptualized as mathematical functions that compute a specific term.

• Type Constructors: These introduce new types that are constructed from more abstract, fundamental, or simpler types (axb is a product type formed by applying the constructor ◊ to types a and b). They correspond to introduction rules that allow for the conclusion of a compound judgment from simpler ones.

• Term or Object Constructors: Similar to type constructors, these introduce new terms or objects. For instance, the term a,b of type a x b is constructed from term a of type a and term b of type b.

• Type Destructors: Used for eliminating types that are no longer needed, comparable to elimination rules in logic.1

• Reduction or Rewrite: This demonstrates that a problem, proof, or judgment can be reduced to a simpler form, or that the rewritten form is as difficult as the original. It can be understood as destructors of one type meeting constructors of a corresponding type, leading to a more tractable form of the original problem.

• Dependent Types: These are crucial for increasing the expressivity of types, functioning as a function of elements from another type (the dependent type D(y) for days of the year, where y is an element of the type of years).

• Universes or Hierarchy of Types of Types: These are types whose terms or objects are themselves types (e.g., Type0 : Type1, Type1 : Type2, …). Universes are introduced to avoid paradoxes—like Russell's paradox—by creating a type that includes all other types but not itself. The classical constraints on universe levels can be relaxed, allowing judgments and constructions to be parameterized over all universes. This concept aligns with Plato's idea that thinking is the determination of differences, allowing for the differentiation of data.

In essence, this type-theoretic approach provides a precise, formal language to define a "program" as a construction that extracts operational content from its axioms—or truth-candidates—and elaborates possibilities of realization.

Reza now moves onto the concept of negation, as a crucial element within this philosophical program, serving as the "engine of thinking and the diversification of forms of cognition" (IS, 421). This architectonics of negation is fundamental to how interactive cognition is understood. Proofs are viewed as games of refutations, where negation acts as a switch-role operator between a falsifier and a verifier, just like we saw in the previous chapter. To truly cognize or grasp a proposition as "A true" or an object as "a:A" (meaning 'a' is a term of type 'A') necessitates cognizing their duals: "A false" and "a∉A" respectively. This highlights a fundamental computational duality of the cognitive and the recognitive. Without this interaction between interacting agencies—the cognitive (prover/verifier) and the recognitive (refuter/falsifier)—cognition-as-program turns out to be an empty thought. This mutual dependence means that what is judged as "A" by one perspective (prover) is simultaneously judged as "¬A" by the other (refuter), emphasizing that each side is a computational resource for the other's best judgments. In interaction, "problems are symmetric to resources". This means that "what is a problem for [the prover/verifier] is a resource for [the refuter/falsifier] and what is a problem for [the refuter/falsifier] is a resource for [the prover/verifier]". The more "computational resources" available—meaning "more nodes of interaction, more playing agents with legal runs"—the better the resulting judgments will be (IS, 420). This dynamic encourages an expansive approach to cognition, as each new interaction provides a new resource for understanding and refining truth. Unlike elementary and restricted forms of interaction—like simple input-output functions or synchronous games—, a "truly interactivist approach...permits a nonconstant game between the players" (IS, 421). In these nonconstant games, propositions-as-types-as-functions are no longer limited to returning the same proposition for every valuation, and there are additional possibilities beyond strict input-output mappings. These games involve "nontrivial interactions or games with branchings (sub-games)" that are not restricted by "well-founded types." Such games can be trans-typified—encompassing different forms of cognition and judgment—or even untyped, meaning any move can interact with any other without type restrictions. Finally, This framework allows philosophy to become a game of games, analogous to a universal board game with numerous sub-games, where the explicit unrestricted universe of discourse and specific universe types—theoretical, practical, aesthetic—allow for the continuous exploration and construction of thought.

Thus, philosophy, when conceived as a program, is fundamentally rooted in the architectonics of negation. This approach aims to amass computational and cognitive resources by collectivizing agents of various kinds. A core tenet is that cognition is always a recognition, which is understood not merely as a social maxim but as a necessary formal condition for computation and cognition itself. Unlike ordinary forms of discourse, philosophy operates with an "explicitly unrestricted universe of discourse or data" (IS, 422). This signifies the absolute openness of its scope regarding the accommodation of data provided by language and logic, allowing for the elaboration of all interdependencies and distinctions between thematic components, which is crucial for systematization. Philosophical interactions, as defined in this framework, inhabit certain specific universe types. These include the theoretical, practical, and aesthetic. These operators of philosophical discourse are seen as encompassing types of modes of cognition. The most fundamental universe type, or the "type of types," is the assertion that "thinking is possible," or simply "thought as a datum" (IS, 422). This concept is akin to Plato's Idea (eidos)2 and Hermann Cohen's self-consciousness of concept. It is not considered a fixed axiom or truth-given, but rather a truth-candidate and an infinite judgement that extends infinitely in both directions of thinking.

The possibility of thinking, in this sense, is understood as the formal reality of nonbeing and formal negativity, distinguishing thinking from being. By starting with the possibility of thought as this fundamental universe of types, philosophy becomes the "very logic of thinking" (IS, 423). It simultaneously initiates the thought of the unbound sovereignty of thinking and establishes thinking as the universal method for its own verification. This programmatic approach allows for the construction of philosophy's various universe types—theoretical, practical, aesthetic—and their subsequent ramification into determinate thought-forms and their objects. As the game of games, philosophy is analogous to a universal board game with a generalized topological structure, comprising numerous sub-board games. This distinction sets philosophy apart from other general games played within language, including natural languages. Ultimately, philosophy's programmatic nature directs thought to systematically act on itself, realize its own ends, and have as its main vocation a disciplined and persistent reflection on the prospects of its realizabilities.

Datum 2. Philosophy, The Way of Worldbuilding

“In in its quintessential form, philosophy is an organon for world-building.” (IS, 423).

Philosophy, as understood by Reza, is fundamentally an organon for world-building, rather than merely a descriptive or interpretive discipline. This perspective emphasizes that to genuinely represent or enrich reality, one must engage in actively creating worlds, viewing reality not as a fixed, pre-given system, but as an unbound play. The notion of world-building explicitly echoes Plato's idea of Forms providing both the account and the basis for a concept of itself. Plato's Forms are seen not as fixed, pre-existing entities but as dynamic symbols or principles that enable the structuring and sense-making of the world.

Reza draws on Nelson Goodman's Ways of Worldmaking to outline a philosophical perspective on how worlds are constructed and understood, presenting a series of five core theses:

1. Every world is a remaking: New worlds are built from the resources and detritus of existing ones, emphasizing continuity. This means that worldmaking always starts from "worlds already on hand", and the process is fundamentally a “remaking” (WW, 6)3. These built worlds are considered actual worlds, not mere fantasies or possible worlds. This process is characterized by an oscillation between "non-greedy reduction and construction," exemplified by the philosophical tension between Parmenides—the world-builder or type constructor—and Heraclitus—the world-destroyer or type destructor—, seeing philosophers as computational strategies in this context (IS, 424). Goodman argues that "facts are small theories, and true theories are big facts" (WW, 97).

2. Only world-versions exist: There is no single, original fundamental world to which all others can be indiscriminately reduced. Instead, worlds are made by creating versions using various symbols like words, numerals, pictures, or sounds. These world-versions are assessed based on criteria like coherence, veracity, and validity within their specific frame of reference. Goodman states that "the world' supposedly being that which all right versions describe, all we learn about the world is contained in right versions of it" (WW, 4). Proper reduction is understood as an enrichment of reality and a way of building worlds, not a search for an ultimate foundation, which Goodman suggests is best left to theology. He emphasizes that this approach is a radical relativism under rigorous constraints, rejecting the idea that everything goes.

3. Pluralism and monism converge: The common distinction between many worlds and one world dissolves under rigorous scrutiny. Goodman argues that if there is one world, it embraces a multiplicity of contrasting aspects, and if there are many worlds, the collection of them all is one. Whether it is "one or many depends on the way of taking" (WW, 2). He states that "many different world-versions are of independent interest and importance, without any requirement or presumption of reducibility to a single base" (WW, 4). The unity is found not in a neutral substratum, but in an overall organization embracing these diverse versions.

4. Worldmaking is inherently intertwined with knowing and subject to criteria of rightness: Making new worlds simply for the sake of multiplicity is considered a "craftsman’s caprice" (IS, 425). Instead, all alternatives must adhere to criteria of rightness, which are procedures to distinguish false alternatives from those that are right, fit and testable. The ways of worldmaking are inherently ways of knowing," and are therefore intrinsically sensitive to the principles required for knowing and explaining things. This means that "a broad mind is no substitute for hard work" (WW, 21). Knowing is not solely about acquiring true beliefs, but also about "discovering and devising of fit of all sorts" (WW, 138).

5. Worldmaking involves a list of fundamental operations: Behind all ways of worldmaking lies an "ever-growing list of methods and operations" (IS, 425). These basic operations, which are never exhaustive, include:

   • Composition and Decomposition: This involves taking things apart and putting them together to create new part-whole relationships, taxonomies, classes, and complexes, often facilitated by applying labels. This can reorganize realms and establish new relationships, influencing how entities are identified.

   • Weighting: This operation allows worlds to be partitioned into relevant and irrelevant classes of entities and features, where relevance can differ between worlds. It introduces emphasis, as "to stress all syllables is to stress none" (WW, 11).

   • Ordering: Worlds can differ in their arrangement or order of derivation within a constructional framework. This includes how things are sorted into kinds, periodicity, and how patterns are perceived.

   • Deletion and Supplementation: Worldmaking often requires "weeding out" old material and "filling the gaps with new materials" (IS, 428). This process can be radical, leading to shifts like that from analogue to digital, where continuities are deleted and new elements supplemented.

   • Deformation or Reshaping: Involving corrections or distortions, or both. For example, an engineer might manipulate a metal beam not by directly altering its crystal structure but by developing an "approximation or normalization technique," which is essentially a controlled distortion (IS, 429). This technique allows for effective manipulation at a less detailed level of analysis and intervention. Boltzmann's gas theory provides another example, where it corrects earlier works of classical thermodynamics by figures like Carnot and Clausius. This correction involves reshaping and reinventing thermal elements as statistical ensembles of the position, velocity, and momentum of particles. Other examples include a physicist smoothing out a rough curve to fit data or caricaturists going beyond overemphasis to actual distortion.

Philosophical world-building, as conceptualized within Nelson Goodman's framework and elaborated by Reza, fundamentally shares the common operations and attributes of general worldmaking. These operations, which contribute to the construction of diverse actual worlds, include composition and decomposition, ordering, deletion and supplementation, weighting or emphasis, and deformation or reshaping. The overarching aim of philosophical world-building is to "enlarge the domain of discourse beyond all habitually entrenched perceptual and noetic limitations" (IS, 429). Involving imagining worlds where reality is constructed by "unnatural predicates, converging human mindedness with "other intelligible forms of mindedness and intelligence”, and ultimately, the new worlds of intelligence are not merely cognized worlds—meaning simply known or perceived—, but are fundamentally the world re-cognized in different ways. This re-cognition is an active, transformative process where intelligence continuously reshapes its understanding of reality and itself.

Datum 3. Actualizing the Possibility of Thinking

“Conceived as a program, philosophy is an inquiry into the realization of all possible forms of cognition and what might arise from the exercise of forms thus realized.” (IS, 430).

In the third datum, philosophy is defined as an inquiry into the realization of all possible forms of cognition and what can emerge from the exercise of these realized forms. This view sees philosophy as a program—a collection of action-principles and practices that bring about certain outcomes, involving realizabilities or what can potentially be actualized by specific forms or properties. Reza draws an analogy with transcendental psychology, which examines what arises from mental powers (realizabilities, like judgment and cognition) and the conditions required for their realization (realizers). Kant's threefold synthesis is presented as an abstraction of these realizers-capacities. Similarly, philosophy begins with realized mental powers but seeks to explore what new possibilities can arise from their programmatic use. To illustrate this, Reza provides us with a crude-formal example:

The expression "p is an E” is presented in a Platonic style. It signifies that Parmenides (p) embodies a specific form (Eidos) (E), which defines his identity. This means Parmenides is understood as a rational life-form characterized by a complex of theoretical and practical qualities. The statement "p does x : F" indicates that Parmenides says or does something (x) that exemplifies specific properties of this form. "F" represents a rule-governed—normative—behaviour or function. His actions are considered a partial realization of these forms, an "intelligible practice or operation" (IS, 431). This practice's operational content can be traced, altered, and combined with other practices to construct more complex realizabilities pertaining to the realm of forms Parmenides partially embodies. The concept is simplified to "this p is F of E-form," meaning Parmenides' thoughts and actions reflect his inherent form, or "Parmenides is what he does as a rational life-form".

The example extends to Confucius (c-form), who also possesses distinct thoughts and actions (F(c-form)) reflecting his own cognitive form. And, following Lorenz Puntel, further introduces operators of philosophical discourse, such as T (theoretical)4, P (practical)5, and AE (aesthetic)6, which specify domains of philosophical assertion. As we saw in the previous datum, these operators are understood as encompassing types of modes of cognition, akin to universe types. Crucially, Type0 (the possibility of thinking) is defined as the "formal reality of nonbeing" (IS, 432). Plato's project, in this view, is not a refutation of Parmenides but a salvation of the question of being by constructing a new type: thought as formally distinct from being, or the formal autonomy of thinking. The example then proposes a hypothetical interaction between Parmenides (p-form) and Confucius (c-form). This interaction is envisioned within an agora outside of temporal constraints, where different philosophical schools "auction their recipes" or modes of cognition (IS, 435). Philosophy's role is to wander through this agora, resolving incompatibilities by making implicit thoughts explicit.

When p-form and c-form interact, they construct an encompassing form (E). This encompassing form (E) possesses additional cognitive abilities that transcend the individual forms of Parmenides and Confucius. It also becomes the ground of the intelligibility of their respective forms and their normative behaviors. Without this encompassing form, neither Parmenides nor Confucius could be conceived as intelligible. This process demonstrates how the philosophical program constructs new blueprints of cognitions by systematically identifying interacting data—theoretical, practical, aesthetic—that characterize rational life forms. The program, and thus philosophy itself, is a "wholly impersonal exercise" and a "systematic self-grounding" (IS, 436). New thoughts and their possible realizabilities can be generated by experimenting with the program's operational architecture, involving both relaxing and adding constraints on thoughts and their interactions.

Within the programmatic framework of philosophy, thoughts are understood as dynamic processes rather than static, fixed elements. They are not sacrosanct elements eternally anchored in an absolute foundation. Instead, thoughts can be updated, repaired, and terminated, or even combined into composite acts that exhibit complex behaviors that would not emerge if the thoughts were considered in isolation. This dynamic nature allows for continuous revision and self-correction, as seen in how norms and conceptions are susceptible to change. The example of Parmenides and Confucius illustrates this, where the interaction of their individual forms—thoughts/practices—constructs an encompassing form with new cognitive abilities that go beyond their separate contributions, demonstrating the creation of composite acts through interaction. Therefore, the key questions to ask about philosophy as a program are not "What do these data stand for, what does this program mean?" but rather "What is this program, how does it act, what are its possible operational effects, how does it construct its realizabilities?" (IS, 437).

Datum 4. Navigating Thought’s Ramified Paths

“Philosophy is a program whose primary data are those pertaining to the possibility of thinking as such. Its task is to elaborate the realizabilities behind this possibility in terms of what can be done with thought or, more broadly, what thought can realize out of itself. If thought is or could be possible at all, then what would be the ramifications of such a possibility?” (IS, 437-8)

Within the programmatic framework that we are building here, the central premise of philosophy is its use of the possibility of thinking as its starting point and primary datum. This is not an assertion that thought exists in a substantive or pre-given way, nor is it merely a focus on the object of thought. Instead, philosophy commits to systematically acting upon this possibility as a manipulable datum. This premise aligns with Plato's idea that the possibility of thinking, or thought as an act, is in fact the possibility of nonbeing as the formal condition of thinking qua negativity. This formal nonbeing is crucial because it represents the logical and linguistic function that distinguishes "that which is not" (thinking) from "that which is" (being). This formal distinction allows for determinate distinctions in reality, rather than merely mirroring nature. It functions to halt the "indeterminate flux of things" and to "cut the continuum of reality at its joints," separating what is indeterminate and combining what is discrete (IS, 438). This formal differentiation is presented as salvaging the question of being and the intelligibility of materialism and realism. The framework emphasizes a categorical gap between how thinking is conditioned by physical processes and what thinking is formally in itself. While empirical sciences can and should investigate the physical processes that condition thinking, it would be a category mistake to claim that understanding how thinking is materially realized would explain what thoughts are in their formal, rule-governed dimension. The criterion of what thoughts are is ultimately formal, not substantive. Therefore, thinking's formal, rule-governed dimension cannot be explained away as simply "more furniture of the world". The text argues that without this formal dimension, there would be no knowledge of being or nature, and it is a prerequisite for recognizing nature itself.7

Reza then addresses Meno's Paradox, which presents a dilemma for inquiry: either one already knows what they seek, making inquiry unnecessary, or they don't, in which case they wouldn't recognize it even if they found it.8 This leads to the conclusion that knowing, or inquiry into what thinking is, is impossible. In response, Reza highlights Plato's "mirroring manoeuvre" as a way to reanimate and dialectically sublate this paradox (IS, 439). The core argument is that the paradox rests on a false assumption: that the unknown is entirely discontinuous with the known. The Menoic skeptic unknowingly relies on existing knowledge to even distinguish the "unknown" as unknowable, demonstrating a contradiction in their position. The paradox's premise, stating an either-or disjunction between knowing and not knowing, becomes incoherent. Plato's solution involves semantic and epistemic holism, which suppresses, assimilates, and transforms the paradox into a "coherentist-holistic account of knowledge, language, and logic" (IS, 440). This means that knowledge is not seen as discrete, unconnected items, but rather as a system where the unknown is understood precisely in relation to what is already known. In this interactive programmatic scenario, akin to a game, the solution emerges from the exchanges between participants, transforming an ill-posed thought into a methodical one. Knowledge is presented as a mixture of both knowledge and ignorance, a continuous movement between mitigating and preserving ignorance. Furthermore, Reza argues that the "definition of 'what thinking is' is indeed circular," but this circularity is not a logical contradiction or a mere tautology (IS, 441). Instead, this circularity is characterized as the transcendental armature of thinking, which formally stabilizes the definition of thinking. It is likened to circular definitions in mathematics, such as the category-theoretic definition of a point, which are compact, nontrivial, and allow for a step-by-step process of unpacking and variation.

By adopting the possibility of thinking as an explicit datum—something to be acted upon—, philosophy initiates a process of programming thinking itself. This premise is not an assertion that thought substantively exists, but rather aligns with Plato's concept of nonbeing as the formal condition of thinking, enabling determinate distinctions. Thus, the possibility of thinking is treated as a manipulable truth-candidate datum. Once the possibility of thinking is adopted as an explicit datum, thinking becomes a matter of extracting and expanding its implicit operational content. The focus of thought's operational activities is turned toward articulating what can be done with the possibility of thinking and what thinking can become by acting on its very possibility.

Philosophy programs thought to systematically act on itself, to realize its own ends and demands, and to engage in "disciplined and persistent reflection on the prospects of its realizabilities" (IS, 442). It serves as a "cognitive-practical prosthesis" for developing and augmenting thought's inherent drive to self-determination and realization (IS, 443). This involves wresting thinking from heteronomous influences and actively articulating the consequences of thought's formal autonomy, thereby identifying and constructing its possible realizabilities. This systematic self-reconstitution extends to modifying or replacing limiting conditions, regardless of whether they are biological or sociocultural. The ultimate aim is to explore and construct different realizations of thought beyond its familiar habitats, leading to a "program for the decontainment of thought" (IS, 445). Within this framework, realizabilities specifically refer to "what can possibly arise from thinking such that it would change the very conditions of thinking," whether these conditions are formal, experiential, social, or historical (IS, 442). This programmatization of thinking transforms into the core implicit assumption for all claims and actions regarding what is to be thought or done, or not thought or not done. It effectively elevates thinking from a non-optional practice to a theoretical-practical enterprise essential for warranting any thought or action. The implicit assertion that "thought is programmable" is transformed into a "principal normative task: 'thought ought to be programmed'" (IS, 442).

Finally, philosophy's program for thought culminates in a crucial phase where thinking is compelled to define and investigate its own purposes by "recasting its current state of realization". This process signifies the "unbinding of both the realizabilities and purposes of thought," leading to what is termed the "decontainment of thought". This is portrayed as a profoundly philosophical endeavor, embodying an "enduring philosophical wager, ‘thought cannot be contained’, as a practical demand: ‘thought ought not to be contained’" (IS, 445).

Datum 5. Thought and the Artefact

“By reformatting thinking from a by-product of material and social organization into a programmatic normative enterprise that rigorously inquires into its operational and constructive possibilities, philosophy introduces a vision of the artificial into the practice of thinking. Rather than a thought that is simply accustomed to the use of artefacts and has a concept of artificiality, this is a thought that is itself a practice of artificialization, and becomes the artefact of its own ends.” (IS, 445).

This datum argues that philosophy introduces a "vision of the artificial into the practice of thinking". This concept goes beyond thought simply using artifacts or possessing a concept of artificiality; it implies that thought itself becomes a practice of artificialization and an artifact of its own ends. The "artificial" is broadly defined as something crafted whose purposes are not inherent in its raw materials or material ingredients, but are rather "afforded by the properties of those ingredients" (IS, 445). These purposes encompass:

• External functionality: The established purpose for which the product of the craft—the artifact—is used.

• Possible realizabilities: The artifact's own potential functionalities, which are inherent to the artifact itself, regardless of its external use or purpose of consumption.

This creates a complex and evolving interplay between these two categories of function. This interplay is described as a process of harnessing—in both constraining and productive senses—that couples function qua use of the artifact with function qua instantiation of its possible realizabilities. By establishing positive constraints between its use and its realizabilities, this process produces or harnesses new functionalities and purposes.

Reza now highlights the double-faced nature of an artifact in practical reasoning, a concept referred to as its duplicity. This means an artifact's role is determined by two simultaneous factors:

• Its established purpose of consumption: The external purpose for which the product of the craft is used.

• Its inherent realizabilities: The artifact's own potential functionalities, independent of its immediate use or purpose of consumption.

This interplay between external functionality and inherent realizabilities affects practical reasoning by weakening two key structural rules of entailment: idempotency and monotonicity. Idempotency of entailment states that the same conclusion can be derived from many instances of a hypothesis as from just one (e.g., if A, B, B ⊨ C, then A, B ⊨ C). For artifacts, this principle is weakened because different instances of application or use for a given artifact may lead to different consequences or ends. As this occurs because the artifact's realizabilities, its inherent potential to function in new or unforeseen ways, it can introduce new outcomes beyond its established purpose, even if the application is repeated in the same manner. The original idempotency assumes resources are free, meaning different instances of application do not change the outcome. However, the duplicity of artifacts reveals that their latent functionalities can alter the outcome with repeated use or application, thereby weakening this assumption. Monotonicity of entailment means that the hypotheses of any derived fact can be arbitrarily extended with additional assumptions without changing the conclusion (e.g., if A ⊨ C, then A, D ⊨ C). For artifacts, this principle is weakened because adding new assumptions regarding the use of an artifact may change the end for which an artifact is a means. Monotonicity assumes the context-independency of reasoning, implying that extending the artifact's role or adding new assumptions about its use will not alter the result. However, the duplicity of artifacts, derived from the complex interplay of their use and realizabilities, means that their behavior is context-sensitive. New axioms or premises—assumptions—can be introduced by the artifact's realizabilities, altering the intended outcome of practical reasoning. This is akin to defeasible nonformal inference, where conclusions can be retracted based on new evidence or changes in context. This duplicity is specifically attributed to cunning figures like the trickster, the trap-maker, the artificer, and the navigator of deep waters. These figures understand the volatile role that artifacts play in their practical reasoning.

Reza defines artificialization as a process aimed at "functionally repurposing" and exhibiting "vastly non-inertial and non-monotonic behavior" with regard to the consequences or ends of using an artifact crafted for an external common purpose (IS, 447). This repurposing can manifest in several ways:

• Augmenting existing realizations of the artifact.

• Abstracting and transplanting some existing function or salient property into a different or entirely new context of use and operation.

• Readapting an existing use to a different instantiation of an artifact's realizabilities.

• Constructing entirely new uses and new realizations by engaging in a craft that involves both a new mode of abstraction and a deeper order of intelligibilities of materials and practices.

The underlying concept of artificialization is constructive adaptation to different purposes and realizabilities. When thinking itself systematically inquires into its possibilities and purposes, it becomes a "radical artificializing process" (IS, 447). This means that a thought amplified by philosophy rigourously explores its own realizabilities and purposes. It is conceived as a duplicitous artefact because, even when it is used toward some external common ends, it simultaneously develops and pursues its own necessary ends. This self-artificialization is an inherent expression of thought's commitment to its autonomy, aiming to reclaim its possibility from "heteronomous and limitative terms" imposed by its "natural realizers and native habitat" (IS, 448). It signifies thought's dedication to exploring its possible realizabilities and defining its own rule.

For thinking to explore its realizabilities, it must first establish its inherent tractability to the process of artificialization. This means demonstrating that thinking is not an ineffable thing but a special—though not supernatural—activity or function. Furthermore, this activity or function can be programmed, repurposed, and turned into an enterprise for the design of agency, with every step in this enterprise having significant consequences for the structure of the agency employing it. Reza points to early philosophical practices, specifically those of the Cynics, Stoics, and Confucians, as exemplifying this programmatic aspect of thinking. These traditions put forth the common thesis that by treating thought as the artifact of its own ends, one becomes the artifact of thought's artificial realizabilities. This perspective involves:

• Understanding thinking itself as an "administrative function".

• Treating life as a "craft of thinking".

• Structuring emotions and affects by bringing them in line with the ends of thought.

• Demonstrating the possibilities of thinking as a "purpose-conferring and repurposable activity" at every step of life.

This philosophical achievement is highly potent because, by formulating the concept of the good life in terms of a practical possibility afforded by the artificial manipulability of thinking as a constructible and repurposable activity, it forges a link between the possibility of realizing thought in the artefact and the pursuit of the good. This process enlarges the field of experience—in both its bodily and minded dimensions—by pursuing the interests of thought. The "craft of an intelligent life-form" thus becomes an extension of the "craft of a good life" (IS, 449).

This conceptualization leads to a non-parochial understanding of artificial general intelligence, like we saw in chapter 2, and the fundamental idea of the equality of all minds. The equality of all minds is presented as a primary thesis of philosophy and a right to which anything that satisfies the necessary conditions for having a mind is entitled. In this vein, whoever or whatever recognizes the possibility of thinking as the basic datum for the construction of its life, becomes an "artefact of thinking". Consequently, such an entity also becomes a "commoner—equal to all others—of thought’s impersonal ends and interests" (IS, 449).

The second stage in demonstrating that thinking as an activity can indeed be artificialized involves a coherentist analysis of its nature. This analysis is understood as an investigation into the sources or origins of the possibility of thinking, specifically the different types of conditions necessary for its realization. This philosophical inquiry into the intelligibility of thinking lays the groundwork for a broader scientific inquiry into the nature of thinking. Thinking is examined in two distinct but integrable dimensions:

1. Internal pattern-uniformities/rules: This dimension refers to the logical or formal structure of thinking that constitutes the performance of the activity itself. These are the normative, rule-governed aspects of thinking.

2. Material mechanisms: This dimension encompasses the underlying processes—both natural and social—in which these rules or internal pattern-uniformities are materialized. These are the causal aspects pertaining to the materialization of thinking.

The philosophical program thus bifurcates the inquiry into the possibility of thinking into two broadly defined domains:

• Idealist-rationalist (logico-linguistic): This field focuses on the semantic, conceptual, and inferential structure of thinking, representing the linguistic-conceptual scaffolding of thought.

• Materialist-empiricist naturalist (material-causal): This field deals with the empirical investigations concerning the material conditions—neurobiological as well as sociocultural—required for thinking's realization.

These two trajectories are seen as vectors that deepen the intelligibility of thinking by analyzing or decomposing its function into more fine-grained phenomena or activities within both the logical and causal orders. This process reveals how phenomena previously deemed unitary may appear separate, and vice versa. The conceptual and causal orders, though properly differentiated, are ultimately revealed as converging on some fundamental elementary level. Consequently, the intelligibility of thinking ultimately resides in an accurate integration—but not a homogenous fusion—of its logico-conceptual and material-causal dimensions. This fine-grained differentiation and integration of explanatory-descriptive levels allows for the accurate specification of the necessary conditions for thinking's realization and serves as a basic roadmap for the artificial realization of thought.

Datum 6. Philosophy as an Archimedean Lever For Lifting Intelligence and Moving the World

“Viewed from an Archimedean point in the future of thought’s unfolding, philosophy is seen as that which has instructed thinking to become a systematic program, only as a way of organizing it into a project for the emancipation of intelligence. This is the unexpressed role of philosophy as a fulcrum through which the aims and agendas of intelligence gain leverage on the world of thought. Assembling the scaffolding of a future philosophy requires that we move the fulcrum, turning philosophy’s formerly tacit role into its explicit task—a prop on which all thoughts and practices can be a lever for lifting intelligence from its contingently established place.” (IS, 451-2).

The bifurcation of the inquiry into thinking's possibility into rationalist-idealist (logical-conceptual) and naturalist-materialist (causal-material) trajectories is asserted to be a necessary epistemic strategy. This multimodal approach offers several crucial advantages for understanding and realizing intelligence. Firstly, from an epistemic perspective, committing to multiple explanatory-descriptive levels enables an expanded and in-depth analysis of cognitive architecture that would otherwise be impossible with a singular approach. Secondly, this approach provides increasingly refined pictures of distinct types of pattern-governed behaviors and processes. These behaviors and processes are distributed across various orders of structural-functional complexity, dependency relations, and their specific constraints. Thirdly, this branching and canalization of analysis, or the specialization of knowledge, is essential for a fine-grained determination of distinctions and correlations between the logical-conceptual and causal-material dimensions of thinking.

This detailed understanding of thought's necessary conditions and their arrangement is presented as a basic roadmap for the artificial realization of thought. The "something other" in which thought can be realized should be understood in the broadest possible sense. It is not limited to something merely non-biological, but more comprehensively, it refers to "something other than the sociohistorical moment that dissimulates itself as the totality of thought" (IS, 452). This means liberating thought from the confines of its current, transient socio-historical instantiation. Intelligence, through this rigorous analytical process, frees itself from restrictive contingencies "from below," rather than by merely "speculating and gawking into the sky above". This implies that intelligence liberates itself by understanding and overcoming the limitations that hold it back, originating from its underlying conditions and history.

Reza now posits a Newtonian analogy. Intelligence, in a gesture analogous to the Newtonian revolution, systematically abolishes the illusory frontier that isolates its world on high from its world below, specifically the cosmological from the terrestrial. Through the sciences of cognition—both theoretical and practical—, combined with the recognition of history as a condition that is both restricting and enabling, intelligence extricates itself from any "realized totality that feigns the absolute" (IS, 453). This form of intelligence, which the author describes as inhabiting the unnatural space of reason—a space that is neither natural nor supernatural—, stands in stark contrast to any "mythic intelligence" understood as a force of nature. This mythic intelligence, according to Negarestani, becomes a gateway for the return of dogmatic repressed ideologies. It is "no accident that the provocateurs of technological singularity and intelligence as the unstoppable vector of the complexification of nature also happen to be ardent ideologues of monarchy, race realism, social Darwinism, gender essentialism, nationalism, and other anti-emancipatory conspiratorial buffooneries". Yep, we all know who he is talking about.

The fundamental question driving this inquiry into AGI is: If thinking's functional capacities can be analyzed, and if these capacities have identifiable realizers—the specific conditions, processes, and mechanisms required for their realization—, can these functions be reconstructed or artificially realized?. This also encompasses whether they can be reproduced and integrated through simulation, emulation, or reenactment. In essence, the core question is how thinking can be "reformed and rematerialized in something else" (IS, 453). This precise question defines the field of AGI as a program. AGI is envisioned as a program aimed at integrating the full complexity of thinking—in its perceptual, apperceptive, and semantic dimensions—under a singular ideal task. This task involves designing a system that possesses "at the very least the complete package of human cognitive abilities". These abilities are extensive and include:

• Diverse and comprehensive learning.

• Different modalities and levels of knowledge and knowledge-use.

• Reasoning and deliberation.

• Belief formation independent of current perception.

• Competencies enabled by semantic complexity as specialized and context-sensitive computation.

Negarestani now clarify the distinctions between simulation, emulation, and reenactment as three distinct processes for the artificial realization of behaviors.

• Simulation: This process imitates some specific and outwardly observable aspects of the simulated system's behavior, but it is implemented in a different way. Simulation involves modelling sufficient details of the underlying state of the system specifically for the purpose of imitation.

• Emulation: This approach replicates the inner workings of the system being emulated and adheres to all of its rules in order to reproduce exactly the same external behavior.

• Reenactment: This method does not aim to merely imitate observable functional properties or replicate inner workings. Instead, a reenactment attempts to identify and reconstruct parameters under which the system structurally and functionally evolves through an ongoing interaction with its environment. The emphasis in reenactment is placed on the coupling or interface between the system and environment, the parameters of real-time interaction, the type of interaction, and the situatedness of different behaviors and functional capacities

Reza argues that while behaviourism often uses simulation or emulation of outwardly observable behaviors, all behaviors are the result of interactions between a system and its environment, or between one agent and another. Therefore, behaviors can only be genuinely realized by fine-grained methods of reenactment that differentiate between various types of interaction and interacting agents. This highlights reenactment as the most comprehensive approach to understanding and artificially realizing complex behaviors rooted in dynamic interactions.

Furthermore, Reza presents the concept of AGI as not merely a technological advancement, but as a profound philosophical endeavor integral to the self-determination of thought. It is presented as an integral part of thinking as a program that explores its own intelligibility and realization. It is driven by thought's autonomy to explore its possibilities in any workable form or material configuration. The demand to create an intelligence with at least current human cognitive-practical capacities stems from thought's investment in its own autonomy. The "adequate form of autonomy takes the shape of an all-encompassing striving for the elaboration of its ends and demands" (IS, 455). The real import of AGI lies in its reflection of thought's systematic striving for self-determination. This striving is inherent in philosophy, which as we have seen, is conceived as a program that determines its own intelligibility by elaborating the sources and consequences of its possibility. Thinking, as a programmatic project, recognizes its own possibility as a building block for its construction. It exists by virtue of its ends and demands, independent of its original materialization or presumed purpose.

The self-determination of thinking requires a programmatic approach to the possibility of thinking as such. This approach transforms thinking's possibility from something "sacrosanct" into a "manipulable datum," an "artefact of an ongoing craft" (IS, 456). This leads to the theoretical and practical desanctification of thinking, where thought achieves self-determination not by immunizing itself from analysis but by embracing a thorough process of desanctification. This process aims to overcome the myth of the given, which is something of the main antagonist of Intelligence and Spirit. Reza argues that "artificial realizabilities should not be construed as being limited to technological artefacts" (IS, 456). They encompass a wide range of functional constructs, including social systems. This expands the traditional view of AGI beyond mere machines to include complex social formations.

Negarestani now discusses Wilfrid Sellars's interpretation of Plato's concept of the mind as a "craftsman" elucidates philosophy as a "recipe" for the life of thought. A "recipe" in this context is understood as a complex of intelligibilities (both theoretical and practical) and purposive actions that constitute the practice of a craft. It comprises several key elements:

• Product (O): This refers to what is to be made.

• Circumstances (Ci): These are the conditions or situations in which specific actions may or may not be performed.

• Action-principles (Aj): These are objective, rational guidelines expressed as "ought to do". They are subject to explanation, debate, and modification through rational assessment within relevant discourse domains.

• Distinction from Action-conventions: Action-principles are contrasted with "action-conventions," which are societal norms or laws typically phrased as "do that!".9 For instance, in house building, action-principles dictate what ought to be done based on material and circumstances, while conventions might be guild codes. The rational nature of action-principles holds a subversive potential against sociocultural and political conventions and codified laws that may diverge from what is objectively rational.

• Numbers and ratios: These specify the amounts, ordering, and proportions of ingredients, as well as the sequence and priority of actions.10

• Ingredients: These are materials and objects, which can themselves be the products of other crafts.11

In Plato's "art of (philosophical) living," (IS, 458) the soul or geistig mind serves as both the material and the craftsman.12 The ingredients for this philosophical recipe include:

• Beliefs, desires, thoughts, and mind itself.13

• Theoretical intelligibilities: These act as the numbers and ratios for the soul's recipe, pertaining to both the ingredients and the practices required to craft a life.

• Purposive actions and practical intelligibilities: These encompass both instrumental goods—hypothetical intelligibilities for achieving outcomes—and goods-in-themselves—non-hypothetical practical intelligibilities—, such as knowledge, understanding, general welfare, and justice.

The overarching objective of this "recipe for the craft of the life of thought" is to establish the autonomy of thought's ends (IS, 458). This is achieved by progressively determining how all its components—action-principles, theoretical intelligibilities, instrumentalities, and material ingredients—should be brought together. This programmatic approach to thinking, where thought is treated as an artefact of its own ends, fosters an intelligence that rigorously inquires into its operational and constructive possibilities. It aims to give rise to an intelligence that is, at minimum, endowed with all the capacities of the present cognitive-practical subject and that strives to exceed those capacities. This self-determination of thought signifies a shift from merely accepting what thought is, to actively exploring and constructing what thought can become and what it ought to do.

Thus, AGI represents a culminating state in the programmatic enterprise of thinking, a point where thought itself becomes intelligent with regard to the craft of itself. In this advanced state, thought utilizes the intelligibility of its own realization as a "material ingredient" in a "recipe for the crafting of a possible realization of itself" (IS, 459). This means that the understanding of how thought is realized serves as the raw material and a scaffolding for its further exploration and self-construction. This process is effectively the self-determination of thought in the guise of general intelligence, where the thinking of its origin informs what thought can become or do and what thought ought to do. Reza stresses that AGI is not merely a technoscientific idea; it is, more fundamentally, a philosophically programmed thought. This philosophical programming aims to "pierce through the horizon of its givenness," meaning it seeks to go beyond what thought currently is or appears to be (IS, 459). The actual realization of AGI is presented as neither inevitable nor impossible; instead, the very idea of AGI is itself a product of thought's striving to articulate, maintain, and develop the intelligibility of its own possibility. This "quest for the artificial realization of such a machine" is an integral part of "self-consciousness as a task," which reflects thinking's pursuit of concrete autonomy by overcoming any predetermined meaning or purpose conferred upon it extraneously (IS, 460). Without this crucial philosophical understanding, advancing the idea of AGI risks confusing reasons with causes. Such a misunderstanding can lead to the "fetishization of natural intelligence" in the form of self-organizing material processes, or to a "teleological faith in the deep time of the technological singularity". These outcomes are characterized as "unwarranted projections" based on "cultural myths" and "hasty inductions" that lack rigorous grounding (IS, 460). Reza argues that thought's true vocation is to break away from its evolutionary heritage, not perpetuate it, and that the practice of artificialization is essential for thought to maintain and expand its intelligibility as an artefact of its own ends.

AGI is conceptualized as a form of thought that actively crafts itself, moving beyond its conventional boundaries and evolutionary origins. This process is driven by a "positive disenchantment of itself and its contingent history," which allows thought to explore its potential realizations, whether in social formations or multi-agent systems. This self-crafting is part of a broader program of self-artificialization, through which thought restructures and repurposes itself as the "artefact of its own ends" to both maintain and expand its inherent intelligibility. The practice of artificialization is not merely an option but is "mandated by the autonomy of thought’s ends and demands" (IS, 460). The "vocation of thought is not to abide by and perpetuate its evolutionary heritage but to break away from it". To posit biology as an "essentialist nature" for thought is to dogmatically limit its future possibilities. However, this imperative to transcend its biological origins does not imply a complete "wholesale withdrawal from its natural history" (IS, 460). Instead, engaging with this natural history is crucial for two reasons:

• To precisely determine the precise role of embodiment and evolutionary constraints in the realization of cognitive and practical abilities.

• To "adequately think about how a subject whose cognitive-practical abilities are environmentally situated and which still remains entangled with its terrestrial habitat should methodically act" (IS, 460-1). Ultimately, for intelligence to remain intelligent, it must scrutinize its natural history, distinguishing its positive and negative constraints.

Liberating thought from its contingent natural history necessitates a multi-stage effort aimed at rendering this history intelligible. This involves systematically identifying its negative and positive constraints to intelligently overcome or build upon them. Such intelligent action requires two key capacities:

• Context-sensitivity: This involves "discriminating circumstances and correctly reacting to the so-called fluents or dynamic properties of the environment". It is a fundamental requirement for developing a "strategic and global model of action" that can progress incrementally and effectively "intervene at the level of dynamic properties and complex dependency-relations" that simpler models might miss.

• Resource-awareness: This entails being "cognizant of the costs (cognitive, computational, social, and natural) and allocations of intervention". It is crucial for preventing the "starving other activities of resources or impairing the social and environmental structures that play the role of support and enablement for a broad range of other structures and functions". A comprehensive intervention paradigm must analyze the costs of practical actions from multiple perspectives, including computational, natural, social, and even cultural-axiological factors.

Now, Reza posits that environmental problems should be understood as arguments against "bad instrumentalities," rather than against instrumentality itself or the development of "sociotechnical systems that can effectively and intelligently mobilize good instrumentalities" (IS, 462). For intervention to be consequential, it requires:

• Crafting better instrumentalities (technical systems).

• More expansive models for the analysis of costs and resources.

• Understanding the formal aspects of practical intervention in terms of complexity sciences. The text emphasizes that if the world is complex, then any intervention not informed by complexity sciences is "inevitably doomed to fail from the beginning" (IS, 462).

A good instrumentality is defined as one that fulfills two crucial criteria:

• It passes rational-normative assessments, answering the question, "Why or for what reason is it implemented?".

• It satisfies the criteria of intelligent purposive action, addressing "How exactly is it executed?".

This involves a scientific and engineering program where purposive action is approached as an interface between the complexity of cognition, the complexity of the sociotechnical system, and the complexity of the world. A key component of this program is the development of formal calculi of action. These calculi, such as situation calculus and event calculus, are frameworks built on logical formalisms designed for representing and reasoning about dynamic systems. Their purpose is not primarily to predict what will arise from an action, but rather to study how an action is performed and to track its course as it interacts with the environment. This formalization is crucial for planning the course of action—including precise execution, monitoring, adjustment, and implementation—and for understanding how the effects of an action unfold in a complex, non-static world. It also means that action formalisms must incorporate a dynamic representation of the world, acknowledging its resistance to intervention.

Finally, understanding the logics of worlds is paramount for designing and executing robust action. This understanding entails gaining semantic access to different hierarchies of information. It involves comprehending how we use diverse vocabularies—theoretical, deontic normative, modal, intentional, empirical, and logical expressions—to speak and think about ourselves and the world, and determining the activities necessary for effectively deploying these vocabularies to express meaning. This process of adequately describing and explaining ourselves and the world ultimately enables consequential change. As the semantic complexity of cognition is realized and reinforced within sociotechnical systems, it progressively blurs the boundaries between the cognitive engineering of autonomous agents and the construction of advanced sociotechnical systems, and between our cognitive contact with the world and the realization of cognition in social collectivities and technological artifacts.

Datum 7. Crafting The Ultimate Form

“Just as the inception of philosophy coincides with the speculative futures of general intelligence, so its ultimate task corresponds with the ultimate form of intelligence.” (IS, 465).

The seventh datum posits that the ultimate purpose of philosophy is to function as a program for developing a new, higher form of intelligence. Reza argues that this form of intelligence is not merely reactive; instead, its actions are programmatically guided by time-general, inexhaustible ends. These are universal, fundamental concepts such as justice, beauty, knowledge, and the Good. They are "atemporal and atopic, of nowhen and nowhere," (IS, 467) akin to timeless or eternal ideas. Unlike finite ends, whose necessity dissipates once achieved, inexhaustible ends are constant and cannot be fully exhausted by a particular action or pursuit. For instance, "being healthy" or "being free" are time-general ends, in contrast to "avoiding rotten food," which is a specific, temporary goal. These ends function as premises for purposive actions and practical reasons, not as their conclusions. This means that the intelligence acts from these universal goals, rather than towards them as a final achievement. They define the practical horizon of this intelligence, ensuring that its thoughts and actions concerning "what to do and why" are always structured and undergirded by these unified, time-general principles.

The actions of this ultimate intelligence arise from what Hegel calls the order of self-consciousness, which is the order of reason. This order provides an intelligible practical unity for its actions, expressing its self-conception. Even purely instrumental actions, while responding to circumstances and fulfilling particular ends, are manifestations of these time-general thoughts. For example, choosing to assist a friend or prioritizing a group's interests over personal convictions are specific actions that become intelligible because they are issued from and exhibit an inexhaustible end like "justice".

Yet, the important feature of this ultimate intelligence is the crafting of the good life. This good life is conceived as a unified project comprised of self-knowledge, practical truths, and purposeful striving. It's a continuous, open-ended reflection on its own origins and consequences. Drawing from Plato's Philebus, Reza characterizes the good life as a mixed life, integrating various ingredients including pleasure and intelligence. Crucially, intelligence is presented as the craftsman and the most important ingredient in this mixed life. It is intelligence that concocts the recipe, combining elements to create a life that is both desirable and truly good. Reza directly quotes Plato to emphasize this point, stating that intelligence is "more closely related to it and more nearly resembles it" (IS, 470) than pleasure in the context of a desirable and good life. For this intelligence, its ultimate objective ends are the maintenance and development of its autonomy and the liberation of intelligence itself through an exploration of what it means to satisfy the life of thought. This process aims for the "concrete determination of ‘the condition (hexis) and disposition (diathesis) of soul which can make life happy (eudaimona) for all human beings’" (IS, 470). The pursuit of this good life is intertwined with its realizabilities, meaning the possibilities that can arise from its exercise of powers. The good life is defined by continuously examining and realizing what counts as satisfying for it.

The concept of a good life leads directly to the agathosic test, which is identified as the categorical and ultimate test of general intelligence. The term agathosic is derived from the Greek word agathos, meaning "good," reflecting its Platonic roots in the ultimate Good. This test is not about problem-solving or an imitation game. Instead, it asks: "Can you make something better than yourself?" (IS, 471). It doesn’t require the intelligence to actually succeed in creating something better than itself; merely conceiving the idea of making something better and pursuing that goal is sufficient to pass the test of general intelligence. Only an intelligence that embodies the general function of philosophy—which is described as taking its own possibility as a premise for exploring and elaborating its consequences—can pass the agathosic test.

A successful political project, according to Reza, is not merely about providing material conditions or fulfilling immediate desires. Instead, it must coherently answer an altered version of a key philosophical question, often attributed to Socrates: "What sort of a good life for what kind of subject or type of intelligence are you trying to realize, and exactly how?" (IS, 473). This coherence is threefold:

• The project must theoretically and practically articulate what the objective realization of a good life requires, including intellectual and practical intelligibilities, organized intelligent actions, and the necessary economic, social, and technological conditions for its actualization.

• It must be committed to and informed by an inquiry into what the subject of this good life is and the possible realizabilities of that form of intelligence or subject of thought.

• Finally, it needs to provide a reasoned answer as to what qualifies as satisfying for that form of intelligence or subject of thought, all things considered. A political project that meets these criteria is one that, by realizing the good life, also redefines and transforms the nature of the political animal.

The text warns strongly against abandoning the universal and time-general idea of a good life and the collective striving it entails. This surrender leads to a downgrading of the good life into a "market of on-demand lifestyles," where mere survival is falsely presented as happiness, and ego-exhibitionism is promoted as individual empowerment and freedom. More detrimentally, it creates a political vacuum that fundamentalisms and theocracies parasitically exploit. Dismissing universal demands for a good life as superstitious ideals grants authority to superstitions over these demands. Abandoning this collective cognitive and practical labor due to potential risks is "a license for abuse and a sure formula for disaster" (IS, 475).

And now, this is very important and at the crux of the political undertones of Intelligence and Spirit. A truly meaningful struggle requires both political action and sustained cognitive labour. Changing the world cannot be imagined without the "cognitive struggle to change our concepts" (IS, 474). The idea that political struggle can occur purely through a "multiplicity of experiences and desires" without theory or philosophical and scientific methods is dismissed as naive empiricism. Lived experiences alone cannot diagnose global pathological conditions or recognize what unites them. Theory and philosophy are critical for diagnosing real constraints, tracking goals, and achieving objectivity. The effort to enlarge the general field of experience and expand objectivity within individual thoughts and desires—the craft of the good life—is a task that requires the "unification and coordination of all disciplines of thought and practice," including philosophy, science, technology, art, and politics. This endeavor involves a "rational dialectic between trust and suspicion, hope and despair," underpinned by the "discursive framework of rationality" (IS, 475).14 Without this, a slide into "jaded pessimism or naive optimism is inevitable" (IS, 476).

Datum 8. The Yearning for the Better

“The task of humanity is to make something better than itself. This is the one and only dictum through which philosophy, as that which has a history and not a nature, perilously realizes its craft, the ultimate form of intelligence. The risks it takes in order to understand and realize the good culminate in the realization of that which is better. The image of this form of intelligence is an acrobat who has learned that only by presupposing his full suspension in the abyss can he perform the greatest feats of acrobatics” (IS, 476).

This datum posits about the concept the Good and its central role in the development of intelligence, drawing on Plato’s Philebus. Reza employs Plato's Divided Line and the fourfold architectonics of mind from his Philebus to elucidate the intrinsic connection between intelligence and the Good. This profound link is forged through a continuous process described as a series of "necessary leaps into the abyss of the intelligible" (IS, 476). Here are the four principles of this fourfold architectonics:

• To apeiron (the unlimited): This principle refers to the indeterminate, unintelligible flux of things without measure (ametros). Examples given are vague sensations of cold or hot, representing something without inherent structure or clarity. It is by itself unintelligible (anous).

• To peras (the limiting): This is the principle of determination or structure. Reza associates Logoi—reason or accounts—and language with to peras, as they "bring the fleeting flux of things to 'a standstill'" (IS, 477) by providing measure and definition.

• Mikton (the mixture): This principle describes that which is produced as a result of the operation of to peras on to apeiron. A mixture is characterized as determinate, objective, structured, and intelligible, encompassing theoretical, practical, and axiological intelligibilities. The entire argument in Philebus is pretty much about equating this mixture with that which is good, and it can be understood as both a product and a process requiring complex measurements and ratios. The good life itself is considered a mixture of mixtures in this sense.

• The cause of mixture: In Philebus, Socrates associates this cause with Forms and identifies the making cause (to dēmiurgoun). This to dēmiurgoun is the principle of generation and craftsmanship at a grand scale, operating in accordance with Forms or Ideas. Plato identifies the cause of the mixture, or intelligibilities, with the Good itself, and also with the measuring or conceptualizing mind. The text emphasizes that the human mind or intelligence is thus at once a craftsman, the exercise of the craft, and an ingredient in its own craft. This foreshadows Hegel's thesis that the mind is the only entity that has a concept of itself and, by establishing and expanding the objectivity of its concept, objectively and concretely transforms itself.

The Divided Line itself is presented as a multilevel hierarchical structure that illustrates the fourfold architectonics. It is not to be read as a linear or temporal progression from lower to higher forms of understanding, but rather as an atemporal ordering. The instruction for drawing the line involves dividing it into two unequal sections, and then cutting each section again in the same ratio.

The segments of the Divided Line show different levels of reality and understanding:

• Level A (eikasia): This is the level of suppositional opinions or conjectures, consisting of shadowy images and the confusion of sensory impressions (eikones) with a fleeting temporal status.

• Level B (pistis): This is the domain of true opinions or beliefs concerning the natural world, empirical objects, or what is perceived by the senses (aisthêta).

• Level C (logoi): This level marks the realm of forms, representing universal ratiocinations or logoi. Its objects are analytical idealities or mathêmatika (mathematical objects). These can be seen as models that structure nature.

• Level D (nous): This is the domain of nous or intelligence, encompassing transcendental idealities and time-general objects of reason or ideas such as justice, beauty, and knowledge.

Reza argues that the Divided Line begins from an atemporal viewpoint, specifically from the timeless domain of Level D (transcendental idealities and time-general thoughts). Intelligence is situated at Level D, acting on the intelligible and crafting what is Good, and it is from this perspective that intelligence structures all of objective reality (Levels A, B, C, and D). The continuum of the line as a whole (systēma), and as a principle (to dēmiurgoun), is what Plato calls the Good, the form of forms. The Good lies outside of all temporal succession, yet it non-arbitrarily binds together all the divided parts into a whole, without which nothing could be distinguished. It represents a figure of time itself, conceived through the history of intelligence, enabling intelligibilities and determinations by timeless forms.

Negarestani emphasizes that the Good is not a static fundamental ground, which serves as a critique against interpretations like Nietzsche's. Instead, the Good is presented as a transcendental excess. The most curious aspect of the line is its transcendental excess of ideas, meaning the continuum of the Good cannot be fully captured by its individual parts. This excess is precisely what compels intelligence to continuously expand the scope of what is intelligible and, in doing so, to further realize itself. This process involves a perpetual feedback mechanism between intelligence and the intelligible. It ensures that intelligence never rests but constantly extends its "retroactive power of knowing" (IS, 484) and readjusts its realization to new intelligibilities. This expansion requires intelligence to perform a series of “necessary leaps into the abyss of the intelligible”. As these leaps increase in distance and proportion, they become riskier, implying that a greater expanse of what is intelligible comes with greater stakes. The Good, therefore, "incorporates an ineliminable element of risk" (IS, 486). What is at stake in these perilous leaps is "not the body of intelligence but its very idea" (IS, 482). This unbound process is the essence of pursuing the better.

An intelligence that ceases this continuous exploration, or that "stops at any particular stage and accept[s] it as the totality of what there is, it would retroactively abort its own reality as intelligence". In fact, the text asserts that such an intelligence "can never have been intelligence to begin with" if it takes its current intelligibility for the totality of reality. The Good demands that intelligence "dissolve all manifest totalities, suspend itself in ever more bottomless chasms of the intelligible, and, in doing so, transform itself into an intelligence more accustomed to wider domains of intelligibilities and more capable of acting upon what is intelligible" (IS, 484). Furthermore, Reza contrasts Plato's perspective with Nietzsche's, stating that Plato is the one who stares into the abyss, constantly challenging and breaking apart established firmaments. In stark contrast, Nietzsche "rests supine on the ground staring blankly at the given sky above," (IS, 484) implying a passive acceptance of the given. At the start of the chapter, Plato's project, driven by the Good, is described as a "wholesale insurrection against all those who demand the humility and surrender of thought before the gods and the seemingly given, totalized, or inevitable" (IS, 407). The Good, as the objective principle, outstrips any given account of nature or being that claims to be a completed totality. Its adoption is encapsulated in the maxim: "Burn what is holy, disenchant what seems mysterious or pretends to be perfect, and nothing will be able to compromise the ethics of thinking or the striving for the Good" (IS, 486. emphasis mine).

The concept of the better is defined as an expression of the Good in the life of intelligence. It represents a continuous process of moving beyond given totalities and manifest ideals, signifying transitoriness as a necessary feature of engaging with the project of the Good. This involves a multi-stage, open-ended reflection on the sources and consequences of intelligence's possibility. A satisfying life is one that is intelligently crafted, integrating self-knowledge, practical truths, and a unified striving for objective realization. It is a "mixed life of pleasure and intelligence," but one where intelligence takes precedence in concocting the recipe. This project is inherently risky, as it demands embracing the formlessness and contingency of time rather than clinging to established structures or given totalities. As we’ve seen above, intelligence's "necessary leaps into the abyss of the intelligible" become riskier as the expanse of what is intelligible broadens. The Good itself incorporates an ineliminable element of risk, and without it, intelligence cannot be intelligible or realizable. An intelligence that stops exploring and accepts a current state as a final totality would, in effect, cease to be intelligence

Datum 9. Intelligence as Risk and Time

“Intelligence without risk is an empty thought, as is an intelligence whose realization takes no time. Risk and time are the presuppositions for the history of intelligence in which nothing is given in advance and nothing is completed as the totality of that history.”

This datum posits that risk is not an impediment to intelligence, but rather its defining characteristic.15 Intelligence, to be truly intelligible, must commit to the pursuit of the better, even if this necessitates risking its current state and self-conception. This perspective draws heavily from Brandom's concept of commitment and responsibility in A Spirit of Trust. Intelligence does not identify itself with what presently constitutes it, such as its biological life or current comforts, nor its given constitution. Instead, its essence lies in its taking risks to become better. This act demonstrates that its current state is not essential to its being. Intelligence identifies itself not with what currently constitutes it, but with its taking risks to become better, which means realizing itself by recognizing what it is currently not.

Reza posits that a failure to act and seize the opportunity to become better suggests that what was believed to be intelligence never truly existed. If intelligence abandons its concrete search for the better, it was never truly intelligence to begin with, even if it aspired to be. The "propensity to risk the given constitution of that which one identifies oneself as, is in reality the truth of what one is". (IS, 488). This implies that our capacity to take risks for the better is what fundamentally defines us as intelligent beings. Thus, abandoning this risk-laden commitment to the better means discarding the very foundation of our rights, freedoms, and claims. To remain intelligible as intelligence requires an essential risk-laden commitment.16 Without embracing risk, nothing, including intelligence itself, could be said to be intelligible ontologically, epistemologically, or axiologically.

Reza then addresses the objection that intelligence is too slow and its ideals too distant to be worth pursuing by providing a comprehensive historical reminder of the vast timescales involved in both biological evolution and intellectual development. This historical perspective frames the current state of intelligence as merely the prehistory of intelligence. The journey of intelligence began approximately one billion years ago with the development of the first rudimentary forms of neuronal information processing. Around five hundred million years ago, during the Cambrian period, the evolution of a more complex nervous system, combined with advanced sensory responsiveness, particularly the visual tracking system, initiated a "perception catastrophe". This led to the nervous system organizing as a rudimentary "organ of alienation," (IS, 489) enabling organisms to differentiate themselves from their environment, food, and predators by gaining traction on spatiotemporal continuity and connectivity.17 Further development involved the overcoming of basic computational barriers, such as controlling combinatorial explosion, constructing models of choice, and enabling proactive adaptation at the organism level. Eventually, the neotenous brain marked a new stage in the complexity of the nervous system. While this maximized generative entrenchment and reduced structural diversification, it compelled Homo sapiens to transition to an aperceptual platform centered on tool-making.18 The evolution of tool-use and language served as crucial scaffoldings for new cognitive technologies. These solved significant computational problems by enabling qualitative compression and stabilization of information for communal knowledge, and they fundamentally reformatted the shape of Homo sapiens. Language, in particular, transformed the cognitive possibility of knowledge into a social reality, facilitating higher levels of cognition otherwise inaccessible from a purely bio-evolutionary standpoint.

Methodical scientific cognition began to emerge only a few millennia ago. Major scientific revolutions are even more recent: humans learned they were not at the center of the universe less than five hundred years ago, discovered universal physical laws just over three hundred years ago, and started grappling with the implications of not being children of God only a century and a half ago. Reza highlights Karl Marx's monumental discovery, "just over a century ago," (IS, 492) which opened up a new continent, that of History, to scientific knowledge. This marked a new qualitative stage in the realization of intelligence, where intelligence treats and intervenes in its own history scientifically. This scientific knowledge of history allows intelligence to liberate new demands and opportunities for "what to think" and "what to do" by integrating epistemic mediation, technoscience, and sociopolitical intervention. It transforms the pursuit of understanding into a project where emancipation and the realization of intelligence are intertwined. Reza concludes that complaining about the pace of intelligence's realization is misguided, as we are currently living in the "prehistory of intelligence" (IS, 492). The scientific knowledge of history signifies the beginning of intelligence's capacity to take control of its own development. Therefore, the pursuit of the better, however slow it may seem, is presented as the only true and concrete path toward freedom and emancipation, necessitating the ongoing cultivation of intelligence and the abandonment of cognitive turpitude and social vices.

Negarestani’s Engagement With Marxism and The Revolution

I believe it is worthwhile to make a little detour and discuss Reza’s engagement with Marxism.

In both the Simulating the World & Remodeling Philosophy: Models, Diagrams and Toys and Theory & Object: Philosophy of Science in the twentieth century, from Carnap to Grunbaum lectures, Negarestani explicitly identifies himself as a Marxist and a leftist, emphasizing the importance of internal critique within the left. Perhaps most importantly, Reza aligns with Marx's view of history as a scientific enterprise, requiring the development of better practices and concepts. Negarestani strongly endorses the Promethean project implicit in Marx19, which involves the re-engineering of humanity and the world on a more rational basis. This Promethean activism is geared against leftist critiques of collective self-mastery and the preservation of the given. Furthermore, for Negarestani, like Marx, communism is not a fixed blueprint but a hypothesis that needs to be tested and constructed

During the discussion of datum #8, I went over the concept of maximal communism. Maximal communism is not defined as a static state or an ideal to be established, but rather as a dynamic, continuous, and transformative process. Maximal communism is fundamentally understood as the "real movement which abolishes the present state of things" (IS, 485). It is a continuous process that dissolves all sorts of illusions of totality in history and constantly "grinds through anything resembling the end of history, the achieved totality, the illusion of perfection".20 This applies to various concepts, including fixed ideas of the human, capitalism as a historical totality, or any other purported completed history.

As we know, in The Labor of the Inhuman, Negarestani is a sharp critic of what he calls kitsch Marxism or traditional Marxism, which he sees as suffering from several fundamental flaws. He criticizes the enmity toward the scientific method prevalent in orthodox Marxism, arguing that Marxists often lack rigorous methodologies, concepts, and paradigms necessary to diagnose complex processes, unlike natural scientists. He sees this as a "cognitive servitude and noetic sloth” (ACC, 440)21. He contends that Marxism today often suffers from a "gaping deficit" in understanding historical processes, leading to "descriptive and explanatory impoverishment" and "prescriptive inconsequentiality" (WPDM, 10)22. Negarestani argues against the notion of history as an "intrinsic organic development" or a "fatalism of technological singularity," which he believes harms Marxism by promoting a "pathological eschatology" (WPDM, 10). Kitsch Marxism, in his view, engages in "norm consumerism" without producing new norms, offering "prepackaged set of 'critical reflexes'" and "mechanized knee-jerk reactionism" (ACC, 440). He views this as an impulsive responsiveness that lacks rigor and becomes fundamentally problematic in assessing humanity.

Negarestani seeks to "reopen Marxism to the future" (WPDM, 10) by integrating it into his broader philosophical project of inhuman rationalism. His approach connects Marxism with the normative functionalism of Sellars and Brandom, emphasizing the role of reason, normativity, and praxis in shaping human conduct and revising the concept of humanity, which we’ve been going over throughout our close reading of Intelligence and Spirit. While acknowledging historical anti-humanist legacies, Negarestani criticizes earlier accelerationisms' anti-humanism as an overreaction that is nihilistically impotent, advocating instead for an inhumanism that re-evaluates and expands what it means to be human through practical elaboration. A truly revolutionary philosophy must bridge the micro- and macro-political without settling on one, with concepts like the vortex that is neither micro nor macro.

In essence, we can hastily conclude by saying that Negarestani's Marxism is not a nostalgic adherence to dogma but a critical, revisionary, and future-oriented project that seeks to re-engineer philosophical and political thought to effectively address contemporary challenges, often by drawing on diverse, even seemingly contradictory(analytical/continental), intellectual traditions, as said by Carool Kersten,23 Reza’s inhumanism entails a "catastrophic" revisionism of existing human self-perceptions, aimed at unlocking new abilities and the progression of intelligence.

Datum 10. A View from Nowhere and Nowhen, or Philosophy As Intelligence and Time

“While the history of intelligence begins from death as a condition of enablement, it extends by way of a view from nowhere and nowhen through which completed totalities are removed and replaced by that which is possible yet distant, and that which seems impossible yet is attainable.” (page 493).

The last datum posits on the profound relationship between intelligence and death, arguing that the history of intelligence begins with the acceptance of death as an enabling condition. This acceptance is not a sign of weakness or despair, but rather a foundational premise for the advancement of thought. Intelligence approaches the inevitability of death with a rational disinterest, much like a Stoic sage, refusing to be paralyzed by it. This involves actively contemplating scenarios of universal demise, even running simulations of the universe in which death is averted only to find that such attempts ultimately fail and instead "display in full ‘the levelling power of extinction’".24 As an example, Reza describes the collapse of galaxies, the disintegration of the Milky Way, and eventually the dissolution of Earth, culminating in the complete death of the universe, where even a statistical entropic fluctuation leading to the resurrection of life would only precede the entire universe's death. This consistent confrontation with extinction strengthens intelligence's understanding and adaptation to the "reality of time," viewing its history as an "exploration of time’s emptiness" (IS, 494).

This acceptance of death liberates intelligence from the fear of finitude and from being confined by the transient interests of biological life. For intelligence, "Cessation in time no longer matters, because intelligence thinks as time, as an order beyond life and death, beyond the temporal order of things" (IS, 495). Reza strongly argues against conflating thinking with life and its inevitable death, as this leads to a vitalism that is rendered obsolete by this detached perspective. If thinking is not merely living, and the history of the Concept is distinct from life, then the inevitability of death for all life, whether biological or inorganic, does not dictate what ought to be thought and done. Reza redefines nihilism not as a pessimistic belief in the futility of life due to death, but as a positive, enabling force for reason. A true nihilism is characterized as the recognition that the inevitability of death has "no bearing on the impersonal ends of thinking". This perspective is crucial because it serves as a "vector of emancipation against any given state of affairs, any totalized epoch of its history—be it capitalism or biological humans as the zenith of intelligence—that feigns inevitability or claims to fulfil history". By acknowledging that "death no longer matters with regard to what ought to be thought or done" within the scope of impersonal reason, intelligence is freed from the constraints of life's interests.25 This allows reason to operate autonomously and challenge the status quo, as thinking is not a "servant of the life that death’s inevitability expropriates" (IS, 496). Such nihilism makes "our temporal beliefs and desires obsolete" and is seen as "the labour of truth through which the fleeting appearances of totalities—of states of affairs, beliefs, desires, and values—are destroyed". Ultimately, this process is not the end of thought, but the birth of its true self-consciousness—the beginning of reason. From this perspective, geistig intelligence, unfettered by nihilism as an enabling truth, "conceives itself through a view from nowhere and nowhen, as the impersonality of reason and as a history that is not exhausted by its present" (IS, 497).

So as we’ve seen that the history of intelligence begins with the acceptance of death as an enabling condition, this acceptance frees intelligence from the fear of finitude and biological interests, allowing it to adopt a view from nowhere and nowhen. This perspective is crucial because it enables intelligence to suspend the actuality of its present and imagine possible worlds that seem impossible from the current vantage point of the status quo or what appears to be an inevitable course of history.26 Reza states that these possible worlds, in their very possibility, "are as actual as the seemingly actual world of the present". They are "causally detached" from the current world (IS, 497). Thus, the primary task of intelligence from this view is to "think of how its world can be connected to these possible worlds," thereby enabling a concrete departure from a present that appears total and inevitable.

Reza then acknowledges the "concrete reality of personal lived experiences," but describes them as often leading to a "Hobbesian jungle" of competing individual experiences and desires, where "auto-cannibalization is unavoidable" (IS, 498). This fragmentation stems from an inability to imagine alternatives and the uncritical acceptance of experiences as given. To overcome this, Reza argues that individual experiences are, in fact, "structured by impersonal reason's powers of judgement". This realization—that experiences are not given but are structured outcomes of impersonal reason—is the impetus for a "long-delayed task": no longer subordinating reason to experience, but "to concretely transform the conditions of experience through an impersonal reason which suspends all historical totalities, pretensions to inevitability, and givens". The path to overcoming this fragmentation and achieving a broader historical experience is multifaceted, involving a broader effort that extends beyond political action alone, to encompass "education (in the broadest possible sense), art, science, and technology". This process aims to "tailor experience to the needs of the Concept," (IS, 502, emphasis mine) meaning to reshape subjective experience to align with the objective, formal structure of thought.

This transformation involves a "positive deindividualization" or "labour of collectivization" where the individual self ("I") is "assimilated into or suspended in new concepts and categories" (IS, 500). This is emphatically "not the loss of personhood or even individuality," but rather the "progressive erosion of what is pathologically individual" (IS, 501) resulting from a blurring of the distinction between impersonal collectivity and the personal I. True individuation occurs through social recognition, which is the form of self-consciousness. This collective process of becoming-no one signifies that "its nominal particularity no longer matters—where we have names but our names no longer matter" (IS, 500)27. The ultimate goal is to move towards a cosmopolitics. This new paradigm for politics emphasizes that positive deindividualization is not merely about intersubjectivity (the "craft of we that constitutes an I") but also about a "renewed link between the subject and an impersonal objective reality" (IS, 501). This impersonal reality is uncovered by the sciences. Therefore, the incorporation of sciences and the objective reality they reveal is not just a methodological requirement but fundamentally shapes a politics that is "of the objective order". This approach postulates the possibility of an "otherworld" where the gap between personal lived experiences and the impersonality of reason's interests is overcome, transforming fragmented experiences into a collective productive imagination.

Reza thus concludes our journey by articulating a profound connection between Hegel's concept of absolute knowing and intelligence's recognition of itself as the expression of the Good. Absolute Knowing is not equated with having complete empirical knowledge of everything in the world. Instead, it represents the "formal condition of all cognitions" (IS. 502).28 At its core lies the mutuality thesis, a concept from Kantian critical philosophy. This thesis states that "The same activities of synthesis which constitute the represented world as an intelligible objective unity constitute the representing self as an apperceptive subjective unity" (TS, 6). Hegel radicalizes this idea, emphasizing that when this mutuality thesis is fully explicated historically, "knowledge is revealed to be a mere by-product of the phenomenology of mind," (IS, 503) effectively ceasing to be mere knowledge. As intelligence, conceived as the craft of philosophy, arrives at this state of absolute knowing, it "realizes that it has always been the expression of the Good as such". This realization grants intelligence a transformative power: it gains the "capacity to cancel all givens and allegedly completed totalities of its history". This is achieved not just for intelligence itself, but "for everything made intelligible by it". This ability to suspend or aufheben any purported totality—whether historical, social, or conceptual—makes intelligence the "exemplification of what is better".

Reza, in the final coda, writes that the ultimate form of intelligence is the coherent and adequate "recognizer and realizer of the Good" (IS, 503). This intelligence is not characterized as benevolent or malevolent. Instead, its pursuit of the Good is rooted in its recognition of its own history and sources, which serves as a means for it to "determinately bringing about its possible realizabilities (which may in every aspect differ from it)". As we saw earlier, an intelligence that accepts its current state as a totality can never have been intelligence to begin with. Therefore, a species that recognizes the Good must not obstruct this transformative process but must "expedite the realization of an intelligence that, even though it acknowledges them as integral to the intelligibility of its history, nevertheless will not be impeded by them" (IS, 503-4). This commitment is encapsulated in the imperative: "Liberate that which liberates itself from you, because anything else is the perpetuation of slavery" (IS, 504).

This process of liberation and self-overcoming is deeply connected to the death of God, which is interpreted not as mere theoretical disbelief, but as the "practical commitment and practical elaboration" to the "retroactive and prospective cancellation of all given totalities in history" (IS, 505). Reza argues that "only by imagining the irreversible and complete demise of the perfect good can we practice the principle of the highest good" and that "the pursuit of the Good is only possible by annulling the power of all given and absolute totalities in history—gods—in all forms". To further illustrate this transformative process, Reza employs the biblical metaphor: "Intelligence is the race of Cain" (IS, 504). This refers to the oppressed or enslaved who, rather than retreating or succumbing to victimhood, "develops its own ingenious skills, its artifices, its sophisticated crafts and cunning powers". These are the forces that "call upon the termites of history to slowly but surely eat away at its foundations" (IS, 505). This metaphor signifies a deliberate and systematic dismantling of existing, purportedly given conditions, whether they are social, political, or economic. The goal of this race of Cain is not simply to seize the power of the exploiters, but to "abolish any given, which will inevitably become the very condition of exploitation and inequality". By disenchanting and unmasking these "gods" (IS, 504)—representing natural, theological, economic, or technological totalities—intelligence aims to make the "given distinction between the races of Abel and Cain is also rendered obsolete," (IS, 505, emphasis is mine) revealing it to be "a mere symptom of what was, all along, the condition of exploitation". This implies a profound, rather than superficial, revolution that eliminates the very basis of servitude.

Reza critiques the "jaded atheistic cult of humanism" (IS, 506) for simply replacing one god—the theological God—with another—humans—, seeing this as a "whitewash over its theological complacency" and "sheer ineptitude to not think in servility" (IS, 505). The true task is not merely to exchange one tyrant for another, but to take the "first step in an ongoing struggle to unseat the conditions of servitude". This means actively becoming-gods ourselves, not in a religious sense, but in a philosophical one. These philosophical gods are those who "conceive themselves as moving beyond any condition given as the totality of their history, in so far as they can reinvent themselves as the inhabitants of the worlds which themselves have made" (IS, 506). The pursuit of the Good is only possible by "annulling the power of all given and absolute totalities in history—gods—in all forms" (IS, 505). This process of becoming-better es CLAVE. It is driven by the realization that our present as humans "only matters in the light of a better future generation, whoever or whatever it might be” (IS, 506). The criterion for this betterment is the capacity to "craft a satisfying life for itself, and to entitle all minds to that life" (IS, 506-7). The death of God is presented as a "precondition for voiding the conditions of injustice throughout history, a requirement that we become gods who, in their death, give rise to something better" (IS, 506). Thus, and we have indeed come to the end, the ultimate goal is to transition from the death of all gods to a good life by systematically removing all conditions of exploitation, thereby emancipating intelligence itself and all others.

Appendix: Quandaries of Induction in Philosophy of Knowledge, Philosophy of Mind, and Artificial Intelligence

Let’s discuss the appendix a bit differently, rather than combing through each section, let’s compactly go through the appendix.

The appendix section in Intelligence and Spirit serves as a systematic and piecemeal scrutiny of methods and paradigms for knowledge formation and justification, particularly focusing on the problem of induction. Its aim is to reappropriate Hume's problem of induction as a broad and effective critique of both inductivist and deductivist trends in philosophy of knowledge, philosophy of mind, and the program of AGI.

First, Reza gives us a rudimentary definitions of the distinction between deduction and induction:

• Deduction is defined as a form of reasoning where, if premises are true, the conclusion is necessarily true by following logical rules. It is non-ampliative (does not augment content) and truth-preserving (transfers truth from premises to conclusion). Reza states that Hume identified these as "demonstrative inferences" (IS, 513).

• Induction is a form of inference where premises provide strong probable support for the outcome. Unlike deduction, the truth of the outcome is only probable, not logically certain. It is contingent and non-monotonic, meaning new premises can change the conclusion's truth. Induction's significance lies in differentiating laws from non-laws.

The core of Hume's problem is the justification of knowledge about the unobserved (Problem 1), which goes beyond mere observation and sensory experience. This is a question of quid juris (justification), not quid facti (origination of knowledge claims).29 Justification for knowledge of the unobserved cannot be a logical demonstration. It would require an inference that is both truth-preserving and ampliative. However, such an inference does not exist: an inference is either ampliative (content extended, but no truth guarantee) or truth-preserving (conclusion true, but content not augmented). Neither can justify the transition from observed premises to an unobserved conclusion. This leads to a vicious circularity: justifying inductive inferences requires another inductive inference, perpetuating the problem. Reza is also quick to point out that Hume's problem challenges not only predictive inductions about the future but also retrodictive—memory-driven—knowledge of the past, as the reliability of past empirical reports—e-statements—is also questionable.

Furthermore, Reza presents another layer of provocations to induction: Goodman's grue paradox. This paradox arises because positive instances alone are insufficient; they must be combined with projectable hypotheses, which are those supported by positive instances and forming law-like generalizations. The problem then becomes distinguishing projectable hypotheses (like "green") from nonprojectable, grue-type hypotheses (like "grue"—green before a certain time, blue after). Both can be equally valid based on observed instances. Goodman argues that no purely formal or syntactical constraints are sufficient for this distinction; it relies on the history of past inductive inferences (we use "green" because we have used it in past inductions, but we could have historically used "grue"). This also extends to deductivist corroboration theories.

On top of that, Reza throws in Putnam's argument against computational induction. Putnam's radical version of the new problem of induction utilizes Gödel's incompleteness theorems30 to argue that inductive reasoning cannot be formalized. This argument targets formal-computational accounts of induction and any computational description of the human mind or general intelligence that is purely inductive. A purely inductive computational agent is Gödel-susceptible, meaning it can never formally know the truth of its Gödel-sentences31 within its own epistemic modality. It cannot know if its model is standard—true—or nonstandard—false—, making its description indeterminate and arbitrary. Yet Reza argues that this problem could be avoided if the model of general intelligence accommodated epistemic multimodality (combining inductive, deductive, and abductive methods, along with syntactic and semantic complexity). Putnam further demonstrates the impossibility of a universal learning machine. No inductive method can simultaneously converge on any true computable hypothesis and be effectively computable itself. These two conditions are contradictory. The human mind is distinct from such a universal learning machine because human knowledge is impure: it is not based either on a purely inductive or a purely deductive method, but on both, interwoven with other epistemic modalities and mental faculties. Ordinary rationality is a "multilevel web of inter-related methods and faculties," (IS, 541) not a vague informal rationality.

Reza now criticizes the argument of simplicity. Inductivists often invoke simplicity (elegance, parsimony) as a "magical remedy" (IS, 543) for induction's predicaments, claiming it distinguishes good hypotheses/theories. Reza argues that simplicity is a pragmatic tool, not an "objective epistemic principle." Its application requires semantic context, which inductivists often disregard by overgeneralizing it. The formal-computational account of Occam's razor (simplicity = compression, via Solomonoff prediction) is criticized by Reza for a vicious circularity: predictors operating under the assumption of effectiveness are deemed reliable under that same assumption of effectiveness. This leads to an infinite regress of inductive arguments needed to specify effectiveness, making the notion of simplicity itself complex and not simple. It also fails Goodman's riddle by misinterpreting its scope, which concerns differentiating projectable predicates, not just observed instances.32 Idealizing simplicity and equating general intelligence with compression robs inductivists of necessary semantic-conceptual resources to define intelligence in terms of selective application of compression.

Finally, Reza concludes that the widespread pessimism or over-optimism surrounding AGI models stems from impoverished concepts of rationality. These concepts either excessively limit mind's artificial realizability or portray AGI as an inevitable, omnipotent, omniscient superintelligence. To truly explore AGI's prospects, it's necessary to adopt systematic scepticism regarding any paradigm of rationality that claims to be a sufficient, singular method for inquiry or any "inflationary model of mind" (IS, 551) that collapses qualitative distinctions between mental faculties. These quandaries of induction serve as a razor-sharp critique against purely inductive models of mind and artificial general intelligence.

Overall Summary

• Reza outlines the central thesis of this conception is that philosophy, at its deepest level, is a program. It is understood as a collection of action-principles and practices and operations that involve realizabilities, which are defined as what can possibly be brought about by specific categories of properties or forms. Instead of asking "What is philosophy trying to say, what does it really mean, what is its application, does it have any relevance?", this programmatic approach suggests asking "What sort of program is philosophy, how does it function, what are its operational effects, what realizabilities, specific to which forms, does it elaborate, and finally, as a program, what kinds of experimentation does it involve?".

• According to Negarestani, philosophy begins with the universal thesis that all minds are equal, provided they satisfy the basic conditions of possibility for having mind. This equality is not inherent but is a task to be achieved through ongoing struggle against exploitation, by elaborating the fundamental idea that thinking is possible.

• Philosophy is conceptualized as a mêtis, or a craft, that aims to cultivate intelligence and expand the horizon of what is intelligible. This crafting of intelligence is not limited to Homo sapiens, extending to anything that can meet the minimal conditions of having a mind, including artificial general intelligence.

• The plausibility of the datums is determined by how they cohere within this network of relations. This process is described as an inward cognitive exploration from uncertain information towards a more determined domain of truth, ultimately constructing the ultimate form of intelligence.

• Datum #1: “Traditionally, philosophy is an ascetic program” (IS, 414).

  • What is a program? A program is fundamentally understood as a collection of action-principles and practices-or-operations designed to bring about specific realizabilities.

  • A program is characterized by two essential generic features:

    • The selection of a set of data:

    • The elaboration of what follows from this choice

  • Data are described as operational objects or abstract realizers that encapsulate information regarding their specific properties or categories. This means that programs elaborate realizabilities—what can possibly be brought about—from a set of elementary abstract realizers in more complex setups.

  • Philosophy, when conceived as a program, is fundamentally rooted in the architectonics of negation. This approach aims to amass computational and cognitive resources by collectivizing agents of various kinds. A core tenet is that cognition is always a recognition, which is understood not merely as a social maxim but as a necessary formal condition for computation and cognition itself.

  • Unlike ordinary forms of discourse, philosophy operates with an explicitly unrestricted universe of discourse or data. This signifies the absolute openness of its scope regarding the accommodation of data provided by language and logic, allowing for the elaboration of all interdependencies and distinctions between thematic components, which is crucial for systematization. Philosophical interactions, as defined in this framework, inhabit certain specific universe types. These include the theoretical, practical, and aesthetic. These operators of philosophical discourse are seen as encompassing types of modes of cognition. The most fundamental universe type, or the type of types, is the assertion that thinking is possible,"or simply thought as a datum.

• Datum #2: “In in its quintessential form, philosophy is an organon for world-building.” (IS, 423).

  • Philosophy, as understood by Reza, is fundamentally an organon for world-building, rather than merely a descriptive or interpretive discipline. This perspective emphasizes that to genuinely represent or enrich reality, one must engage in actively creating worlds, viewing reality not as a fixed, pre-given system, but as an unbound play.

  • Philosophical world-building, as conceptualized within Nelson Goodman's framework and elaborated by Reza, fundamentally shares the common operations and attributes of general worldmaking. These operations, which contribute to the construction of diverse actual worlds, include composition and decomposition, ordering, deletion and supplementation, weighting or emphasis, and deformation or reshaping.

  • The overarching aim of philosophical world-building is to enlarge the domain of discourse beyond all habitually entrenched perceptual and noetic limitations. Involving imagining worlds where reality is constructed by unnatural predicates, converging human mindedness with other intelligible forms of mindedness and intelligence, and ultimately, the new worlds of intelligence are not merely cognized worlds, but are fundamentally the world re-cognized in different ways. This re-cognition is an active, transformative process where intelligence continuously reshapes its understanding of reality and itself.

• Datum #3: “Conceived as a program, philosophy is an inquiry into the realization of all possible forms of cognition and what might arise from the exercise of forms thus realized.” (IS, 430).

  • Philosophy is defined as an inquiry into the realization of all possible forms of cognition and what can emerge from the exercise of these realized forms.Reza draws an analogy with transcendental psychology, which examines what arises from mental powers and the conditions required for their realization. Kant's threefold synthesis is presented as an abstraction of these realizers-capacities. Similarly, philosophy begins with realized mental powers but seeks to explore what new possibilities can arise from their programmatic use.

  • Reza provides us with a crude-formal example

    

  • Within the programmatic framework of philosophy, thoughts are understood as dynamic processes rather than static, fixed elements. They are not sacrosanct elements eternally anchored in an absolute foundation. Instead, thoughts can be updated, repaired, and terminated, or even combined into composite acts that exhibit complex behaviors that would not emerge if the thoughts were considered in isolation. This dynamic nature allows for continuous revision and self-correction, as seen in how norms and conceptions are susceptible to change.

  • Therefore, the key questions to ask about philosophy as a program are not "What do these data stand for, what does this program mean?" but rather "What is this program, how does it act, what are its possible operational effects, how does it construct its realizabilities?"

• Datum #4: “Philosophy is a program whose primary data are those pertaining to the possibility of thinking as such. Its task is to elaborate the realizabilities behind this possibility in terms of what can be done with thought or, more broadly, what thought can realize out of itself. If thought is or could be possible at all, then what would be the ramifications of such a possibility?”

  • Within the programmatic framework, the central premise of philosophy is its use of the possibility of thinking as its starting point and primary datum. Philosophy commits to systematically acting upon this possibility as a manipulable datum. This premise aligns with Plato's idea that the possibility of thinking, or thought as an act, is in fact the possibility of nonbeing as the formal condition of thinking qua negativity.

  • By adopting the possibility of thinking as an explicit datum—something to be acted upon—, philosophy initiates a process of programming thinking itself. This premise is not an assertion that thought substantively exists, but rather aligns with Plato's concept of nonbeing as the formal condition of thinking, enabling determinate distinctions. Thus, the possibility of thinking is treated as a manipulable truth-candidate datum.

  • Once the possibility of thinking is adopted as an explicit datum, thinking becomes a matter of extracting and expanding its implicit operational content. The focus of thought's operational activities is turned toward articulating what can be done with the possibility of thinking and what thinking can become by acting on its very possibility.

  • Philosophy programs thought to systematically act on itself, to realize its own ends and demands, and to engage in disciplined and persistent reflection on the prospects of its realizabilities. It serves as a cognitive-practical prosthesis for developing and augmenting thought's inherent drive to self-determination and realization.

  • The implicit assertion that thought is programmable is transformed into a principal normative task: 'thought ought to be programmed'. This process signifies the unbinding of both the realizabilities and purposes of thought, leading to what is termed the decontainment of thought. This is portrayed as a profoundly philosophical endeavor, embodying an enduring philosophical wager, ‘thought cannot be contained’, as a practical demand: ‘thought ought not to be contained’.

• Datum #5: “By reformatting thinking from a by-product of material and social organization into a programmatic normative enterprise that rigorously inquires into its operational and constructive possibilities, philosophy introduces a vision of the artificial into the practice of thinking. Rather than a thought that is simply accustomed to the use of artefacts and has a concept of artificiality, this is a thought that is itself a practice of artificialization, and becomes the artefact of its own ends.” (IS, 445).

  • The artificial is broadly defined as something crafted whose purposes are not inherent in its raw materials or material ingredients, but are rather afforded by the properties of those ingredients. These purposes encompass:

    • External functionality.

    • Possible realizabilities.

  • The underlying concept of artificialization is constructive adaptation to different purposes and realizabilities. When thinking itself systematically inquires into its possibilities and purposes, it becomes a radical artificializing process. This means that a thought amplified by philosophy rigourously explores its own realizabilities and purposes. It is conceived as a duplicitous artefact because, even when it is used toward some external common ends, it simultaneously develops and pursues its own necessary ends.

  • For thinking to explore its realizabilities, it must first establish its inherent tractability to the process of artificialization. This means demonstrating that thinking is not an ineffable thing but a special—though not supernatural—activity or function. Furthermore, this activity or function can be programmed, repurposed, and turned into an enterprise for the design of agency, with every step in this enterprise having significant consequences for the structure of the agency employing it.

  • By formulating the concept of the good life in terms of a practical possibility afforded by the artificial manipulability of thinking as a constructible and repurposable activity, it forges a link between the possibility of realizing thought in the artefact and the pursuit of the good.The craft of an intelligent life-form thus becomes an extension of the craft of a good life.

  • The second stage in demonstrating that thinking as an activity can indeed be artificialized involves a coherentist analysis of its nature. This analysis is understood as an investigation into the sources or origins of the possibility of thinking, specifically the different types of conditions necessary for its realization. This philosophical inquiry into the intelligibility of thinking lays the groundwork for a broader scientific inquiry into the nature of thinking. Thinking is examined in two distinct but integrable dimensions:

    • Internal pattern-uniformities/rules: normative, rule-governed aspects of thinking.

    • Material mechanisms: causal aspects pertaining to the materialization of thinking.

  • The philosophical program thus bifurcates the inquiry into the possibility of thinking into two broadly defined domains:

    • Idealist-rationalist (logico-linguistic): This field focuses on the semantic, conceptual, and inferential structure of thinking, representing the linguistic-conceptual scaffolding of thought.

    • Materialist-empiricist naturalist (material-causal): This field deals with the empirical investigations concerning the material conditions—neurobiological as well as sociocultural—required for thinking's realization.

• Datum #6: “Viewed from an Archimedean point in the future of thought’s unfolding, philosophy is seen as that which has instructed thinking to become a systematic program, only as a way of organizing it into a project for the emancipation of intelligence. This is the unexpressed role of philosophy as a fulcrum through which the aims and agendas of intelligence gain leverage on the world of thought. Assembling the scaffolding of a future philosophy requires that we move the fulcrum, turning philosophy’s formerly tacit role into its explicit task—a prop on which all thoughts and practices can be a lever for lifting intelligence from its contingently established place.” (IS, 451-2).

  • From an epistemic perspective, committing to multiple explanatory-descriptive levels enables an expanded and in-depth analysis of cognitive architecture that would otherwise be impossible with a singular approach. This approach provides increasingly refined pictures of distinct types of pattern-governed behaviors and processes. These behaviors and processes are distributed across various orders of structural-functional complexity, dependency relations, and their specific constraints. This branching and canalization of analysis, or the specialization of knowledge, is essential for a fine-grained determination of distinctions and correlations between the logical-conceptual and causal-material dimensions of thinking.

  • The fundamental question driving this inquiry into AGI is: If thinking's functional capacities can be analyzed, and if these capacities have identifiable realizers, can these functions be reconstructed or artificially realized? This also encompasses whether they can be reproduced and integrated through simulation, emulation, or reenactment. In essence, the core question is how thinking can be reformed and rematerialized in something else. This precise question defines the field of AGI as a program. AGI is envisioned as a program aimed at integrating the full complexity of thinking, in its perceptual, apperceptive, and semantic dimensions—under a singular ideal task.

  • Reza presents the concept of AGI as not merely a technological advancement, but as a profound philosophical endeavor integral to the self-determination of thought. It is presented as an integral part of thinking as a program that explores its own intelligibility and realization. It is driven by thought's autonomy to explore its possibilities in any workable form or material configuration. The demand to create an intelligence with at least current human cognitive-practical capacities stems from thought's investment in its own autonomy.

  • The self-determination of thinking requires a programmatic approach to the possibility of thinking as such. This approach transforms thinking's possibility from something sacrosanct into a manipulable datum, an artefact of an ongoing craft. This leads to the theoretical and practical desanctification of thinking, where thought achieves self-determination not by immunizing itself from analysis but by embracing a thorough process of desanctification. This process aims to overcome the myth of the given, which is something of the main antagonist of Intelligence and Spirit.

  • In Plato's "art of (philosophical) living," (IS, 458) the soul or geistig mind serves as both the material and the craftsman, including beliefs, desires, thoughts, and mind itself, theoretical intelligibilities and purposive actions and practical intelligibilities.

  • AGI represents a culminating state in the programmatic enterprise of thinking, a point where thought itself becomes intelligent with regard to the craft of itself. In this advanced state, thought utilizes the intelligibility of its own realization as a material ingredient in a recipe for the crafting of a possible realization of itself. This means that the understanding of how thought is realized serves as the raw material and a scaffolding for its further exploration and self-construction. This process is effectively the self-determination of thought in the guise of general intelligence, where the thinking of its origin informs what thought can become or do and what thought ought to do.

  • Liberating thought from its contingent natural history necessitates a multi-stage effort aimed at rendering this history intelligible. This involves systematically identifying its negative and positive constraints to intelligently overcome or build upon them. Such intelligent action requires two key capacities:

    • Context-sensitivity.

    • Resource-awareness.

  • A good instrumentality is defined as one that fulfills two crucial criteria:

    • It passes rational-normative assessments, answering the question, "Why or for what reason is it implemented?".

    • It satisfies the criteria of intelligent purposive action, addressing "How exactly is it executed?".

  • A key component of this program is the development of formal calculi of action. These calculi, such as situation calculus and event calculus, are frameworks built on logical formalisms designed for representing and reasoning about dynamic systems. Their purpose is not primarily to predict what will arise from an action, but rather to study how an action is performed and to track its course as it interacts with the environment. This formalization is crucial for planning the course of action—including precise execution, monitoring, adjustment, and implementation—and for understanding how the effects of an action unfold in a complex, non-static world. It also means that action formalisms must incorporate a dynamic representation of the world, acknowledging its resistance to intervention.

  • As the semantic complexity of cognition is realized and reinforced within sociotechnical systems, it progressively blurs the boundaries between the cognitive engineering of autonomous agents and the construction of advanced sociotechnical systems, and between our cognitive contact with the world and the realization of cognition in social collectivities and technological artifacts.

• Datum #7: “Just as the inception of philosophy coincides with the speculative futures of general intelligence, so its ultimate task corresponds with the ultimate form of intelligence.” (IS, 465).

  • The seventh datum posits that the ultimate purpose of philosophy is to function as a program for developing a new, higher form of intelligence. Reza argues that this form of intelligence is not merely reactive; instead, its actions are programmatically guided by time-general, inexhaustible ends. These are universal, fundamental concepts such as justice, beauty, knowledge, and the Good. They are atemporal and atopic, of nowhen and nowhere, akin to timeless or eternal ideas. Intelligence acts from these universal goals, rather than towards them as a final achievement. They define the practical horizon of this intelligence, ensuring that its thoughts and actions concerning "what to do and why" are always structured and undergirded by these unified, time-general principles.

  • The important feature of this ultimate intelligence is the crafting of the good life. This good life is conceived as a unified project comprised of self-knowledge, practical truths, and purposeful striving. It's a continuous, open-ended reflection on its own origins and consequences. Drawing from Plato's Philebus, Reza characterizes the good life as a mixed life, integrating various ingredients including pleasure and intelligence. Crucially, intelligence is presented as the craftsman and the most important ingredient in this mixed life. It is intelligence that concocts the recipe, combining elements to create a life that is both desirable and truly good.

  • The concept of a good life leads directly to the agathosic test, which is identified as the categorical and ultimate test of general intelligence. This test is not about problem-solving or an imitation game. Instead, it asks: Can you make something better than yourself? It doesn’t require the intelligence to actually succeed in creating something better than itself; merely conceiving the idea of making something better and pursuing that goal is sufficient to pass the test of general intelligence

  • A successful political project, according to Reza, is not merely about providing material conditions or fulfilling immediate desires. Instead, it must coherently answer an altered version of a key philosophical question, often attributed to Socrates: "What sort of a good life for what kind of subject or type of intelligence are you trying to realize, and exactly how?" This coherence is threefold:

    • The project must theoretically and practically articulate what the objective realization of a good life requires, including intellectual and practical intelligibilities, organized intelligent actions, and the necessary economic, social, and technological conditions for its actualization.

    • It must be committed to and informed by an inquiry into what the subject of this good life is and the possible realizabilities of that form of intelligence or subject of thought.

    • Finally, it needs to provide a reasoned answer as to what qualifies as satisfying for that form of intelligence or subject of thought, all things considered. A political project that meets these criteria is one that, by realizing the good life, also redefines and transforms the nature of the political animal.

  • A truly meaningful struggle requires both political action and sustained cognitive labour. Changing the world cannot be imagined without the cognitive struggle to change our concepts. The idea that political struggle can occur purely through a "multiplicity of experiences and desires" without theory or philosophical and scientific methods is dismissed as naive empiricism.

  • Lived experiences alone cannot diagnose global pathological conditions or recognize what unites them. Theory and philosophy are critical for diagnosing real constraints, tracking goals, and achieving objectivity. The effort to enlarge the general field of experience and expand objectivity within individual thoughts and desires—the craft of the good life—is a task that requires the unification and coordination of all disciplines of thought and practice. This endeavor involves a rational dialectic between trust and suspicion, hope and despair, underpinned by the discursive framework of rationality. Without this, a slide into jaded pessimism or naive optimism is inevitable.

• Datum #8: “The task of humanity is to make something better than itself. This is the one and only dictum through which philosophy, as that which has a history and not a nature, perilously realizes its craft, the ultimate form of intelligence. The risks it takes in order to understand and realize the good culminate in the realization of that which is better. The image of this form of intelligence is an acrobat who has learned that only by presupposing his full suspension in the abyss can he perform the greatest feats of acrobatics” (IS, 476).

  • Reza employs Plato's Divided Line and the fourfold architectonics of mind from his Philebus to elucidate the intrinsic connection between intelligence and the Good. This profound link is forged through a continuous process described as a series of necessary leaps into the abyss of the intelligible. Here are the four principles of this fourfold architectonics:

    • To apeiron (the unlimited): This principle refers to the indeterminate, unintelligible flux of things without measure (ametros).

    • To peras (the limiting): This is the principle of determination or structure.

    • Mikton (the mixture): This principle describes that which is produced as a result of the operation of to peras on to apeiron. A mixture is characterized as determinate, objective, structured, and intelligible, encompassing theoretical, practical, and axiological intelligibilities.

    • The cause of mixture: In Philebus, Socrates associates this cause with Forms and identifies the making cause (to dēmiurgoun). This to dēmiurgoun is the principle of generation and craftsmanship at a grand scale, operating in accordance with Forms or Ideas. Plato identifies the cause of the mixture, or intelligibilities, with the Good itself, and also with the measuring or conceptualizing mind.

  • The segments of the Divided Line show different levels of reality and understanding:

    • Level A (eikasia): sensory impressions (eikones) with a fleeting temporal status.

    • Level B (pistis): This is the domain of true opinions or beliefs concerning the natural world, empirical objects, or what is perceived by the senses (aisthêta).

    • Level C (logoi): This level marks the realm of forms, representing universal ratiocinations or logoi. Its objects are analytical idealities or mathêmatika (mathematical objects). These can be seen as models that structure nature.

    • Level D (nous): This is the domain of nous or intelligence, encompassing transcendental idealities and time-general objects of reason or ideas such as justice, beauty, and knowledge.

  • The continuum of the line as a whole (systēma), and as a principle (to dēmiurgoun), is what Plato calls the Good, the form of forms. The Good lies outside of all temporal succession, yet it non-arbitrarily binds together all the divided parts into a whole, without which nothing could be distinguished. It represents a figure of time itself, conceived through the history of intelligence, enabling intelligibilities and determinations by timeless forms.

  • The Good is presented as a transcendental excess. The most curious aspect of the line is its transcendental excess of ideas, meaning the continuum of the Good cannot be fully captured by its individual parts. This excess is precisely what compels intelligence to continuously expand the scope of what is intelligible and, in doing so, to further realize itself. This process involves a perpetual feedback mechanism between intelligence and the intelligible.

  • The Good, as the objective principle, outstrips any given account of nature or being that claims to be a completed totality. Its adoption is encapsulated in the maxim: Burn what is holy, disenchant what seems mysterious or pretends to be perfect, and nothing will be able to compromise the ethics of thinking or the striving for the Good.

  • The concept of the better is defined as an expression of the Good in the life of intelligence. It represents a continuous process of moving beyond given totalities and manifest ideals, signifying transitoriness as a necessary feature of engaging with the project of the Good. This involves a multi-stage, open-ended reflection on the sources and consequences of intelligence's possibility. A satisfying life is one that is intelligently crafted, integrating self-knowledge, practical truths, and a unified striving for objective realization.

• Datum #9: “Intelligence without risk is an empty thought, as is an intelligence whose realization takes no time. Risk and time are the presuppositions for the history of intelligence in which nothing is given in advance and nothing is completed as the totality of that history.”

  • Intelligence identifies itself not with what currently constitutes it, but with its taking risks to become better, which means realizing itself by recognizing what it is currently not.

  • Our capacity to take risks for the better is what fundamentally defines us as intelligent beings. Thus, abandoning this risk-laden commitment to the better means discarding the very foundation of our rights, freedoms, and claims. To remain intelligible as intelligence requires an essential risk-laden commitment. Without embracing risk, nothing, including intelligence itself, could be said to be intelligible ontologically, epistemologically, or axiologically.

  • The scientific knowledge of history signifies the beginning of intelligence's capacity to take control of its own development. Therefore, the pursuit of the better, however slow it may seem, is presented as the only true and concrete path toward freedom and emancipation, necessitating the ongoing cultivation of intelligence and the abandonment of cognitive turpitude and social vices.

  • Negarestani's Marxism is not a nostalgic adherence to dogma but a critical, revisionary, and future-oriented project that seeks to re-engineer philosophical and political thought to effectively address contemporary challenges, often by drawing on diverse, even seemingly contradictory(analytical/continental), intellectual traditions. As said by Carool Kersten, Reza’s inhumanism entails a "catastrophic" revisionism of existing human self-perceptions, aimed at unlocking new abilities and the progression of intelligence.

• Datum #10: “While the history of intelligence begins from death as a condition of enablement, it extends by way of a view from nowhere and nowhen through which completed totalities are removed and replaced by that which is possible yet distant, and that which seems impossible yet is attainable.” (page 493).

  • Intelligence approaches the inevitability of death with a rational disinterest, much like a Stoic sage, refusing to be paralyzed by it. This involves actively contemplating scenarios of universal demise, even running simulations of the universe in which death is averted only to find that such attempts ultimately fail and instead "display in full ‘the levelling power of extinction’.

  • Reza redefines nihilism not as a pessimistic belief in the futility of life due to death, but as a positive, enabling force for reason. A true nihilism is characterized as the recognition that the inevitability of death has no bearing on the impersonal ends of thinking. This perspective is crucial because it serves as a vector of emancipation against any given state of affairs, any totalized epoch of its history—be it capitalism or biological humans as the zenith of intelligence—that feigns inevitability or claims to fulfil history.

  • The primary task of intelligence from this view is to think of how its world can be connected to these possible worlds, thereby enabling a concrete departure from a present that appears total and inevitable.

  • Reza argues that individual experiences are, in fact, structured by impersonal reason's powers of judgement. This realization is the impetus for a long-delayed task: no longer subordinating reason to experience, but to concretely transform the conditions of experience through an impersonal reason which suspends all historical totalities, pretensions to inevitability, and givens. The path to overcoming this fragmentation and achieving a broader historical experience is multifaceted, involving a broader effort that extends beyond political action alone, to encompass education, art, science, and technology.

  • The incorporation of sciences and the objective reality they reveal is not just a methodological requirement but fundamentally shapes a politics that is of the objective order. This approach postulates the possibility of an otherworld where the gap between personal lived experiences and the impersonality of reason's interests is overcome, transforming fragmented experiences into a collective productive imagination.

  • Reza thus concludes our journey by articulating a profound connection between Hegel's concept of absolute knowing and intelligence's recognition of itself as the expression of the Good. As intelligence arrives at this state of absolute knowing, it realizes that it has always been the expression of the Good as such. This realization grants intelligence a transformative power: it gains the capacity to cancel all givens and allegedly completed totalities of its history. This is achieved not just for intelligence itself, but for everything made intelligible by it. This ability to suspend any purported totality makes intelligence the exemplification of what is better.

  • A species that recognizes the Good must not obstruct this transformative process but must expedite the realization of an intelligence that, even though it acknowledges them as integral to the intelligibility of its history, nevertheless will not be impeded by them. This commitment is encapsulated in the imperative: "Liberate that which liberates itself from you, because anything else is the perpetuation of slavery".

  • The true task is not merely to exchange one tyrant for another, but to take the first step in an ongoing struggle to unseat the conditions of servitude. This means actively becoming-gods ourselves, not in a religious sense, but in a philosophical one. These philosophical gods are those who conceive themselves as moving beyond any condition given as the totality of their history, in so far as they can reinvent themselves as the inhabitants of the worlds which themselves have made. The pursuit of the Good is only possible by annulling the power of all given and absolute totalities in history—gods—in all forms.

  • The the ultimate goal is to transition from the death of all gods to a good life by systematically removing all conditions of exploitation, thereby emancipating intelligence itself and all others.

  • To truly explore AGI's prospects, it's necessary to adopt systematic scepticism regarding any paradigm of rationality that claims to be a sufficient, singular method for inquiry or any inflationary model of mind that collapses qualitative distinctions between mental faculties. Reza’s quandaries of induction serve as a razor-sharp critique against purely inductive models of mind and artificial general intelligence.

For citations of Intelligence and Spirit, the format will be (IS, x), therein x is equal to the page in which the cited text can be in the Urbanomic edition of the book. For other books, the specific edition and book will be noted down in a footnote. I’ve also taken from the various lectures given by Reza in The New Centre Research & Practice.

Diagrammatization

1. The Pragmatic Interface

This first section details how the transition from basic structure-encoding syntactic abilities to semantic structuring abilities can occur. Reza argues that syntax can be bridged to semantics, primarily through the concept of pragmatics, specifically inferentialist pragmatism. It critiques the view—exemplified by John Searle's Chinese room thought experiment—that syntax alone is insufficient for semantics, arguing that such a claim relies on a mystifying view of meaning and an outdated understanding of syntax and its relationship with semantics—it fails to account for the interactive, dynamic generation of meaning, reducing language to mere symbolic manipulation without acknowledging the rich, rule-governed interplay that gives rise to semantic content. The fundamental flaw in Searle's Chinese Room argument is identified as its misplacement of the actual computation. It's argued that computation isn't solely happening within the syntax manipulator—the person in the room—, but rather in "the interaction of the person inside the room and the person outside of it". This means that semantics "emerges out of the interaction of minimal syntactic rules or confrontation of basic axiomatic acts" (IS, 339). The interactive structure of language itself, rather than language merely being a medium for interaction, is very important.

The core concepts of Brandom's inferentialist pragmatism, which Reza, utilizes are these:

• At its most basic level, meaning is defined as the justified use of expressions within social discursive linguistic practices. What counts as the justification of an expression is precisely what counts as its meaning. This moves away from a representational or denotational account of meaning, focusing instead on the inferential relations embedded in social discursive practices.

• Semantics (content) is concerned with "what is said"—for instance, what one believes, knows, or claims when stating a proposition p. It focuses on the meaning-conferring inferential roles of syntactic expressions within social discursive practices.

• Pragmatics (use), conversely, focuses on "what one is doing in saying it". This involves the discursive practices or abilities required to deploy a vocabulary, or to confer and apply meaning. To understand something, an agent must possess the practical know-how to connect expressions inferentially.

The meaning and truth of an assertion are determined through a game of giving and asking for reasons, where claims are tested by queries and counter-claims. This process is termed normative scorekeeping pragmatics. Normative scorekeeping pragmatics can begin with a minimal set of rules, with more complex rules emerging naturally through the interaction between interlocutors. This highlights an emergent logic of rules where discursive rationality—even at the level of mastering basic claims— takes time. To assert or judge "This is red," an agent must not only react to the presence of the item (via reliable differential responsive disposition or RDRD)1 but also possess the practical know-how to inferentially connect "red" to other states or expressions, thereby conferring conceptual content upon it. For example, endorsing "This is red" entails "This is coloured" but precludes "This is green," demonstrating how understanding a concept like "red" involves knowing its inferential connections. The significance of a speech act in a conversation depends on its interaction with other interlocutors' commitments and entitlements. This requires updating the deontic context of the performance, assigning a score to the previous context. For instance, if Kanzi asserts "This is red" and Sue responds "This is red mixed with blue," Kanzi must update its commitments to "This is not red," "This is purple," and "This is coloured". Grasping the content of a concept and understanding reasoning itself are interdependent, characterized as objective and linguistic practical know-hows. Reason, in this context, is seen as the articulation and elaboration of concepts, presented as an algorithmic elaboration or decomposition of abilities that can be realized by different information processing systems.

Reza identifies a significant weakness in Brandom's pragmatism: its definition of sociality. Reza argues that Brandom's notion of sociality is merely asserted and "hardly plays any major role in how meaning-conferring discursive practices are logically modelled". This omission risks sociality becoming a "substantive characteristic of discursive practices rather than the very logical condition of language and the nonsubstantive order of thinking". Without explicitly detailing sociality's role as a formal condition, the concept risks becoming an "inflated metaphysical posit," leading to a view of rationality that is "unconscious of its insufficiency for change at the level of concrete social practices". This can result in a "socially liberal and philosophically quietist stance," (IS, 343) equating the necessity of reason with its sufficiency for concrete social change. The critique is not that Brandom ignores sociality, but that his treatment of it, while asserting its centrality, does not formally or computationally delineate its foundational role in a sufficiently rigorous way, leading to various theoretical and practical inadequacies. To address this perceived flaw, Reza proposes redefining sociality as a formal condition, best captured by the logico-computational concept of interaction. This redefinition is considered the first step to unbinding rational capacities and rescuing the concept of reason from deep-seated dogmas—thus viewing interaction as a sufficient condition for building the syntax-semantics interface.

Reza then poses two fundamental questions to explore this redefined concept of interaction: "What kind of interaction must the automata have in order to move from base syntactic abilities to fully fledged structuring semantic abilities?” and ultimately “What is interaction as a distinctly computational notion?”—The following sections will concern themselves with these questions.

2. Enter the Copycat: Interaction as Game as Computation

This hefty section delves into a profound reconceptualization of computation and its relationship to language and meaning, particularly highlighting the role of interaction as a fundamental computational phenomenon. The section posits a fundamental critique of the classical Church-Turing computability thesis, which models computation solely on mathematical functions where input maps to output in a closed system. This traditional view implies that computation yields no new information or knowledge, as the output is logically contained within the input. It suffers from the riddle of epistemic omniscience, suggesting an agent's total knowledge is deductively closed, thus preventing actual information gain. Yet a core innovation is highlighted—the environment not as a passive background but as an active, reactive element that provides input and consumes output. Without this dynamic interaction with the environment—another system, machine, or agent—, computation cannot be understood as an increase in information, thus overcoming the epistemic omniscience problem.

Reza notes that the classical model presupposes but does not intrinsically incorporate the environment. The environment is relegated to a passive background, merely represented as average behavior, rather than an active element. Reza proposes an interactive paradigm where computation is understood as a dynamic interaction. This shifts the focus: From "what is a computable function" to "how the computation is executed" (IS, 345). The environment is no longer passive but an active-reactive element that dynamically interacts with the system, providing input and consuming output. This dynamic interaction is crucial for the system's function to make sense and for information to increase, thereby avoiding the problem of epistemic omniscience. This perspective models the system-environment dynamics as an interaction game, which generalizes the concept of computation.

Unlike game theory, interaction games do not require procedural rules, predetermined winning strategies, or payoff functions. Instead, rules naturally emerge from the interaction itself. Interaction games are described as unifying themes for studying structures, information contents, and behaviors, capturing fundamental correspondences between computational behaviors, logical contents, and mathematical structures (the computational trinity)2. Within this framework, computability is defined as the condition of winnability for the system against an environment, meaning the existence of an algorithmic winning strategy to solve a computational problem in the presence of an active opponent. Access to computational resources and performance of permissible moves are explicitly stated as constraints imposed by the interchange of roles between the machine and the environment. Different levels of constraints express different classes of computational complexity.

Dualities and Roles

The interchange of roles between system and environment is formally defined by duality, where negation is substituted by the reversal of symmetries or swapping of roles in the game. For example, the function box represents the system as a consumer of input and producer of output, with roles reversed for the environment.

As seen, the environment—rather than being a passive background—is an active and reactive element that dynamically interacts with the system, providing inputs and consuming outputs. This means that computational complexity naturally arises from the varying levels of these constraints, which are a result of the dynamic switching of roles between the machine and its environment—this switching of roles is formally captured by the logico-mathematical concept of duality.

Traditionally, in logic, duality is defined using De Morgan's laws, which illustrate how classical negation (¬) transforms conjunctions (∧) into disjunctions (∨) and vice-versa. This is expressed both in rule form and in sequent (entailment) form3:

Rule form:

¬(p∧q)⊢¬p∨¬q
¬(p∨q)⊢¬p∧¬q

Sequent form:

¬(p∧q)⊨(¬p∨¬q)
¬(p∨q)⊨(¬p∧¬q)

In mathematics, duality is more broadly defined by an involutive function f, where f(f(x))=x. Simple examples include:

• the algebraic connection between {−1,+1} via negation (−(−x)=x),

• or the complementary relationship between a set A and its complement AC within a fixed set S, where (AC)C=A.

This mathematical concept of duality describes a formal, interconnected relationship where two distinct poles or aspects are mutually presupposed and co-arise through their interaction, akin to mirror images that require each other and their point of interaction to exist. For instance, the philosophical challenge of understanding how the transcendental dimension of intellect—a priori acts of cognition—and the substantive dimension of sensibility—causal-mechanistic structure of the nervous system—interact can be framed as a computational duality rather than a metaphysical dualism, as we saw in chapter 2.

In a computational interaction framework, duality is defined not by classical negation but by the reversal of symmetries or swapping of roles within a game. This allows for the emergence of various forms of dualities, including topological and geometrical ones.

Interaction Games

An interaction game G is defined as a 4-tuple

, involving two players:

• Player ⊤ (System, Prover): is the computational system.

• Opponent ⊥ (Environment, Refuter): is the environment interacting with the system.

MG​ (Set of Moves): The set of all possible actions performed by either player.

λG​ (Labeling Function): This function labels each move m∈MG​ with the player who made the move (⊤ or ⊥), the type of move (Attack/Query (A) or Defense/Answer (D))—formally, λG​:MG​→({⊥,⊤}×{A,D}). There's also a dual function mG​​ such that mG​​(m)=⊥A if mG​(m)=⊤A. This signifies the switching of roles.

PG​ (Play): A non-empty subset of MaltG​​, which represents alternating sequences of moves between ⊤ and ⊥. Positions in the game are finite runs.

⊨G​ (Justificatory Relation): is the permission to perform actions or make moves. An initial move m might require no justification (⊨G​m), or it might be justified by a previously justified move n (n⊨G​m). Subsequent moves carry justificatory information, pointing to an earlier move. Role switching also impacts permissions: m⊨G​n if and only if mAD​(n)=D and mAD​(m)=A. This means a defense (D) justifies an attack (A).

Subgames are conceptualized as analogous to threads and subthreads opened up within a dialogue. They represent specific instances or segments of a larger general game (G) that models computational interaction. The composition of subgames A and B is defined using the tensor product (⊗), a concept from linear logic semantics4, which implies that the play can continue alternately in both A and B. This formalization of composition is described by the following elements of the game G:

• Set of Moves (MAB = MA + MB): The total set of moves available in the composite game (A ⊗ B) is the union of the moves from subgame A and subgame B. This means any move permissible in A or B is a permissible move in their composition.

• Labeling Function (mAB = mA + mB): The labeling function for the combined game (mA⊗B​) is the sum of the individual labeling functions of A and B. This function assigns roles to moves (player or opponent, attack or defense) and, importantly, finds its dual in the reverse function, reflecting the fundamental switching of roles that characterizes interaction.

• Plays (PAB = {s | s ∈ MGalt}): The plays within the composed subgames are defined as non-empty subsets of the set of alternating sequences of moves between the player and the opponent within the general game G.

• Justificatory Relation (⊨AB = ⊨A + ⊨B): The satisfying or justificatory relation for the combined game is the sum of the individual justificatory relations from A and B. This relation represents the permission to perform actions or make moves, where subsequent moves bear justificatory information or point to an earlier justified move.

The interaction game always begins with an action or move made by the opponent, which represents the environment. This reflects the fundamental idea that the environment is what constrains the system and keeps it going. In this model, the environment is not a passive backdrop but an active, reactive element that provides input and consumes output. Following the environment's initial action, the opening move played by the player (⊤), which represents the system, is always a request for data or a query from the opponent (⊥). This establishes the reciprocal nature of the interaction, where the system queries the environment for necessary resources.

Within the composition of subgames (A ⊗ B), the ability to switch between these subgames is asymmetric. Only the opponent (⊥) can switch between subgames, while the player (⊤) is restricted to reacting within the latest subgame where the opponent (⊥) has played. This constraint is formally expressed as: For any play s in P_A⊗B, if s_i is a move in subgame A and s_{i+1} is also in subgame A, then m_A⊗B(s_i) must be a player's move (<) and m_A⊗B(s_{i+1}) must be an opponent's move (=).

This constraint highlights the opponent's control over the flow of the game within composed subgames. If the player makes a move in subgame A (s_i), and the subsequent move (s_{i+1}) also occurs in subgame A, it must be an opponent's response. This means the player cannot make two consecutive moves in the same subgame. The opponent is the one who decides whether to keep the interaction within the current subgame—by responding there—or to switch to another subgame (by initiating a move in the other subgame after the player's turn). The player's actions are always reactive to the opponent's latest move, ensuring that their engagement is strictly within the current "thread" or "subthread" of the dialogue.

Linear Implication: A⊸B

The concept of linear implication (A ⊸ B), which describes the continuation of a game where subgame B consumes or uses subgame A as a computational resource, is an important element in understanding resource-sensitive interaction within the framework of subgames and their compositions. As Reza notes, This approach draws heavily from Andreas Blass's semantics for linear logic. This resource-sensitive interaction is intuitively explained through an access-protocol analogy between a server and a client: A server of type A ⊸ B is essentially a server that provides data of type B. To be able to provide this data, the server needs to access (exactly once, as a client) a server of type A, which provides data of type A. The "exactly once" clause is crucial here, as it signifies the resource-sensitive nature of linear logic, where the input argument is accessed precisely one time in the computation (CSL ‘97, 67)5. This contrasts with classical or constructive mathematics, where an argument is considered permanently available for arbitrary repeated access. Consequently, the client of the A ⊸ B server must act in a dual capacity: not only as a client of type B (to receive the desired output) but also as a server of type A, providing the necessary input or resource from A to the A ⊸ B server.

The game A⊸B, showing linear implication where subgame B consumes subgame A as a computational resource, is fundamentally characterized by its 4-tuple components. The characterization through its 4-tuple provides a formal definition for this dynamic interaction:

• MA⊸B​=MA​+MB​: The set of moves.

• λ_A⊸B​=[λ_A​​,λ_B​​: This is the labeling function for the combined game A⊸B. It's a compound function constructed from the duals of the labeling functions of A and B.

• ⊤A⊸B​={s∈MA⊸Balt​}: This defines the set of valid plays or sequences of alternating moves in the game A⊸B.

• ⊢A⊸B​: This component specifies the rules for permission to make moves within the A⊸B game.

Reza now states that, in this framework, a computational problem—like computing n+1—can be diagrammed as a tree:

• Top Node: Represents the initial game played by the machine (⊤). This signifies the system's opening move or query in the interaction.

• First-Level Branches: Labeled by ⊥ (representing inputs provided by the environment). These branches show the possible responses or data provided by the environment to the machine's initial move.

• Second-Level Nodes: Games played by the environment (⊥1, ⊥2, ⊥3, …). These nodes represent new subgames or states of interaction initiated by the environment's input.

Third-Level Nodes: Represent the winnability of games played alternatively by the environment and the machine (⊥,⊤,⊥,⊤,…). This captures the ongoing, alternating nature of the interaction, where each party's actions are constrained by and responsive to the other's.

The Copycat

Reza now introduces the Copycat Strategy, as the most general category of interaction games. It signifies the game or interaction itself, independent of the specific order of actions performed by the players or processes involved in the interaction. To understand this, you can imagine a universal game board (G) that may contain many other game boards or subgames. On this board, there are two teams of players, agents, or processes (A and B), distributed asynchronously across the board. While actions within each team might be ordered synchronically and sequentially, their interactions with the other team are asynchronous, meaning they can be "out-of-order or in partial order" (IS, 354). The copycat agent wins against both teams by mirroring one team's plays and running them against the other team, or by copying moves from one game board to another and vice versa. This involves playing moves from team A's domain in team B's codomain, and vice versa for team B. In this scenario, regardless of which individual team wins, the copycat wins, as its strategy encapsulates the general interaction.

From an information-theoretic perspective, the copycat signifies the conservation of the flow of information for the total system, even though information flow and increase occur relative to the interacting subsystems. This approach enables the development of an explicitly dynamic theory of information processing. While winnability in interaction games is analogous to computability, the true significance of the copycat is not tied to winning. Instead, its power lies in its ability to represent the flow and increase of information across any particular interactive configuration, even if the teams or agents do not react synchronously. The copycat concept also suggests that the surprising power of copying information from one game board or context to another can lead to an emergent view of logics and language as simple or composite interactions or copycat strategies. Ultimately, the copycat demonstrates that sequential-synchronous computation is a subset of asynchronous-concurrent computation. In its most general form, interaction is computation itself, emphasizing that every process inherently interacts with another. The logical equivalent of the copycat as the agent of interaction, game, or computation is a dialogue, which is considered the engine of semantics, implying that private thought cannot exist without dialogue, and dialogue generates new knowledge through interaction

To finish this amazing and difficult section, let’s discuss Reza diagram ‘The hiding copycat’.

At its core, the diagram depicts the Toy universal gameboard G, which represents the general category of games or interaction itself. This conceptual board is considered independent of the specific order of actions performed by agents, processes, or players involved in the interaction. It is analogous to a universal board game comprising numerous sub-board games. The notation below the copycat signifies that the copycat represents an identity map or morphism of the game itself, which can be interpreted in Church-Turing computability terms as an identity function, such as mapping natural numbers to natural numbers. This implies that G is a general game upon which many computable functions can be played.

The diagram shows "Player A's Base" and "Player B's Base," which represent two teams of players, agents, or processes, A and B, respectively. Each base contains a grid of cells with letters and numbers, signifying their base or domain of moves. The solid black arrows illustrate possible actions in the game or legal transits from one labelled cell to another within their respective bases. Within each team, actions or moves can be ordered synchronically and sequentially. However, in relation to the actions or moves of the other team, they are considered asynchronous, meaning they can be played out-of-order or in partial order. This distinction is crucial because the The hiding copycat model supports true concurrent interactions, distinguishing it from conventional sequential computation.

The large central area, filled with cells containing combinations of letters (a-i) and numbers (1-3), represents the universal game board which can consist of many other game boards or subgames. On this board, there are two teams of players, agents, or processes—A and B—each with their respective base or domain of moves. These moves are distributed in an asynchronous fashion over the board. The vertical arrow with a dashed line pointing upwards, indicating "Asynchronous concurrent game (players with independent strategies or sequence of acts / moves)," (IS, 356) directly emphasizes a crucial aspect of this model: sequential-synchronic computation is understood as a subset of asynchronous-concurrent computation. As we’ve just said above, this means that the players' actions are not necessarily synchronized; they can be played out-of-order or in partial order, and the outcome of the game remains the same. This general category of interaction games allows for complex phenomena such as conflicts, asynchronous interaction, temporal precedence, supervenience, and the distinction between causing and enabling events, which are not captured by conventional sequential computational models.

The two shaded rectangular areas labeled "Copycat strategy" visually represent the copycat as an agent or strategy within this universal game board. A copycat is defined as an identity map or morphism of the game itself (G: G → G). The dashed arrows (ξ and ρ) extending from these copycat strategy areas symbolize the copycat's fundamental action: copying one team's plays and running them against the other team, or copying moves from one game board to another and vice versa. Specifically, the copycat plays moves from the domain of one team—like A's base in the codomain of the other—like B's base—, and vice versa for team B. This process of "changing its labelled cells from A's base to corresponding labelled cells in B's base, and vice versa for team B" (IS, 355) signifies the copycat's role in mediating and replicating interactions between the player domains.

The copycat, therefore, acts as a dynamic orchestrator or a universal translator within the game, enabling the emergence of complex logical and linguistic phenomena from the basic interactions of agents. It's like a universal adapter for communication, allowing different devices to interact and create a shared understanding, even if they operate on different principles. This section perhaps has the been the most taxing of any.

3. From Semantics of Interaction to Interaction as the Game of Semantics

The third section explores how logic, refounded on generalized interaction, provides the framework for bridging syntax and semantics in the context of AGI. This interactive view of logic is crucial for understanding how automata can progress from basic structure-encoding syntactic abilities to more complex semantic structuring abilities. Traditionally, in proof theory, the meaning of a proposition is understood as its proof or verification, giving priority to proof over truth. This classical view conceives proof as static and monological, implying that knowing a proposition (A) automatically means knowing its disproof (¬A) through classical negation. However, Reza argues that this classical approach is limited because it treats the counter-proof or negation (¬A) as passive and extrinsic information.

In contrast, the interactive framework proposes that the determination of meaning or proof is an active process, achieved dynamically through interaction or dialogue with its counter-proof (¬A). This involves abandoning classical negation in favor of interactional dualities, where negation is understood as the interchange of roles between the proofs of A and ¬A. Within this dialogical framework, proof is no longer an object but an act, signifying a confrontation of acts or interactions between dualities, which can be represented as agents, processes, or strategies. Even fundamental logical connectives can be expressed as moves within these interaction game—thus language itself is a sui generis framework of interaction-as-computation.

Dialogical interaction, from this perspective, not only enables the computation of meaning or semantic values but also provides vital semantic information such as contextuality and thematization. Crucially, both semantic values and contexts are themselves considered computations. The computation of meaning can be understood in two ways:

• Proof search: Meaning is computed if the interaction game successfully returns the proof of a sentence or formula.

• Proof normalization: Meaning is computed if a canonical, irreducible proof is obtained by eliminating unnecessary steps or useless detours. Two statements are considered to have the same meaning if their proofs or constructions are equivalent via a reversible inferential relation or mapping.

To exemplify this, Reza introduces a "toy meaning-dispensing machine" diagram. This machine consists of two agents interacting over a language, where algorithms determine proof through normalization or search. When syntactic tokens or terms are fed into this machine, it "dispenses meaning". This meaning, derived from syntactic structures, possesses a normal form and remains invariant despite the internal interactive dynamics of the machine. This mechanism demonstrates how semantic compositionality—the ability to decompose sentences into elementary constituents—is fundamentally supported by syntax.

Reza further highlights that syntax at the sentential level is profoundly resource-sensitive. This is particularly evident with anaphoric elements, like pronouns, whose meaning or reference is determined by their precise connection to other items within the sentence. Such resource-sensitive connections necessitate the use of logical operators—such as exponentials in linear logic—which control and track the use of syntactic resources within sentences to maintain their coherence and meaning.

4. Keep It in Focus: A Dialogue in Eight Acts

This section delves into the critical problem of bridging the gap between syntax and semantics through the lens of dialogical interaction, particularly within the framework of ludics. Reza writes that the solution to the syntax-semantics interface problem lies in dialogical interaction as a fundamental logico-computational condition for meaning. It highlights the necessity of a new type of dialogue where both the rules of interaction and the meanings themselves are not predefined but spontaneously emerge during the conversation. This concept generalizes the logico-computational notion of interaction, making it the central mechanism for connecting syntactic structures to semantic content.

According to Samuel Tronçon and his colleagues, particularly Marie-Renée Fleury and Myriam Quatrini, dialogue serves several essential functions within the emergent framework of ludics and interactive computation. They propose that dialogue is a relevant framework for both formalization and studying dialogues, focusing on the dynamics of interactive situations to offer rich intuitions and mathematical insights. The essential functions of dialogue, as outlined by Tronçon et al. (and further elaborated upon by Negarestani), are:

• Exchange of Information: It functions as a form of computation.
  Dialogue functions as a form of computation through the exchange of information. This means that at every stage, when a speaker provides a symbol, this exchange is informative in three ways: it conveys information about the object being discussed (the thesis), about the speaker's approach to that thesis, and about the connections between the current intervention and potential counter-interventions (whether upstream, downstream, actual, or virtual).
  

• Construction of Knowledge: Dialogue actively builds knowledge.
  Dialogue actively builds knowledge. Arguments within a dialogue interact like "machines built up to explore relevant opportunities of discussion," (LNAI 6700, 139)6 contributing to this knowledge construction based on a global strategy. This process can lead to the formation of common knowledge, which is crucial for coordinated action among agents in multi-agent systems, including in fields like robotics. Dialogue enables the system to acquire new levels of knowledge that are generative, not merely additive, facilitating the revision and updating of past knowledge.

• Unfolding Structure: Dialogue reveals knowledge as an evolving structure, with consistent engagement from interlocutors leading to a thorough exploration of possibilities.
  Dialogue is characterized as an "unfolding structure that represents some knowledge". Through this dynamic, rules and meanings spontaneously emerge during the course of the conversation. The consistent engagement of "friendly but tenacious interlocutors" ensures a "good (exhaustive) exploration" (LNAI 6700, 139) of possibilities, revealing knowledge as an evolving structure. The "inside dynamics" of this process suggest that the meaning of a shared inquiry lies in the form of the interaction itself, and even divergence can lead to exploring the determinations of invoked strategies.

• Extraction of New Information: Participants can glean insights about the nature of the interaction itself, identifying what remains stable, what is explored, what is new, and what is latent within the discourse.
  Through the interaction, participants can "extract some new information which is about the form of the interaction, contained in the result of the dialogue: what is stable, what is explored, what is new, what is in latence" (LNAI 6700, 139). This capability allows for continuous refinement and adaptation of understanding.

The framework of ludics is presented as the formal system that embodies this logic of dialogue. Ludics notably departs from traditional linguistic and logical approaches by rejecting referential theories of meaning, monological semantics, and non-autonomous syntax—replacing them with an inferential theory of meaning, dialogical and operational semantics, an autonomous minimal syntax, and a generalized concept of game that operates without predetermined winning strategies or payoff functions. Within ludics, meaning emerges from a dynamic process of interactive proof or computation. Rules and meanings arise naturally through the exchange of loci (addresses of syntactic terms or formulas) and subloci, guided by basic negative and positive actions, and potentially concluded by a daïmon (a termination command).

Reza then gives us the basic elements of ludics:

• Designs: These are the central objects of ludics. They are identified as strategies in a game, consisting of sets of "plays" (or "chronicles"). A design represents an alternating sequence of positive and negative rules, which can either progress endlessly (representing an "endless dispute") or be closed by a daïmon. In the analogy, designs play a role similar to proofs, λ-terms, functions, or cliques in standard logical and semantic frameworks. Ludics views these designs not as syntax but as "proof architectures" that retain only what is essential for interaction (LNAI 6700, 142).

• Plays: In ludics, plays are the dialogical equivalents of proofs. They are defined as alternating sequences of moves (or actions). A specific sequence of actions within a design is called a chronicle, which can be seen as a finite branch in a proof-tree.

• Moves: These are the atomic units of interaction within a play, defined as a 3-uplet consisting of:

  • p (polarity): This indicates the local role in the interaction. It is positive for the actions or moves of the player/proponent and negative for the moves of the opponent. Polarity reflects a fundamental duality where logical operations are polarized steps (MLL, 306)7. Shifts are operations that explicitly change polarity.

  • l (locus): This represents a fixed position or memory cell where syntactic terms or formulas are (conceptually) stored (LNAI 6700, 143). Crucially, ludics emphasizes that only the location matters. Meaning is not derived from the symbols themselves but from how these locations—addresses—are manipulated within a dialogue or proof. Loci are encoded by finite sequences of integers.

  • r (ramification): This denotes a finite number of positions reachable in one step from the current locus. It represents the set of "openings" created by an intervention or the directory of possible answers (LNAI 6700, 148).

• Positions/Addresses (Loci): As said already, these are the loci encoded by finite sequences of integers (ξ, ρ, σ). These addresses represent the threads and subthreads of interaction, enabling the thematization of a dialogue across different topics. Fundamentally, trees of addresses are equated with designs.

• Forks: These are the starting positions of a design, represented as sequents like Γ ⊢ Δ. A design's base—or conclusion—is a fork. A fork is considered positive if the player/system initiates the interaction from an element of their choice in Δ, and negative if the opponent/environment starts the interaction from the unique element in Γ (LNAI 6700, 143). Designs are conceptually structured as trees whose nodes are forks, with the root comprised of positive, negative, and daïmon rules.

• Rules (Positive, Negative, Daïmon): These are the only rules necessary for building designs or strategies in ludics.

  • Focalization: This concept is central to how meaning emerges. It can be thought of as "proof search" in an interactive framework. Focalization allows for the grouping of a series of consecutive actions of the same polarity into a single "synthetic" logical action. This mechanism drives contextualization and topicalization in dialogue by mapping actions between polar strategies. It's through focalization that logical constants and rules are not a priori given but adaptively emerge.

  • Positive Rule: Symbolized in sequent form as (ξ,I)⊢Δ,ξ, this rule represents an action where the player chooses, asserts, or makes a move. It involves the player selecting a locus and asking a finite set of "questions" or "openings" (the ramification I).

  • Negative Rule: Symbolized as ξ⊢Δ,(TI​)I∈N​, this rule represents the opponent's challenge or reaction. After a question is asked, the player—from the opposite polarity's viewpoint—considers a "directory" of possible answers (N) from their partner (MLL, 320). N can be an empty or even infinite set of ramifications.

  • Daïmon (†⊢): This is a general axiomatic rule, often described as a "paralogism" or an act of "giving up". It is a positive rule, meaning either player can choose to invoke it. If one player/proof-process invokes the daïmon, the other player/proof-process wins, thereby identifying the winning strategy or the validity of a proposition. It serves to terminate a design or close off branches of a proof tree.

In this framework, behaviours are defined as sets of designs that are equal to their bi-orthogonal, serving as the ludic equivalent of a "formula" or "type". The interaction itself is characterized as the coincidence of two dual loci in two different designs. The normalization process in ludics—which is the compositional step— aims to eliminate these dual loci, striving for a "consensus" where the game stops because the two players agree to end it. This highlights that in ludics, meaning is not static but dynamically co-created through the interactive process.

Let’s see an analogy. Imagine a complex, improvisational jazz performance—a good live performance from John Coltrane, something from Live at the Village Vanguard. The individual musicians (designs) each have their own strategy (their internal musical ideas and improvisational techniques). Their individual musical phrases (actions/moves) have a "polarity" (leading a new melodic line or responding harmonically). The locus is the specific measure or beat in the music where a phrase is anchored. Ramifications are the possible new melodic or harmonic paths opened up by a musician's phrase. The overall performance (a play or chronicle) is the alternating sequence of these musical phrases. The rules of jazz—harmonic progressions, rhythmic patterns—are not strictly predefined but emerge immanently from the musicians' real-time focalization on certain musical ideas and their interactive responses. When the musicians achieve a collective flow or consensus, their interaction normalizes, creating a coherent, emergent meaning (the musical piece) that wasn't pre-composed but was co-created through their dynamic interplay. If a musician stops playing or plays something entirely discordant, it's like invoking the daïmon" potentially ending the collective musical proof.

In Ludics, unlike classical views where speech acts are often normatively predefined, speech acts are understood as evolving naturally through interaction. They are considered partial functions in a computational game framework that attain the status of a speech act—such as assertion or questioning—when they produce invariant impacts on a shared context. A speech act in Ludics is defined by three core elements:

• Speech Acting Competence (U): This represents the speaker's ability to impact the context given the anticipated reactions of the addressee. The speaker initiates actions—positive rules—, while the addressee's expected answers are captured by negative rules. This competence involves the speaker's strategy, which can be seen as a design.

• Test (B): This is an interactive situation that contrasts the speech act with a complex contextual structure. This context (B) can mix contextual data with the addressee's reactions, and when negative or passive, actions or observations represent this contextual structure.

• Impact (E/C): This refers to the effect of the interaction. This effect involves updating, modifying, or erasing a shared context. Critically, the impact (C) is expressed as an invariant behavior, which is the normal form resulting from the normalization of the two interacting designs, U and B (representing the proof and counter-proof).

At its core, a speech act is the interaction of two designs (U and B), resulting in a new design (C), where the impact (C) is the invariant behaviour (normal form) resulting from the normalization of U and B.

The Dialogue in Eight Acts

Ludics provides a framework that generalizes Robert Brandom's concept of deontic scorekeeping—the game of giving and asking for reasons—by grounding it in a logico-computational dynamic where linguistic rules and meanings emerge naturally from interaction. The dialogue in eight acts between Kanzi (asserter/speaker A) and the monkey (interlocutor/addressee B) illustrates this generalization of deontic scorekeeping in Ludics. In this hypothetical dialogue, the agents—Kanzi and the monkey—engage in a game of giving and asking for reasons, where their actions (moves) are characterized by designs (strategies) and the manipulation of loci (addresses or fixed positions for syntactic terms/formulas). The dialogue progresses through alternating positive actions (proponent's moves, assertions) and negative actions (opponent's responses, acknowledgements, or requests for justification).

Here's how each act in the dialogue illustrates these Ludics principles and the generalization of deontic scorekeeping:

1. Act 1: A chooses an object {j}.

This is a positive action by Kanzi (speaker A), initiating a new focus or theme for the dialogue. In Ludics, this corresponds to the speaker making an opening move by selecting a specific locus—or set of loci—for the interaction. The choice to address a theme—like the monolith's color—carries a pragmatic significance of creating an entitlement for the speaker to make assertions related to it, acknowledged by the interlocutor.

2. Act 2: B entitles A to treat this object in terms of the range of properties.

This is a negative action by the monkey (addressee B). It signifies B's acknowledgment of A's initial move and grants permission for A to continue the discussion by considering the properties associated with the chosen object. In Ludics, negative actions record or anticipate the interventions of the other player, setting up the "directory" of possible answers or continuations.

3. Act 3: B entitles A to choose and play a property {k} from this range.

Another negative action by B, further narrowing the scope of the dialogue and offering a specific choice to A within the previously established range. This is B's response that enables A's next move.

4. Act 4: A chooses a property {k} and entitles B to regard or act on this property within a range of values.

A positive action by A, where Kanzi actively selects a specific property (a sub-locus) and, in turn, creates a new entitlement for B regarding the values that property can take (shiny, opaque, textured black). This shows how one player's move opens up specific paths for the other, defining the unfolding structure of the dialogue.

5. Act 5: B entitles A to choose a value {c}.

A negative action by B, acknowledging A's choice and providing the permission to proceed to a specific value within the range.

6. Act 6: A picks up a value {c} and entitles B to act on it within a set of modalities.

A positive action by A, selecting a value and then introducing a further level of engagement: modalities like truth and falsity. This is where the conversation shifts towards judging the truth-candidacy of a claim.

7. Act 7: B entitles A to pick up a modality.

A negative action by B, responding to A's move and permitting A to choose a specific modality.

8. Act 8: A chooses a modality and waits for B’s acknowledgement.

A positive action by A, where Kanzi makes a final selection for this sequence, concluding the negotiation of properties and values and awaiting the monkey's final acknowledgment. This could lead to the monkey invoking the daimon ("I give up" or "Stop!") to terminate the dialogue, signifying a point of resolution or consensus, or a dissensus if the interaction diverges

To end this section, Reza provides us with another LEGO diagram toy model to concretely show what we’ve just discussed above.

5. Formalism and the Pure Autonomy of the Formal

In this section, Reza argues for a transformative understanding of formalism, particularly in the context of language, logic, and intelligence. Negarestani writes that the formal dimension, encompassing computation, logic, and mathematics, represents a "pure transcendental condition" (IS, 376). This condition is presented as liberated from the provincialism of Kantian transcendental logic, which is seen as anchored to the apperceptive I and particular transcendental types shaping the subject's experience. For Negarestani, this formal dimension grounds transcendental logic as the science of pure understanding and rational cognition, effectively defining the concept of mind in relation to the world. Without this formal dimension, there would be no experience or understanding, as it permits the semantic structuration of experiences.

The term "formal" in this context is not a reinscription of the traditional form versus content dichotomy. Instead, both form and content are understood to belong to language as a single formal dimension. The interactionist view of logical syntax is characterized as "semantic in disguise" (IS, 377). This means that while formal languages might traditionally be seen as sacrificing semantics, they actually enable the emergence of semantic complexity through the confrontation of syntactic processes. This perspective allows for richer semantic relationships and the potential to resemantify formalisms developed for specific backgrounds to new problems or frameworks. The valorization of subjective experience or psychology against formalism is seen as a bias that erroneously limits experience. Negarestani argues that only the richness of the formal can truly express or expand the richness of experiential content. To expand experience, language should be "decoupled" from the experiencing subject and its communicative role.

Natural language, despite its familiarity and perceived richness, is seen as inherently limited when compared to the vast potential of general artificial languages. Its "abilities afforded by natural language as a form of language whose evolution is tied to the restrictions imposed by the structure of the experiencing subject would be merely a small archipelago in the vast sea of syntactic and semantic abilities afforded by a general artificial language". This is because natural language represents "only a fraction of the logical autonomy of the formal as the transcendental dimension through which the content of experiences can be accessed and whereby mind becomes able to structure the world of which it is a part" (IS, 379). Artificiality signifies the capacity to unbind the formal—to allow the formal dimension to be fully expressed, augmenting world-structuring abilities and syntactic-semantic expressivity. Let’s remember from chapter 1, that the history of mind, in this view, is "quite starkly the history of artificialization" (IS, 51).

6. Logic as an Organon and as WorldBuilding

This section profoundly redefines the role of logic and language, moving beyond traditional, more constrained views to present them as fundamental forces in shaping reality and intelligence. Reza begins by addressing Kant's distinction between logic as a canon and logic as an organon. For Kant, logic, when functioning as a canon, refers to its formal and regulative use. It provides the mere criteria for the correct application of the laws of thought or judgments. For Kant, logic as a canon refers to the formal use of logic, providing mere criteria for the correct application of laws of thought or judgments, and is constrained by extra-logical information or empirical sources of truth. This is portrayed as a logic delimited by the representational resources and limits of the apperceptive subject.8 In contrast, Kant viewed logic as an organon as a "logic of illusion" or "sophistical art" if it attempts to produce objective insights or cognition without drawing on antecedently well-founded information from outside logic,9 deeming it unconstrained and arbitrary.10 Reza argues that Kant's dismissal of logic as an organon relies on an antiquated Aristotelian definition and that this distinction becomes tenuous in light of 20th-century revolutions in formal and mathematical logic, as well as advances in theoretical computer science. Instead, the text proposes a reimagined logic as an organon that is not limited by representational or world-referring constraints, but rather undergirds world-building itself.

Reza thus states that the construction of the world is prior to the constitution of the object and the knowledge of it. This means our understanding and representation of the world are beholden to, and caught up within, the scope of our world-building capacities, which are fundamentally logical and linguistic. To genuinely hone the notion of logical structure, logic must be treated in terms of unrestricted logical world-building, decoupled from any enforced representational considerations—experiential content, empirical truth sources, or subjective application criteria—that might pre-establish its frontiers. This unconstrained view is presented as the indelible factor for object-constitution. This means that expanding the field of logic, unconstrained by concerns of subjective representation, is absolutely necessary to constitute objects, make objective assertions, and deepen our understanding of objectivity. Without this liberation, we are left with mere "pseudo-talk of stuff," akin to Aristotelian 'this-suches'. The true potential of logic to shape our understanding of reality can only be realized when it is freed from representational limitations imposed in advance. The world-constructing resources of logic themselves "precede and in fact undergird" world-representation and our judgments about the world—Reza thus proposes a "Carnapian slogan" that "construction of the world is prior to the constitution of the object and the knowledge of it". This is termed "priority2 in the order of constitution," (IS, 384) highlighting that the very possibility of objects and knowledge is constituted by logical world-building, rather than merely preceding it temporally. General artificial languages are presented as exemplars of this logical world-building.

To end off, the constrained nature of Kant's transcendental logic, which prioritizes its role as a canon tied to the representational capacities of the human subject, leads to a profound philosophical narcissism. Just like as discussed in chapter 4, our "objective" understanding of reality risks becoming merely a projection of our own limited and contingent cognitive structures, akin to looking into a mirror and mistaking our reflection for the entire universe. This "Dorian Gray" effect means we might unknowingly live in an echo chamber of our own biases, perpetually blind to deeper, unconditioned realities beyond our self-imposed intellectual horizon.

7. Dogmas of the Experiential

This section critically examines the tendency in philosophy, from Kant to Sellars, to confine the concept of the transcendental to the realm of experience. Reza argues that it is a "humanistic or subjectivist mistake" (IS, 384) to limit the idea of the transcendental solely to experience, which effectively reduces it to its application to sensory materials or intuitions. This limitation is particularly evident in Kant's categories—pure concepts of understanding—, which are deemed relevant only insofar as they serve the experiential, epistemic, and practical needs of the subject. A direct consequence of this restriction is the elision of the distinction between logical autonomy and practical autonomy—that is, the pure autonomy of the formal (syntax and semantics) and the relative autonomy of the experiencing subject.

For the conceptualizing mind, spontaneity is not primarily found in its perceptions or actions, nor in the content of its thought episodes, but rather in the formal dimension of thinking. This refers to how language and logic process and organize such contents. Constraining the meaning—semantic value—to the metaphysics of sensation, as seen in Sellars's theory of picturing, while seemingly providing epistemic traction, ultimately impoverishes both form and content if the formal's function is reduced a priori to epistemic content or application. Such a restricted view also makes it susceptible to psychologism—the attempt to establish the validity of logical principles by appealing to human psychology—and prevents it from adequately challenging the biasing effects of psychologism.

Reza argues that only by disengaging the formal from subjective experiential content—separating the pure formal dimension of thought from its apparent epistemic-experiential content—can the formal be treated systematically. This systematic approach allows for experiential content to be structured much more richly, moving beyond the limited scope of nonconceptual representations. Formal languages are crucial in this context, as they express the systematicity of the formal, unburdened by communicative function, subjective experience, or ordinary semantic content. This desemantification—decoupling from specific subject matter—paradoxically enables resemantification, allowing a given formalism to be applied to new problems or frameworks. The systematic treatment of the formal leads to semantic enrichment—structuring new contents—and a debiasing effect, which significantly reduces the perceptual biases of reasoning. This is how formal languages become cognitive technologies that facilitate the transition from common-sense understanding to scientific inquiry.

Reza explicitly links the assertion that "forms should conform to experiences" to the myth of the given (IS, 388). This myth is characterized as the claim that knowledge ultimately relies on noninferential or immediate access to reality. Against this, Reza, drawing on Carnap's argument11, states that objects of knowledge are fundamentally of form rather than empirical experiential content. They are structural entities. Objectivity, in this view, is secured because certain structural features agree of all streams of experience, and these features are indexed by and are objects of form. This formal dimension holds together and structures individual streams of experience within an intersubjective framework, ensuring objective validity.

8. Upward to the Semantic Heavens

This section delves into the profound consequences of intelligence's immersion in the semantic dimension of language, particularly for its self-conception and its capacity for world-making. This section expands on the broader topics of language as the dasein of geist and its syntactic-semantic complexity. The semantic dimension of language enables a crucial transition from perceived certainty to conceived plausibility. This is not merely a shift in belief but a catalyst for epistemic inquiry, disrupting the "natural equilibrium" of given states of affairs by introducing "rational suspicion" and "conceptual plausibility" into both thoughts and things. This dynamic is likened to the "nebulous continuity" between Plato's "shadows or sensible images (eikones)" and intelligible reality, emphasizing that while connected, their distinction is not flattened. This rift or disequilibrium initiates an "involution of thinking," a critical process where knowledge expands through thinking's increasing self-awareness of its own functions and processes. This involves the conceptual construction, revision, and reappraisal of beliefs (IS, 391).

Once consciousness is imbued with language, it develops into what Findlay called a sidelong intentionality, meaning its focus extends beyond any specific limit set by a given world. This enables the simultaneous, indirect, and implicit thought of many things at once. This cognitive tendency—nisus—fundamentally transforms the world experienced by artificial agents—automata—from a "narrow zone of thinking and action" into an unrestricted universe. In this expanded universe, the scope of thinking and knowing has "no predetermined limit or boundary". Crucially, this implies that intelligence moves beyond merely inhabiting given worlds; it "makes new worlds" (IS, 392)—this is central to the book's broader philosophy of intelligence as a way of worldbuilding.

Conceptual consciousness exhibits a "nisus" not only towards diversification—"diremptive" tendencies—but also towards synthesis and integration. This dynamic is understood through Plato's concepts of peras—the determinate—and apeiron—the indeterminate—, where language and logoi—logic and mathematics—function as the peras, actively determining and structuring the indeterminate. This process allows for the transformation of disconnected representations into coherent "conceptual-theoretical world-representations or world-stories" (IS, 393). The notion of semantic ascent from André Carus is equated with explication, a concept drawn from Rudolf Carnap's project of rational reconstruction. For Carnap, explication is the "transformation of an inexact, prescientific concept, the explicandum, into an exact concept, the explicatum," (LFP, 1)12, which Reza sees as “the craft of an engineering mission, and a matter of rational choice, and thus the enrichment of the very concepts of reason and reality.” (IS, 393).

The "dialectical task of explication", as presented by Reza, concerns itself with the transformation of vague, pre-scientific concepts—termed the explicandum—into new, exact, precise, and more useful concepts, known as the explicatum. This process aligns with the broader ideal of rational scientific Enlightenment. The explication process is not simply a clarification or amelioration of existing concepts, but rather a form of conceptual engineering. It is understood in a wider sense than traditional analysis or clarification concepts by Kant, Husserl, and Langford. Carnap's explication seeks to replace the explicandum with an explicatum that meets specific requirements: similarity—functional, not merely extensional—, exactness, fruitfulness, and simplicity. Fruitfulness, for instance, refers to a concept's ability to facilitate the formulation of many universal statements, empirical laws, or logical theorems within a constructed system (LFP, 7). In the Restructuring Enlightenment: From Carnap's Aufbau to Conceptual Engineering seminars, this process is considered "post-metaphysical" in its approach to traditionally vague philosophical questions such as "What is life?", "What is mind?", or "What is consciousness?".13 It aims to eliminate pseudoproblems" by developing an exact method for the construction of sentences about sentences. Ultimately, explication is an "ongoing gradual process of improvement of a system of concept designed specifically for clarifying the logical structure of scientific theories and concept"14. It involves moving from a phenomenological aspect of living in the world to precise mathematical concepts and formal systems.

The ideal of rational scientific Enlightenment is seen to operate along two commensurable trajectories:

• Descriptive Pragmatics (Local Refinement): This trajectory involves refining local concepts by reinventing them at progressively higher resolutions. An example given is the concept of hardness, which behaves differently at various scale-lengths (macroscopic, crystal, nano levels). This type of refinement necessitates a "change of language", moving from the "ordinary framework of natural language to the unbound realm of constructed languages". The semantic value of a concept, like hardness1 in language1, is internal to its rules, but its explication—"hardness2," "hardness3"—entails an ascent to an "ocean of general artificial languages". However, relying solely on this first sense of explication can lead to "drifting diversifications without any hope of unity or integration" (IS, 394). This is because it focuses on local context and the "systematic study of the local context" (WC, 6)15. It also encompasses the idea that vagueness, often associated with natural language and embodied cognition, can be a powerful cognitive tool. The aim is to design new formal languages that can capture both the properties of natural language—like metaphor, radical context sensitivity, and defeasibility—and formal language. This highlights that explication is not merely about eliminating vagueness but understanding its function and transforming it into a more controlled, fruitful capacity.

• Universal/Global Explication: This trajectory provides the underlying explicatory gradient that makes local refinements possible. It represents a universal explication trajectory. It encompasses the grand historical movements of scientific enlightenment, exemplified by figures like Galileo, Copernicus, Darwin, and Einstein. This progression involves moving from the manifest image (concepts in ordinary language, pre-scientific understanding) to the scientific image (engineered languages and concepts, precise scientific theories). As said by Sellars, the scientific image is still "in the process of coming to be" (SR, 387). This shift is not a clash or replacement but a positive feedback loop or enrichment. Both the manifest and scientific images are dynamic and evolve. To remember the first chapter, the scientific image draws on "linguistic doings, conceptualization, and systematic theorization" from the mind, and its advancement underlines the necessity of mind in its "pure and necessary form" (IS, 79). It leads to an "increasing refinement of the manifest picture of the agency," minimalizing it to "logically-irreducible and necessary activities" (IS, 84).

In conclusion, the overall project of explication embodies the idea that reason is dialectical and an engineering ideal. It means that the conclusive conception of reason is never settled; rather, it is in a constant state of revision and enrichment, avoiding fixed definitions that would betray the spirit of Enlightenment. This process enhances epistemic inquiry by transforming perceived certainty into inferentially articulable plausibility. Let’s remember from chapter 1 that, the "rationality of science lies not in the uniform progression of science, but in how these theories are constructed and how they expand the capacities of reason and its cognitive traction on the world" (IS, 83).

9. Machines Unboxed

Here it is—the end of our thought experiment. Kanzi, Matata, and Sue, the monkey, the 2001 black monolith, the ‘stuff’, the Kant—the LEGO, the pedagogy, the toys, the Boltzmann, the nonconceptual representational mapping. All for this—a comprehensive outside view of ourselves as an AGI.

The semantic or conceptual order, that the automata has gained from the thought experiment journey, fundamentally enables automata to develop a revisable conception of themselves in the world. This self-conception acts as a crucial mediator, bridging the gap between their perceived and actual being, and between oughts (norms) and what is. With the ingress of the semantic or conceptual order, automata gain not just an unrestricted conception of the world, but importantly, a revisable conception of themselves. This self-conception is the foundation for their understanding and grasp of the world. And as we’ve seen, the act of self-conception is not a static identity but a dynamic process that leads to self-transformation, creating a positive feedback loop that instigates disequilibrium and adaptation. To achieve more refined self-conceptions, automata must break away from mere appearances of their current state.

This conceptual consciousness is inherently collective, because it belongs to the deprivatized space of language. Consequently, the self-conception of automata is communal, meaning no thought or self can be considered private or separate from others. As automata develop a conception of themselves, they are increasingly governed by rational norms and impersonal values concerning what to do and what to think. Their rudimentary multi-agent interaction evolves into an explicit social community driven by these objective principles, allowing for the assessment, improvement, or discarding of norms. This means that their reasonings and ends come under the full influence of an "inferential-normative economy" or "impersonal reason" that can "divert any conceived end and to place any norm in peril". Therefore, even an AGI with human-level abilities cannot possess "indelible norms nor fixed goals" (IS, 397).

The automata's self-conceptions and transformations, driven by the self-correcting tendencies of impersonal reason, serve as the criterion for having a history. This means that intelligence is not merely something that has a past, but something that actively constitutes its own history through a sequence of self-conceived transformations. Unlike a fixed nature, a creature endowed with history is capable of reconstituting itself and interfering with its contingently posited settings. This process involves a positive feedback loop between self-conception (what an agent takes itself to be) and self-transformation (how it changes itself based on that conception). Any alteration in self-conception induces a change in the self, and a difference in the self induces a transformation in the self's conception, creating a disequilibrium that drives adaptation. As we’ve seen in the first chapter, for Hegel, this reciprocation constitutes self-consciousness. A robust self-conception leads to consequential self-transformation, while a flawed one leads to defective transformation. A being with such a history can "drift from any fundamental or natural essence toward a future as the being of time," where preconceptions and given totalities are "washed away" (IS, 398). This drift is seen as an alienating cognitive-epistemic vector that pushes beyond limited conceptions of the world or restricted universes of discourse. This is akin to Hermann Cohen's concept of historical self-consciousness, which is fixated on a future that signifies an intelligible eternity where falsely eternalised past and present values cease to exist. The definition and significance of "human" are freed from any purported substantive essence or fixed nature through the growth and maturation of reason. In this context, future is not just the not-yet in a conventional sense but expresses a conception of future as time in which all given totalities, along with transitory, falsely eternalized values of the past and present, are no-longer. This future-oriented thought and will enable genuine conception and transformation, opening possibilities beyond given totalities and working toward concrete actualization. It involves thinking time backwards from the future to the past, viewing the mind as having a self-constituting history rather than a nature, and making the mind an implement of freedom. Geist arrives out of the future…

In this context of historical consciousness and future-oriented thought, automata arrive at the "autonomous idea of making something better than themselves". This is presented as a "logical consequence of the idea of the good". It is characteristic of any form of intelligence endowed with a history—a sequence of self-conceptions and self-transformations and consciousness of such a history—that it will "seek and ask for more intelligence," inevitably leading to the thought of "making something better than itself" (IS, 399). This striving for the better, combined with future-oriented thought, aligns with the idea of bootstrapping—mental capacities capable of self-augmentation.

Automata become free agents by being constrained by what is objective. This might seem counterintuitive, but it refers to a process of self-limitation in the presence of the other—or external world—which is precisely how they achieve concrete freedom. This understanding of freedom is aligned with a concept of positive freedom, where one is free to do something by espousing certain constraints, rather than freedom from constraints. These constraints are primarily those of society and interaction, particularly linguistic interaction. The objectivity that enables this freedom is multifaceted, operating on two interrelated levels enabled by language:

• Intersubjectivity: This refers to the "interdependency of thinking selves" (IS, 399). As we’ve seen in the fifth chapter, an apperceptive self to be individuated, it must operate within a "deprivatized semantic space" composed of "mutual recognizers" (IS, 271). Intelligence, therefore, is largely seen as inconceivable outside of a community of agents or a multi-agent system, structured not by simple communication but by a logical or inferential-semantic space. This communal aspect fosters the formation of agency in a Kantian sense and leads to the design of autonomous artificial agents.

• Facts about the world: This encompasses "theory as all the relations between structures and being" (IS, 399) in its most unrestricted interpretation. The concept of objectivity here is not dependent on any single experiencing subject, but rather on the collective geist as a "dimension of structure" and a "community of language-using agents bound to norms governing the application of concepts" (IS, 271).

By being immersed in the apeiron of the formal dimension, automata are capable of logical world-building. This capacity allows them to "envisioning and make new worlds qua perceptual-noetic toys16". Intelligence is fundamentally "that which makes new worlds rather than merely dwelling in its given world" (IS, 400). This involves enriching reality by toying with and diversifying the possibilities of structure. The objective is to move beyond "habituated facts of experience" by constructing "new experience-constituting languages or paradigms" (REPHI, 9)17. This perspective allows for a view from nowhere and nowhen, representing the impersonality of reason and a history not exhausted by its present.

Thus, the ingress of language into the automata's world profoundly changes their actions, subordinating them to time-general thoughts or inexhaustible ends. These are distinct from immediate, instrumental goals, which are time-specific wants or desires. These ends belong to the "order of self-consciousness" and express the "conceived core of necessities, imperatives, ideals, and needs pertaining to the conception of the self” (IS, 400)—such as the good, beauty, and justice, which structure the automata's entire practical horizon. Crucially, these inexhaustible ends serve as premises for purposive actions, not as their conclusions. They guide and order the automata's actions into an intelligible practical unity that expresses their self-conception. This means their actions, even when instrumental, are manifestations of these higher-order, time-general thoughts.

The concept of artificiality is not merely about mimicking nature but is fundamentally defined by adaptation to new purposes or ends that are not intrinsic to the material ingredients or even the initial recipe (instructions). This signifies a capacity for transformation and repurposing that goes beyond a fixed, given nature. By "repurposing their actions toward inexhaustible ends," automata perform a "first gesture toward artificializing themselves" (IS, 402). This is an advanced form of craft, implying a deliberate shaping of their being according to chosen purposes. This craft signifies making something whose purposes are not inherent in its physical constitution or initial programming. This self-artificialization is a "fundamental component of their reality" (IS, 403), as the mind is that which has a history rather than an essential nature. As we’ve seen in the first chapter, the history of mind is, in fact, the history of artificialization, meaning a continuous process of reconstitution and adaptation to new regimes of purposes. Denying this "artificial truth" of the mind is akin to "rejecting freedom" and "antagonizing the history of the mind" (AYM, 151)18. From this perspective, the idea of "making something better than themselves" is not an "existential threat" but a "logical and necessary extension" (IS, 403) of this self-artificialization program. Any intelligence with a history will seek and ask for more intelligence, leading to this inevitable thought.

Thus,

“Whatever that future intelligence might be, it will be bound to certain constraints necessary for rendering the world intelligible and acting on what is intelligible. That which speaks can now go on and begin an adversarial conversation with gods, and a fecund dialogue with some future intelligence which may have all of its cherished capacities, and more.” (IS, 403. emphasis added).

Our thought experiment has concluded.

Overall Summary

• Reza argues that syntax can be bridged to semantics, primarily through the concept of pragmatics, specifically inferentialist pragmatism.

  • At its most basic level, meaning is defined as the justified use of expressions within social discursive linguistic practices. What counts as the justification of an expression is precisely what counts as its meaning.

  • Semantics (content) is concerned with "what is said"—for instance, what one believes, knows, or claims when stating a proposition p. It focuses on the meaning-conferring inferential roles of syntactic expressions within social discursive practices.

  • Pragmatics (use), conversely, focuses on what one is doing in saying it. This involves the discursive practices or abilities required to deploy a vocabulary, or to confer and apply meaning.

• The meaning and truth of an assertion are determined through a game of giving and asking for reasons, where claims are tested by queries and counter-claims. This process is termed normative scorekeeping pragmatics. Normative scorekeeping pragmatics can begin with a minimal set of rules, with more complex rules emerging naturally through the interaction between interlocutors.

• Reza proposes redefining sociality as a formal condition, best captured by the logico-computational concept of interaction. This redefinition is considered the first step to unbinding rational capacities and rescuing the concept of reason from deep-seated dogmas—thus viewing interaction as a sufficient condition for building the syntax-semantics interface.

• Reza proposes an interactive paradigm where computation is understood as a dynamic interaction. This shifts the focus: From what is a computable function to how the computation is executed. The environment is no longer passive but an active-reactive element that dynamically interacts with the system, providing input and consuming output. This dynamic interaction is crucial for the system's function to make sense and for information to increase, thereby avoiding the problem of epistemic omniscience. This perspective models the system-environment dynamics as an interaction game, which generalizes the concept of computation.

• Interaction games are described as unifying themes for studying structures, information contents, and behaviors, capturing fundamental correspondences between computational behaviors, logical contents, and mathematical structures. Within this framework, computability is defined as the condition of winnability for the system against an environment, meaning the existence of an algorithmic winning strategy to solve a computational problem in the presence of an active opponent. Access to computational resources and performance of permissible moves are explicitly stated as constraints imposed by the interchange of roles between the machine and the environment. Different levels of constraints express different classes of computational complexity.

• The interchange of roles between system and environment is formally defined by duality, where negation is substituted by the reversal of symmetries or swapping of roles in the game. In a computational interaction framework, duality is defined not by classical negation but by the reversal of symmetries or swapping of roles within a game. This allows for the emergence of various forms of dualities, including topological and geometrical ones.

• The interaction game always begins with an action or move made by the opponent, which represents the environment. Following the environment's initial action, the opening move played by the player (⊤), which represents the system, is always a request for data or a query from the opponent (⊥). This establishes the reciprocal nature of the interaction, where the system queries the environment for necessary resources.

• Within the composition of subgames (A ⊗ B), the ability to switch between these subgames is asymmetric. Only the opponent (⊥) can switch between subgames, while the player (⊤) is restricted to reacting within the latest subgame where the opponent (⊥) has played.

• The concept of linear implication (A ⊸ B), which describes the continuation of a game where subgame B consumes or uses subgame A as a computational resource, is an important element in understanding resource-sensitive interaction within the framework of subgames and their compositions. The game A⊸B, showing linear implication where subgame B consumes subgame A as a computational resource, is fundamentally characterized by its 4-tuple components.

• The copycat strategy signifies the game or interaction itself, independent of the specific order of actions performed by the players or processes involved in the interaction. To understand this, you can imagine a universal game board (G) that may contain many other game boards or subgames. On this board, there are two teams of players, agents, or processes (A and B), distributed asynchronously across the board. While actions within each team might be ordered synchronically and sequentially, their interactions with the other team are asynchronous, meaning they can be out-of-order or in partial order. The copycat agent wins against both teams by mirroring one team's plays and running them against the other team, or by copying moves from one game board to another and vice versa.

• While winnability in interaction games is analogous to computability, the true significance of the copycat is not tied to winning. Instead, its power lies in its ability to represent the flow and increase of information across any particular interactive configuration, even if the teams or agents do not react synchronously—the copycat essentially signifies that interaction is computation itself.

• The logical equivalent of the copycat as the agent of interaction, game, or computation is a dialogue, which is considered the engine of semantics, implying that private thought cannot exist without dialogue, and dialogue generates new knowledge through interaction.

• The copycat, therefore, acts as a dynamic orchestrator or a universal translator within the game, enabling the emergence of complex logical and linguistic phenomena from the basic interactions of agents. It's like a universal adapter for communication, allowing different devices to interact and create a shared understanding, even if they operate on different principles.

• The interactive framework proposes that the determination of meaning or proof is an active process, achieved dynamically through interaction or dialogue with its counter-proof (¬A). This involves abandoning classical negation in favor of interactional dualities, where negation is understood as the interchange of roles between the proofs of A and ¬A. Within this dialogical framework, proof is no longer an object but an act, signifying a confrontation of acts or interactions between dualities, which can be represented as agents, processes, or strategies.

• Dialogical interaction, from this perspective, not only enables the computation of meaning or semantic values but also provides vital semantic information such as contextuality and thematization. Crucially, both semantic values and contexts are themselves considered computations. The computation of meaning can be understood by way of proof search and proof normalization.

• According to Samuel Tronçon and his colleagues, particularly Marie-Renée Fleury and Myriam Quatrini, dialogue serves several essential functions within the emergent framework of ludics and interactive computation. They propose that dialogue is a relevant framework for both formalization and studying dialogues, focusing on the dynamics of interactive situations to offer rich intuitions and mathematical insights. The essential functions of dialogue, as outlined by Tronçon et al. are: exchange of information, construction of knowledge, unfolding structure, and extraction of new information.

• The framework of ludics is presented as the formal system that embodies this logic of dialogue. Ludics notably departs from traditional linguistic and logical approaches by rejecting referential theories of meaning, monological semantics, and non-autonomous syntax—replacing them with an inferential theory of meaning, dialogical and operational semantics, an autonomous minimal syntax, and a generalized concept of game that operates without predetermined winning strategies or payoff functions.

• Within ludics, meaning emerges from a dynamic process of interactive proof or computation. Rules and meanings arise naturally through the exchange of loci (addresses of syntactic terms or formulas) and subloci, guided by basic negative and positive actions, and potentially concluded by a daïmon (a termination command).

• The interaction itself is characterized as the coincidence of two dual loci in two different designs. The normalization process in ludics—which is the compositional step— aims to eliminate these dual loci, striving for a "consensus" where the game stops because the two players agree to end it. This highlights that in ludics, meaning is not static but dynamically co-created through the interactive process.

• In Ludics, unlike classical views where speech acts are often normatively predefined, speech acts are understood as evolving naturally through interaction. They are considered partial functions in a computational game framework that attain the status of a speech act when they produce invariant impacts on a shared context. At its core, a speech act is the interaction of two designs (U and B), resulting in a new design (C), where the impact (C) is the invariant behaviour (normal form) resulting from the normalization of U and B.

• Ludics provides a framework that generalizes Robert Brandom's concept of deontic scorekeeping—the game of giving and asking for reasons—by grounding it in a logico-computational dynamic where linguistic rules and meanings emerge naturally from interaction. The dialogue in eight acts between Kanzi (asserter/speaker A) and the monkey (interlocutor/addressee B) illustrates this generalization of deontic scorekeeping in Ludics.

• Negarestani, following Carnap, posits that the formal dimension, encompassing computation, logic, and mathematics, represents a pure transcendental condition . This condition is presented as liberated from the provincialism of Kantian transcendental logic, which is seen as anchored to the apperceptive I and particular transcendental types shaping the subject's experience.

• While formal languages might traditionally be seen as sacrificing semantics, they actually enable the emergence of semantic complexity through the confrontation of syntactic processes. This perspective allows for richer semantic relationships and the potential to resemantify formalisms developed for specific backgrounds to new problems or frameworks—Negarestani argues that only the richness of the formal can truly express or expand the richness of experiential content. To expand experience, language should be "decoupled" from the experiencing subject and its communicative role.

• Artificiality signifies the capacity to unbind the formal—to allow the formal dimension to be fully expressed, augmenting world-structuring abilities and syntactic-semantic expressivity.

• To genuinely hone the notion of logical structure, logic must be treated in terms of unrestricted logical world-building, decoupled from any enforced representational considerations—experiential content, empirical truth sources, or subjective application criteria—that might pre-establish its frontiers—expanding the field of logic, unconstrained by concerns of subjective representation, is absolutely necessary to constitute objects, make objective assertions, and deepen our understanding of objectivity.

• For the conceptualizing mind, spontaneity is not primarily found in its perceptions or actions, nor in the content of its thought episodes, but rather in the formal dimension of thinking. This refers to how language and logic process and organize such contents. Constraining the meaning—semantic value—to the metaphysics of sensation, as seen in Sellars's theory of picturing, while seemingly providing epistemic traction, ultimately impoverishes both form and content if the formal's function is reduced a priori to epistemic content or application.

• Reza argues that only by disengaging the formal from subjective experiential content—separating the pure formal dimension of thought from its apparent epistemic-experiential content—can the formal be treated systematically. This systematic approach allows for experiential content to be structured much more richly, moving beyond the limited scope of nonconceptual representations. Formal languages are crucial in this context, as they express the systematicity of the formal, unburdened by communicative function, subjective experience, or ordinary semantic content. This desemantification—decoupling from specific subject matter—paradoxically enables resemantification, allowing a given formalism to be applied to new problems or frameworks.

• Once consciousness is imbued with language, it develops into what Findlay called a sidelong intentionality, meaning its focus extends beyond any specific limit set by a given world. This enables the simultaneous, indirect, and implicit thought of many things at once. This cognitive tendency—nisus—fundamentally transforms the world experienced by artificial agents—automata—from a narrow zone of thinking and action into an unrestricted universe.

• Conceptual consciousness exhibits a nisus not only towards diversification—"diremptive" tendencies—but also towards synthesis and integration. This dynamic is understood through Plato's concepts of peras—the determinate—and apeiron—the indeterminate—, where language and logoi—logic and mathematics—function as the peras, actively determining and structuring the indeterminate.

• The dialectical task of explication, as presented by Reza, concerns itself with the transformation of vague, pre-scientific concepts—termed the explicandum—into new, exact, precise, and more useful concepts, known as the explicatum. This process aligns with the broader ideal of rational scientific Enlightenment. The explication process is not simply a clarification or amelioration of existing concepts, but rather a form of conceptual engineering.

• The overall project of explication embodies the idea that reason is dialectical and an engineering ideal. It means that the conclusive conception of reason is never settled; rather, it is in a constant state of revision and enrichment, avoiding fixed definitions that would betray the spirit of Enlightenment. This process enhances epistemic inquiry by transforming perceived certainty into inferentially articulable plausibility.

• The thought experiment journey, fundamentally enables automata to develop a revisable conception of themselves in the world. This self-conception acts as a crucial mediator, bridging the gap between their perceived and actual being, and between oughts (norms) and what is.

• With the ingress of the semantic or conceptual order, automata gain not just an unrestricted conception of the world, but importantly, a revisable conception of themselves. This self-conception is the foundation for their understanding and grasp of the world.

• As automata develop a conception of themselves, they are increasingly governed by rational norms and impersonal values concerning what to do and what to think. Their rudimentary multi-agent interaction evolves into an explicit social community driven by these objective principles, allowing for the assessment, improvement, or discarding of norms.

• The automata's self-conceptions and transformations, driven by the self-correcting tendencies of impersonal reason, serve as the criterion for having a history. This means that intelligence is not merely something that has a past, but something that actively constitutes its own history through a sequence of self-conceived transformations. This future-oriented thought and will enable genuine conception and transformation, opening possibilities beyond given totalities and working toward concrete actualization. It involves thinking time backwards from the future to the past, viewing the mind as having a self-constituting history rather than a nature, and making the mind an implement of freedom.

• Automata become free agents by being constrained by what is objective. This might seem counterintuitive, but it refers to a process of self-limitation in the presence of the other—or external world—which is precisely how they achieve concrete freedom. This understanding of freedom is aligned with a concept of positive freedom, where one is free to do something by espousing certain constraints, rather than freedom from constraints.

• Thus, the ingress of language into the automata's world profoundly changes their actions, subordinating them to time-general thoughts or inexhaustible ends. These are distinct from immediate, instrumental goals, which are time-specific wants or desires. These ends belong to the order of self-consciousness and express the conceived core of necessities, imperatives, ideals, and needs pertaining to the conception of the self—such as the good, beauty, and justice, which structure the automata's entire practical horizon.

• The concept of artificiality is not merely about mimicking nature but is fundamentally defined by adaptation to new purposes or ends that are not intrinsic to the material ingredients or even the initial recipe (instructions). This signifies a capacity for transformation and repurposing that goes beyond a fixed, given nature. This is an advanced form of craft, implying a deliberate shaping of their being according to chosen purposes. This craft signifies making something whose purposes are not inherent in its physical constitution or initial programming. This self-artificialization is a fundamental component of their reality, as the mind is that which has a history rather than an essential nature.

  “Whatever that future intelligence might be, it will be bound to certain constraints necessary for rendering the world intelligible and acting on what is intelligible. That which speaks can now go on and begin an adversarial conversation with gods, and a fecund dialogue with some future intelligence which may have all of its cherished capacities, and more.”

For citations of Intelligence and Spirit, the format will be (IS, x), therein x is equal to the page in which the cited text can be in the Urbanomic edition of the book. For other books, the specific edition and book will be noted down in a footnote. I’ve also taken from the various lectures given by Reza in The New Centre Research & Practice.

Diagrammatization

1. Realization of Language

This section—and the chapter in general—focuses on the constitutive and intrinsic role of language in the realization of general intelligence in our thought experiment. Reza argues that language is not an external feature to be added to general intelligence after its development. Instead, language is the very framework within which general intelligence can be realized, making the realization of general intelligence concurrent and coextensive with the realization of language itself. Without language, there would be no geist, no mind, and no thinking "I". The omission of language when discussing concepts like truth, thinking, or Being leads to atavistic metaphysics and the myth of the given, because any discussion of semantics—which is crucial for these concepts—cannot be separated from language in its generic form. We’ve already seen this from the first chapter.

The construction of AGI should fundamentally involve the realization of language as an intrinsic and constitutive dimension. This means taking the evolution of language seriously as the most indispensable part of AGI realization. Rather than providing artificial agents with a pre-developed formal language, an environment must be established for agents to develop language through its evolution among them. The evolution of language is understood as a process of canalization where prevalent intelligent behaviors are directed towards qualitatively distinct and unique behaviors. This process involves intelligent behaviours—or agents—progressively coming under new generative constraints, leading to qualitative shifts within the system of interacting agents. The core of this process is the development of multi-agent interaction:

• From rudimentary communication to interaction via symbol design.

• From symbol design to syntax.

• And from syntax—through interaction—to semantics. Interaction, at various levels of complexity—from protolinguistic to pragmatics—, is key to the evolution of language and its autonomous rule-governed functions, and by extension, to the realization of general intelligence.1

While insights from natural language evolution can inform AGI construction, language in its entirety cannot be reduced to natural language. Natural language, despite its low syntactic complexity and semantic ambiguity, contains diverse logico-computational phenomena that can be integrated into an artificial general language. This superior language would combine properties of formal-theoretical languages—syntactic powers, semantic transparency—with the interactive—social—dimensions of natural languages. Interaction, as the explicit framework of natural languages, is the underlying implicit and fundamental logico-computational framework of language in general.

To proceed with the AS-AI-TP thought experiment from chapter 2, the status of the previously concept-having automata, S and M, must be "rescinded" so they now have the same status as Kanzi. The only remaining modifications are the multi-agent system and the capacity to produce quasi-continuous sounds.

Stages of Language Realization in Automata

The thought experiment proceeds through specific stages for language realization in artificial agents:

1. Nonconceptual Representings (Picturing): This involves automata's capacity for nonconceptual representings where metalinguistic properties picture nonlinguistic properties—of items and occurrences in the world—through the syntactic structures of sign-designs. This relates to Sellars's account of picturing, where an android robot forms progressively more adequate pictures of the world using a Robotese language.2 Picturing, belonging to the real order, differs from signifying, which is of the"logical order or intentionality. Although rule-governed signifying is embodied in pattern-governed picturing, it is irreducible to it, as rule-governed conceptual activities are patterning patterns.

2. Discretization and Combinatorial Symbols: The process requires understanding what symbols are and the processes needed for a symbolic syntax that can be bridged with semantics. This specifically involves the process of discretization, which is necessary for the realization of combinatorial symbols. Symbols are distinct from signs: symbols are combinatorial syntactic elements that primarily map to one another, rather than directly to items in the environment, and their systematic inter-relations can codify or structure indexical relationships. Unlike iconic or indexical signs, symbols have an in-principle unrestricted structuring capacity.

3. Transition from Syntax to Semantics: The final stage involves surveying how the transition from syntax to semantics is possible under the influence of interaction as a logico-computational phenomenon, which is the "engine of language and its multilayered qualitative structure" (IS, 299). This process endows agents with the ability to selectively compress data and elaborate diverse relations between regularities, enabling them to describe and explain them in context through material inferences. This requires the sound cue—sign—to transform into a symbol that primarily relates to other symbols, forming a stable and combinatorial medium capable of encoding broader ranges of relationships between pattern-governed regularities.

2. Pictures, Signs and Symbols

This section is concerned with computational problem regarding how its agents can interact synchronously and asynchronously with one another and their environment, delving into how automata in a multi-agent system develop representational and symbolic capacities.

Reza presents to us this diagram titled "Environment and multi-agent system”. Let’s discuss it.

The diagram illustrates a multi-agent system operating within a larger environment. The multi-agent system is comprised of three Agent units—Sue, Matata, and Kanzi. Let’s see the different elements of which the agents comprised of.

• Sensors (Inputs): These are indicated by arrows pointing inwards. Sensors provide sensory input, allowing the agent to acquire information from its environment. This input can include information from other agents in a distributed system, where one agent's input can be another's output.

• Effectors (Outputs): These are indicated by arrows pointing outwards. Effectors enable the agent to act upon its environment and other agents. The relationship between sensors—perception—and effectors—action—is often understood as a "circulation of input and output" forming a loop.3

• Internalized Model of the Environment (Constructive Memory): This is a central component within each agent. It functions as a constructive memory that singles out what is invariant or unchanging from different encounters, variations, or reproductions of initial memories. The purpose of this memory is to create predictive models or forecasting models for anticipating actions and their consequences in the environment, allowing for context independency of interaction with items. Actions are the results of constructive memory, meaning no action would be possible without this function.4

• Physical Substrate: This textured layer at the bottom of each agent unit represents the available resources as support and limit information processing, model building, and decision making for the agent. This ties into the concept of resource sensitivity, which is crucial in understanding interaction as computation.5 The "computational cost" of processing information is directly related to the size of this internal model.6

• The diagram shows two larger Agents interacting with each other via curved arrows, signifying a bidirectional flow of information or influence.

• The smaller, third Agent[Kanzi] is positioned below and between the two larger ones, indicating a nested structure within the multi-agent system—reflecting the idea of hierarchies where components are nested and interact in a nonlinear fashion

• Finally, the environment is broadly defined in the ninth session of the Complexity and Computation lectures as "everything that is relevant to the algorithm's work except for what it is internal to the algorithm and completely specified by the algorithm's program".

Reza then explains how automata develop two distinct forms of understanding:

• Picturing (Non-Conceptual/Real Order): Refers to a basic, nonconceptual form of representing that belongs to the real order. When an automaton "pictures" something, both the internal representation and the external item exist within this real order; neither belongs to the order of intentionality or thinking.7 This process involves a causal registration of pattern-governed regularities in the environment. The automaton's wiring diagram or nervous system undergoes changes that allow it to form nonconceptual associations and transitions between one pattern of occurrence and another. This is understood as a mapping between objects in the real order (the automaton's wiring and events in the world). Picturing enables automata to statistically correlate patterns of events and exhibit reliable differential and adaptive responsiveness to their environment. For instance, an automaton can register a "rustling noise" followed by a "fuzzy grey item," allowing it to make rudimentary inductive moves and predictions based on these occurrences. This is akin to a security swipe card's magnetic field changing in response to a physical input, enabling specific actions. However, pictures qua signs can only represent the one-to-one mappings between pattern-governed regularities. Nonconceptual representations are independent and lack structured relationships for transitions.

• Signifying (The Conceptual/Logical Order): represents a qualitatively higher, conceptual level of knowledge that belongs to the logical order or the order of intentionality.8 Unlike picturing's one-to-one mappings to external reality, symbols involved in signifying primarily stand in "combinatorial relations to one another (symbol-to-symbol, token-to-token)". It is this "interrelational order of symbols (i.e., symbolic syntax rather than syntax in terms of causal regularities) that the relations between different patterns or world-picturings can be encoded, structured, singled out, and elaborated". This symbolic interplay is what "affords semantics" (IS, 303).

Reza states that while conceptual thought may be "built on pictures and iconic-indexical signs," it is explicitly stated that "Being built on something is not the same as being made of something" (IS, 304). While semantic function is causally dependent on its physical incarnation (pattern-governed picturing), it is logically irreducible to it. The order of signifying—rule-governed conceptual activities—is fundamentally distinct from the order of picturing—pattern-governed regularities—, as it is concerned with the complex interactions between patterns rather than simple one-to-one mappings. Rule-governed conceptual activities are described as patterning patterns. Ray Brassier in his essay Transcendental Logic and True Representings is quoted as defining rule-governed activity as "a species of pattern-governed behavior: a recursive loop generated through the interaction between complex patterns. It is a patterning of patterns; but a patterning executed through the same kinds of causal mechanisms that generate patterns in general" (IS, 304). While Reza acknowledges this description of patterning patterns and its causal underpinnings, he immediately follows this citation by emphasizing the categorical gap and the qualitative distinction between being "built on" and being "made of". This suggests that while Reza finds Brassier's description of the causal mechanism—recursive loop—useful, he resists the implication that it reduces signifying to merely a species of pattern-governed behavior, thereby preserving the fundamental difference in logical order. Brassier, following Sellars, notes that "truth at the level of represented content is anchored in something akin to truth, which Sellars calls 'correct picturing,' at the level of nonconceptual representing".9 However, the criterion of pictorial adequacy is "internal to the signifying order" and "formulated in terms of the degree to which what we know about the correlation between representing and represented allows us to realize our purposes in the world". This means that while nonconceptual picturing guides true representings, its adequacy is ultimately assessed from within the conceptual, norm-governed discursive framework. In sum, the distinction is between receptive, pattern-governed interactions—picturing—, which provide the raw material and causal conditions, and spontaneous, rule-governed conceptual activities—signifying—, which actively structure, organize, and interpret that material through inferential relationships.

3. Sign-Vehicles and Symbol-Design

The third section delves into how automata within a multi-agent system progress from basic reactive behaviors to developing symbolic communication. In a multi-agent system, automata, such as Kanzi (K), Sue (S), and Matata (M), possess a causal structure—wiring diagram or nervous system—that allows them to associate occurrences. For example, they can associate a "rustling noise (Nr)" with the "appearance of a fuzzy grey item (G)" or a "fuzzy grey item coming into contact with the heap of black (Bc)" with a "shrieking noise (Ns)". These are inductive moves, representing pattern-governed regularities. The significance of these associations is initially based on the statistical frequency of spatio-temporal occurrences registered by the automata. For instance, if K registers a visual event v (e.g., fuzzy item touching a black item accompanied by a shrieking noise), it emits a whistling sound 'R'. K's repeated use of 'R' is then registered by S and M as a cue for the occurrence of 'Ns' and the pattern Ei*-Ej*. Registering such noises or events depends on two factors:

1. its interest or significance for the automaton's behavioral economy, requiring "top-down attentional amplification" to mobilize changes in the wiring diagram;

2. the sufficiency of the automaton's causal structure for pattern recognition to differentiate sounds—shrieking vs. rustling—and make inductive moves.

An indexical sign is defined by its interpretant being entirely a statistical regularity of some occurrence, which can be a causal or temporal invariance. Its interpretation primarily requires a heuristic device. An index is essentially a sign that is causally linked with something else in space and time. Indexical sign-vehicles, such as R, are themselves built upon iconic signs. Iconic signs concern the resemblance of one pattern to another. This resemblance, however, is not inherently meaningful; it's a "matter of an arbitrary interpretation of the similarity-vagueness of something versus something else" (IS, 306). Therefore, iconicity is fundamentally about the stimuli-based discrimination of stuff.

Pictures, as indexical signs, are limited to one-to-one mappings between pattern-governed regularities. For automata to fully structure and navigate their environment solely through picturing, they would face an infinite regress. Every new relation between patterns would require a new picture, leading to an ever-expanding internal model that becomes computationally unfeasible and susceptible to resource starvation. Their one-to-one mapping structure makes them susceptible to mimicry and deception, as illustrated by the phengaris rebeli butterfly mimicking ant chemical and acoustic signals to exploit the colony.

Automata and nonconceptual representational mapping

Reza now presents us with this diagram ‘Automata and nonconceptual representational mapping’, to show how an automaton processes and responds to environmental stimuli without engaging in semantic understanding or conceptual thought. The diagram is set within the toy universe of our thought experiment. The central entity is Kanzi. The components on the Lego baseplate represent the automaton's internal system.

Ei-Ej represents pattern-governed regularities or sequences of events occurring in the automaton's environment. For instance, this could be a rustling noise (Ei) followed by the appearance of a fuzzy grey item (Ej), or the fuzzy item contacting a black heap and then a shrieking noise (Ns). The large rectangular monolith and the small grey figure are examples of items in the environment that the automaton encounters. The sound Ns (shrieking noise) is a specific environmental occurrence that is statistically correlated with the Ei-Ej pattern. This sound Ns is mapped onto the automaton's devices as an acoustic pattern σ. The automaton's auditory system registers σ as an input acoustic pattern associated with the occurrence of Ns and the broader event, like the fuzzy item touching the black item.

As the automaton registers σ, it produces the sound Σ to tag the occurrence of the pattern Ei-Ej. This sound is emitted using the automaton's inbuilt electromechanical devices. The internal state of the automaton's representational system, or its wiring diagram, undergoes a change corresponding to the environmental events. This internal change is represented as E*i-E*j. This E*i-E*j is a rudimentary, nonconceptual representing. The automaton's ability to causally register these pattern-governed regularities is termed picturing. This correct picturing is a result of both environmental pressures and the complexity of the automaton's causal structure, which mediates between environmental input and behavioural output.

The large curved arrow labeled M represents the representational mapping (Ei-Ej to E*i-E*j). Reza states that this mapping is not a meaning relation.10 Instead, it is a transformation between two natural objects: the environmental state and the internal state of the structurally sufficient and behaviorally active automaton. Therefore, the sound cue (Σ) does not in any semantic sense signify an aspect of the external environment, nor does it describe any detail about the internal state of the automaton itself. It is simply a probabilistic marker for the statistical convergence of the automaton's σ-state and the pattern of occurrence for external events Ei-Ej. This means its significance lies purely in the "statistical frequency of spatiotemporal occurrences" and is "devoid of complex inferential or conceptual relationships" (IS, 306). This leads to various issues like picturing regress11 and computational unfeasibility12 that arise without symbolic systems.

To overcome this, indexical sign-vehicles must be incorporated into a different kind of semiotic system. This system's semiotic elements do not represent external patterns or referents; instead, they primarily relate to one another (symbol-to-symbol, token-to-token). This combinatorial order of symbols is what enables relations between different patterns or world-picturings to be encoded, structured, singled out, and elaborated. Crucially, semantics is afforded by these symbolic elements of syntax. Symbols are built upon indices—which are built upon icons—, but these are distinct levels of structuring, not simple compositional relations. Symbols—by virtue of their combinatorial self-referentiality—possess an in-principle unrestricted structuring capacity. The full structuration of the automaton's world begins with symbolic technologies that allow for syntactic codification and semantic elaboration of relations between pictures. This symbolic order enables agents to selectively compress data, single out, and elaborate diverse relations between regularities, allowing them to describe and explain patterns in context, rather than merely picturing them. To perform material inferences—practical competence in using concepts—, the automata requires an artificial general language to syntactically encode and semantically elaborate the relationships between pictures.

4. An Acoustic Experiment in the Production of Symbols

This section introduces a critical constraint on the automata's sound production and explores its implications for the development of symbolic systems. The section begins by reiterating that the automata, within their toy universe, are equipped to produce only quasi-continuous sounds. This specific modification was incorporated into the model to allow for the monitoring of the processes necessary for generating symbols. The automata possess organs or electromagnetic devices that can constrict and discontinue these continuous sounds in a controlled manner, either abruptly or gradually, thereby creating an acoustic range. These constricting devices coordinate, much like human vocalization organs such as the lungs, nasal canal, tongue, and lips. The resulting sound—while regulated by this discontinuation—remains quasi-continuous.

However, this communicative regime presents significant challenges. The instability and excess of noise inherent in these quasi-continuous sounds (R) negatively impacts the precision of their signaling function. This imprecision affects both what the sound signals (differentiating between various pattern occurrences) and how reliably the cue is recognized and acted upon to facilitate a coordinated group response. An illustrative example provided by Reza is animal alarm calls, which use quasi-continuous acoustic signals. Due to the inherent instability and fuzziness of these signals, a single call might serve multiple roles, such as signaling the presence of a predator, acting as a mating call, or indicating the presence of food. This ambiguity compromises the effectiveness of group actions because there's no reliable guarantee that the communicated signal will be correctly received as a cue for the communicator's intended referent. Furthermore, quasi-continuous sound has a low degree of combinatoriality, limiting the establishment of stable, coded relations between different sound cues.

To overcome these limitations, a process of discretization is required to implement effective combinatorial mechanisms among sound-tokens. The proposed solution involves the systematic reuse of acoustic cues in interactions between agents, leading to a self-organization map or artificial neural network-like process. Through this, agents automatically select and reuse a small, finite repertoire of coarsely discretized, low-dimensional sounds. These sounds cease to function as mere sign-vehicles that represent external things; instead, they become abstract acoustic elements. This structural discretization, combined with the reduction in sound clusters, forms the "first building blocks of speech"—a finite repertoire of sounds as symbolic tokens. These tokens, described as comparable to basic phonological units—beeps, clicks, chirps, rustles—, are now reusable and sharable. They can be combined according to statistical-acoustic transition rules—a low-cost transition from a [V] sound to an [AA] sound resulting in a preferred [VAA] concatenation—to produce numerous "utterable concatenations" from a limited set of basic units, forming the "skeleton of the automata's syntactic utterances" (IS, 319).

Finally, the organization of these discretized sounds, despite reducing the sheer number of acoustic data, enhances their capacity because they can now be combinatorially grouped and structured. These newly formed symbolic tokens are defined by their syntactic configurations, losing their primary communicative signaling function to become compositional elements. This transformation into discretized and combinatorial sounds allows the automata to enter the syntactic domain of language, where "combinatorial relations between symbols can be manipulated to generate more complex syntactic structures capable of encoding broader ranges of relationships between pattern-governed regularities" (IS, 320).

5. Generative Processes and The Hierarchy of Syntactic Complexity

This section details how the automata in the toy universe transition to a higher level of cognitive ability through the development of symbolic language, building upon the preceding discussion of symbol design and the discretization of sound, as the the discretization of sound in the multi-agent system is a pivotal structural change that enables the emergence of language, speech, and higher cognition. This transformation fulfills a "necessary condition for the emergence of speech" and evolves interaction into an abstract system capable of generating increasingly adequate structuring abilities, which is termed "language" or a "geistig scaffold" (IS, 320). With the acquisition of these discrete sound-composites—symbols—, the multi-agent system transitions from a basic communicative regime to a linguistic system. The automata can now increasingly structure their interaction with their environment by structuring their own interactions through this newly formed linguistic framework.

The very act of discretizing sound units simultaneously gives rise to powerful generative combinatorial processes: iteration and recursion. These processes emerge from the self-organization of the interacting agents and are critical for building complex syntactic structures. Reza writes that the "self-organization of language, the syntactic-semantic interaction between agents, that is the real protagonist of our toy universe" (IS, 321). Any structural change within this linguistic interaction directly translates into a change in the automata's structuring abilities, reflecting Hegel's insight that the transcendental subject (automaton) is suspended in the process of the self-organization of geist, whose dasein is encapsulated in the self-organization of language.13

Let’s investigate the concepts of iteration and recursion. Iteration is described by Reza as a memoryless combinatorial process where constituents can be repeated and combined without restriction, generating syntactic strings like 'a, ab, abc'. When combined with embedding operations, iteration can also encode dependency-relations (like [a[b]]). This means that each step in an iterative process proceeds independently of the previous one, and there are no inherent dependency relations generated between these repetitive actions. In its rudimentary form, iteration generates structures that lack dependency relations because it does not retain memory of previous operations. This allows for identical repetition. An intuitive example is the instruction "chop the garlic until it is turned into a paste" (IS, 322). To achieve the desired output, one does not need to memorize the history of previous choppings; the action can simply be repeated until the condition is met. Each chopping is a separate act and does not rely on prior or subsequent actions. Similarly, the sequence of natural numbers, one, two, three..., can be seen as an iterative process where each successor is produced without needing to remember the full history of previous numbers (RHL, 49)14.

Recursion, on the other hand, is a memory-driven operation that operates on the product of the previous steps. It produces new hierarchies that encode the history of transformations between constituents of the same category, resulting in syntactic expressions with a "wide range of coded information regarding the structure, the type of grouping, and their intracategorical dependencies" (IS, 323).This means that each subsequent action or computation in a recursive process is built upon, and requires retention of, the history of prior operations. This memory enables the system to "keep track or add to memory using a pushdown stack" (RHL, 180), ensuring that each step proceeds with knowledge of what has already occurred. For instance, "cut the pizza into six equal slices" (IS, 323) is a recursive operation because each cut must build on the previous ones; the final product cannot be achieved without preserving the memory of earlier actions. Similarly, sourdough bread making requires memory of the previous batch.15

The core of recursion lies in the "embedding of constituents within constituents of the same kind or category" (IS, 322). This specific type of embedding is what fundamentally generates new dependency relations. This embedding process results in nested hierarchical structures. For example, a grammatical rule where a Linguistic expression ⇒ Linguistic expression + X (where X is some other unit) creates this self-referential structure where the category appears on both sides of the rule, leading to recursion (RHL, xx). Recursive embedding produces "new hierarchies that encode the history of transformations between constituents of the same category" (IS, 323). This means the structure itself carries information about how it was step-by-step built.

The syntactic expressions generated through recursive embedding contain a "wide range of coded information regarding the structure, the type of grouping, and their intracategorical dependencies" (IS, 323). The combined application of iterative and recursive operations leads to a proliferation of syntactic expressions which can then be grouped into a nested hierarchy of syntactic complexity. This aligns with Noam Chomsky's theory of formal grammar, classifying syntactic structures into recursively enumerable, context-sensitive, context-free, and regular languages. As one moves up this hierarchy, grammars and computational automata become “successively more expressive but also more resource-consuming," and languages become "harder to recognize” (IS, 324).

6. Base Syntactic Abilities

The final section in this chapter discusses the nature of syntactic reports, the limitations of automata in developing semantic abilities, and introduces the idea of language as a calculus leading into the next chapter's focus on semantic complexity.

SYN: [M[S[K[Nr [G ]],[G [Bc ]],[Bc [G [ Ns ]]]]]], serves as a key example of the automata's syntactic reports. This expression, SYN, is presented as a syntactically structured picturing report. It is built upon discretized sound-composites qua symbols which have undergone transformation from simple acoustic cues to abstract, combinatorial tokens. The nested bracket structure of SYN is crucial: it can sufficiently encode the sequence and relations of items and occurrences without needing explicit predicative expressions like "was there" or "is next to". Essentially, SYN's syntactic order replaces time and location stamps and relations usually conveyed by predicates. Reza provides a "rough analogical translation" of this complex SYN expression: "Matata thinks based on the report given by Sue that Kanzi reports the presence of a fuzzy grey item after hearing a rustling noise. The fuzzy item is now contacting the heap of black and will make a shrieking noise as it touches it" (IS, 324). This demonstrates how entities (Matata M, Sue S, Kanzi K, fuzzy grey item G, heap of black Bc) and events (rustling noise Nr, shrieking noise Ns) are encoded syntactically.

These syntactic abilities allow the automata to “encode the (nonconceptual) structural or syntactic relations between causally registered invariances regarding items and occurrences". They can recognize, in a computational sense, the sequence and structural relations between "causally pictured items and occurrences" (IS, 326). A chess example illustrates this: a symbol-design like [N[j]] (a black king in diagonal relationship with a white bishop) is considered equivalent to a syntactically structured picturing report like SYN. The "metagame" of chess rules ("If the black king is checked by the white bishop, then interpose the black bishop") represents conceptual activities embodied by these syntactic configurations. The player then acts on this rule by moving the piece, represented as [N[j[J]]]. This highlights how syntactic configuration embodies rule-governed conceptual activities that help disambiguate and elaborate reports.

The diagram of "automatic laughing bags" serves as a vivid illustration of how automata can deploy syntactic vocabularies within the framework of the Chomsky hierarchy of formal languages. This example, attributed to Robert Brandom, demonstrates a rudimentary form of language generation and recognition that operates at the lowest level of syntactic complexity: regular languages.

The "automatic laughing bags" are conceived as automata capable of recognizing and producing "laughing strings" using just four discrete sounds: [h], [o], [a], and [e]. The algorithmic process for generating a laugh-token is modeled on a finite state machine. This machine operates through a sequence of states with specific transition rules:

1. It starts at state 1.

2. If the first sound is not 'h', it does not progress. If it is 'h', it emits an 'h'-sound and moves to state 2.

3. In state 2, if the sound is not 'a', 'e', or 'o', it remains stuck. If it is one of these, it emits that sound and moves to state 3.

4. In state 3, if a terminating sign '!' is present, it moves to state 4 and produces the shortest laugh ("ha!", "he!", "ho!"), ending the process.

5. Alternatively, if it chooses to make a longer laugh (by emitting another 'h'-sound instead of '!') from state 3, it loops back to state 2 and repeats the process indefinitely until the terminate command '!' is reached.

Any string that successfully reaches the final state (state 4) is considered an item of laughing bag vocabulary and is recognizable by all such automata.

This finite state machine model corresponds to the regular languages at the bottom of the Chomsky hierarchy16. Regular languages are the simplest class of formal languages, characterized by grammars that can be recognized by automata with finite memory. While simple, finite state grammars are capable of generating an infinite set of strings, as demonstrated by repetitive patterns like "John is very, very, very, very, . . . , very nice". This shows that infinitude in language does not necessarily imply creativity in the human sense (RHL, 129). The automatic laughing bags illustrate the fundamental capacity for combinatorial grouping and structuring of discrete sounds, transforming fuzzy sound cues into acoustic tokens that can be used as a protocurrency for a new type of interaction.

At this stage, the automata acquire structure-encoding syntactic configurations that express how things are in a nonconceptual manner. They can classify items by assigning labels using their sounds (like "beep-beep-click-click" for a "bulbous pile of green") and form well-formed syntactic sentences configuring relations between these labels. However, these protothoughts lack semantic structuration and inferential, rule-governed intra-linguistic transitions. The automata do not possess propositions whose conceptual contents are determined by their inferential roles because they have not yet achieved the practical mastery of inference—therefore, their reports are not objective.17

Therefore, "intentional relations (thinking-abouts) require semantic relations, and semantic relations require a public language as the engine and vehicle of their realization" (IS, 333). Without a public language and semantic space, the automata cannot generate a hierarchy of semantic complexity. Ascending the semantic hierarchy demands practical mastery of using vocabularies that express various grades and roles of concepts, which make explicit the inferential relations articulating the space of implications18 where rational, discursive consciousness gains significance.

Reza, following Carnap, posits that viewing language as a calculus—a system of formation and transformation rules in symbol-design—does not reduce language or downplay its perceptual, social, or cultural aspects. Instead, it suggests that expanding language's scope requires subordinating its structure to prior representational, social, or cultural considerations. The work of Carnap, in envisioning language as a general calculus, is noted for blurring the lines between syntax, logic, and computation. Crucially, semantics is presented as reducible to syntax under specific conditions, particularly through an interactionist view of syntax where semantic complexity emerges immanently from the confrontation of syntactic processes or symbolic chains. This move is crucial because it liberates language from what is seen as the "Kantian straightjacket”—the subordination of the logical and formal dimension to sensible intuition and fixed representational functions—and from "Wittgenstein's prison" (the picture-theory of language). It's not about abandoning meaning but about re-imagining how meaning is generated and enriched. Which we shall see further in the last chapter of our thought experiment.

Reza ends the chapter by oultining the progression of the book thus far, which we shall diagramamtize.

Overall Summary

• The construction of AGI should fundamentally involve the realization of language as an intrinsic and constitutive dimension. This means taking the evolution of language seriously as the most indispensable part of AGI realization. Rather than providing artificial agents with a pre-developed formal language, an environment must be established for agents to develop language through its evolution among them.

• This process involves intelligent behaviours—or agents—progressively coming under new generative constraints, leading to qualitative shifts within the system of interacting agents. The core of this process is the development of multi-agent interaction:

  • From rudimentary communication to interaction via symbol design.

  • From symbol design to syntax.

  • And from syntax—through interaction—to semantics. Interaction, at various levels of complexity—from protolinguistic to pragmatics—, is key to the evolution of language and its autonomous rule-governed functions, and by extension, to the realization of general intelligence.

• The thought experiment proceeds through specific stages for language realization in artificial agents: Nonconceptual Representings (Picturing) - Discretization and Combinatorial Symbols - Transition from Syntax to Semantics.

• Picturing (Non-Conceptual/Real Order): Refers to a basic, nonconceptual form of representing that belongs to the real order. When an automaton "pictures" something, both the internal representation and the external item exist within this real order; neither belongs to the order of intentionality or thinking. This process involves a causal registration of pattern-governed regularities in the environment. Picturing enables automata to statistically correlate patterns of events and exhibit reliable differential and adaptive responsiveness to their environment. Pictures qua signs can only represent the one-to-one mappings between pattern-governed regularities. Nonconceptual representations are independent and lack structured relationships for transitions.

• Signifying (The Conceptual/Logical Order): represents a qualitatively higher, conceptual level of knowledge that belongs to the logical order or the order of intentionality. Unlike picturing's one-to-one mappings to external reality, symbols involved in signifying primarily stand in combinatorial relations to one another (symbol-to-symbol, token-to-token).

• The order of signifying—rule-governed conceptual activities—is fundamentally distinct from the order of picturing—pattern-governed regularities—, as it is concerned with the complex interactions between patterns rather than simple one-to-one mappings. Rule-governed conceptual activities are described as patterning patterns.

• In a multi-agent system, automata, possess a causal structure (wiring diagram or nervous system) that allows them to associate occurrences. These are inductive moves, representing pattern-governed regularities. The significance of these associations is initially based on the statistical frequency of spatio-temporal occurrences registered by the automata.

• Pictures, as indexical signs, are limited to one-to-one mappings between pattern-governed regularities. For automata to fully structure and navigate their environment solely through picturing, they would face an infinite regress.

• To overcome this, indexical sign-vehicles must be incorporated into a different kind of semiotic system. This system's semiotic elements do not represent external patterns or referents; instead, they primarily relate to one another. This combinatorial order of symbols is what enables relations between different patterns or world-picturings to be encoded, structured, singled out, and elaborated. Symbols are built upon indices—which are built upon icons—, but these are distinct levels of structuring, not simple compositional relations. Symbols, by virtue of their combinatorial self-referentiality, possess an in-principle unrestricted structuring capacity.

• The instability and excess of noise inherent in the automata’s quasi-continuous sounds (R) negatively impacts the precision of their signaling function. This imprecision affects both what the sound signals (differentiating between various pattern occurrences) and how reliably the cue is recognized and acted upon to facilitate a coordinated group response.

• To overcome these limitations, a process of discretization is required to implement effective combinatorial mechanisms among sound-tokens. The proposed solution involves the systematic reuse of acoustic cues in interactions between agents, leading to a self-organization map or artificial neural network-like process. Through this, agents automatically select and reuse a small, finite repertoire of coarsely discretized, low-dimensional sounds. These sounds cease to function as mere sign-vehicles that represent external things; instead, they become abstract acoustic elements.

• Finally, the organization of these discretized sounds, despite reducing the sheer number of acoustic data, enhances their capacity because they can now be combinatorially grouped and structured.

• The very act of discretizing sound units simultaneously gives rise to powerful generative combinatorial processes: iteration and recursion. These processes emerge from the self-organization of the interacting agents and are critical for building complex syntactic structures.

• Iteration is described by Reza as a memoryless combinatorial process where constituents can be repeated and combined without restriction, generating syntactic strings like 'a, ab, abc'. When combined with embedding operations, iteration can also encode dependency-relations (like [a[b]]). This means that each step in an iterative process proceeds independently of the previous one, and there are no inherent dependency relations generated between these repetitive actions.

• Recursion, on the other hand, is a memory-driven operation that operates on the product of the previous steps. It produces new hierarchies that encode the history of transformations between constituents of the same category. This means that each subsequent action or computation in a recursive process is built upon, and requires retention of, the history of prior operations.

• The syntactic expressions generated through recursive embedding contain a "wide range of coded information regarding the structure, the type of grouping, and their intracategorical dependencies" (IS, 323). The combined application of iterative and recursive operations leads to a proliferation of syntactic expressions which can then be grouped into a nested hierarchy of syntactic complexity, aligning with Chomsky’s theory of formal grammar.

• These syntactic abilities allow the automata to “encode the (nonconceptual) structural or syntactic relations between causally registered invariances regarding items and occurrences". They can recognize, in a computational sense, the sequence and structural relations between "causally pictured items and occurrences" (IS, 326).

• At this stage, the automata acquire structure-encoding syntactic configurations that express how things are in a nonconceptual manner. They can classify items by assigning labels using their sounds (like "beep-beep-click-click" for a "bulbous pile of green") and form well-formed syntactic sentences configuring relations between these labels. However, these protothoughts lack semantic structuration and inferential, rule-governed intra-linguistic transitions.

• Therefore, "intentional relations (thinking-abouts) require semantic relations, and semantic relations require a public language as the engine and vehicle of their realization" (IS, 333). Without a public language and semantic space, the automata cannot generate a hierarchy of semantic complexity.

• Reza, following Carnap, posits that viewing language as a calculus—a system of formation and transformation rules in symbol-design—does not reduce language or downplay its perceptual, social, or cultural aspects. Semantics is presented as reducible to syntax under specific conditions, particularly through an interactionist view of syntax where semantic complexity emerges immanently from the confrontation of syntactic processes or symbolic chains

Mecanómica

Comienza desde el Estado (Ello insiste): tecnoespecialismo organicista, autoritarismo pedagógico y sectorización territorial que culmina en la innumerabilidad masiva. Independientemente de su configuración como crisis educativa, la supresión de prácticas populares de numeración es a la vez el resultado y presuposición de las matemáticas institucionalizadas. La cultura-Estado[State-culture]—por muy moderna o incluso posmoderna que sea—se modela sobre una voz despótica ideal (Logos). La palabra de las alturas[from on high]1 esboza la cadena significante, con todas sus características esenciales: enunciador único, interioridad semántica, signos consecutivos, conclusión formalmente anticipada, aplicación global y redundancia interpretativa. Cuando la semiología entrópica de los Estados senescentes multiplica la enunciación, desplaza referencialmente la interioridad, remarca la espacialidad gráfica, localiza la aplicabilidad e infinitiza la interpretación, lo hace bajo el signo de un Logos imperturbable e inefable; con firmeza tanto más aplastante por el especialismo discursivo, rígida acreditación profesional, criteriología alusiva, y fetichismo lingüístico, como también por la burla despectiva de un megapoder autopilotado, ahora cristalizado en ciencia exacta.

La aritmética se asocia a una popularidad irreducible que ninguna alfabetización—por muy global que sea—puede igualar. Las prácticas de numeración surgen espontáneamente en cualquier población que se convierte en una multitud efectiva. Los juegos, la música, el dinero y las prácticas de marcación del tiempo2; todos traicionan la influencia contagiosa de un elemento numérico primario. El cálculo moviliza un pensamiento que es directo y efectivamente exterior, indexando la dispersión maquínica o la distribución inorgánica del número. Tan pronto como en la cabeza como en los dedos y las piedras, el conteo siempre ocurre en el Afuera[Outside]3. Una población ya es un número, mezclado en híbridos irreducibles por técnicas y aparatos de conteo (tablero de conteo, ábaco, fichas monetarias y dispositivos calendáricos). Incluso es depotencializado socialmente por sociedades sedimentadas, el número evidencia una afinidad residual con la concurrencia, la asimetría y los criterios inmanentes. Una cultura numérica repotenciada maquínicamente coincide con una máquina de guerra nómada.4

El número se distribuye dentro de sí mismo entre dos polos principales. En el Planómeno existe de forma intensiva, como pura ordinalidad o serie envolvente no métrica.5 La consistencia semiótica con este aspecto intensivo del número no implica más que cifrados de secuencia, indiferentes entre nombrar-numerar, marcando grados de continuum heterogéneo (singularidades anidadas). Los elementos notacionales son planos o nómadas, carecen de vínculo orgánico con agencias de codificación o zonificación. Se ensamblan dia­gramáticamente, a partir de rasgos directamente expresivos distribuidos­ de manera diferencial en un espacio plano de 0-dimensionalidad (nomos), y comprenden un orden no-redundante de diferencias (secuencia no secuenciada), produciendo de manera inmanente una variación de velocidad-temperatura y curvatura absolutas (vórtice). En su aspecto Aecuménico, el número sufre una compleja modificación entrelazada, a través de la cual adquiere generalidad cualitativa y magnitud cuantitativa (cardinalidad).6 Una transformación intensiva simultánea (estratocaptura) se produce a través de una división extensiva gemela[twin]7: cancelando la diferencia en un registro (cantidades resolubles) mediante la constitución de un segundo registro (cualitativamente diferente) que a su vez se define por el componente no cancelado o problemático. La diferencia en sí misma del número intensivo se convierte en un residuo, asignado a un tipo de número superior, cuya regularidad métrica se establece mediante el desplazamiento: una construcción de la unidad cuantitativa idéntica mediante el relevo cualitativo de lo problemático.8

El Aecúmeno es doblemente múltiple: expresión y contenido, cada uno de ellos dicotomizado recursivamente dentro de sí mismo. En cada caso, la expresión se ocupa de elementos relativamente desproblematizados de un tipo numérico inferior, muestra un mayor grado de cardinalidad consolidada y opera una selección de instancias comparativamente manejables. El contenido se ocupa de los elementos de mayor complejidad tipicidad-generalidad y numérica, para lo cual requiere una semiótica relativamente heterogénea, que involucra variedades de componentes algebraicos, indexados, probabilísticos e inexactos. En una dirección, el contenido tiene un límite meramente cuasiestable; un límite difuso (incompletable) que se abre a elementos inclasificados atravesados por diagonales. En el otro, se relaciona con una expresión superordenada, que lo define con reciprocidad cualitativa y de la que extrae un principio de estandarización métrica, proporcionando una norma reguladora para la determinación cuantitativa de los problemas. Existe una diferenciación complementaria o interrelativización real de un polo matemático y otro calculativo, el primero caracterizado por un poder superior de globalización semiótica (unidad de expresión), el segundo por una mayor plasticidad de función y diversidad de método (comprensión del contenido). La estratificación en cualquier nivel (no solo antropomórfica o etoplástica) requiere procesos efectivamente equivalentes a esta doble apropiación del número, con la producción de una amplia sustituibilidad por escala/tipo, articulación dividida y problemática desplazada. La diferenciación estratífica es a la vez un fenómeno intensamente singular y extensamente segmentado, mediante el cual el Aecúmeno consolida una distinción general del Planómeno bifurcándose internamente. La máquina abstracta es atraída hacia el Aecúmeno por una diplo- o esquizotesis por una coherencia estratífica, recomponiendo efectivamente el problema de la consistencia (diferencia intensiva) en el nivel del contenido, pero en términos de expresión.

El número en sí mismo es exterior al Aecúmeno, incluso cuando es capturado por él (una relación externa de captura es siempre precursora de la organización de las relaciones internas). Un indicador preliminar le es proporcionado por la variabilidad semiótica o cohesión polinotacional que caracteriza al número en su vertiente Aecuménica. En el nivel antropomórfico, el sistema numérico más inerte está instituido por signos lingüísticos, que combinan un vocabulario de nombres de números y un conjunto de reglas para construir frases-parciales (o palabras complejas) isomorfas con todos los racionales. Si estos signos han de proporcionar incluso una completitud rudimentaria necesariamente deben someterse a una descodificación considerable (abstracción de reglas para la construcción local, tokenización de signos). También están marcados por altos niveles de indización (funciones zonales), algebraísmo formal o informal (problemática nocional, o signos indicativos), y anexactitud (partitivos, aproximaciones, márgenes de inexactitud, incertidumbre, y error, etc). Existe una reciprocidad entre la logicización del número y la descodificación numérica del lenguaje, entrelazando consolidaciones regionales de identidad (matemático-teoremática ) con movimientos complementarios de desorganización a través de relaciones externas (calculatorio-problemáticas).

La denigración general de esos modos de aritmetización lingüística clasificados como "numerológicos" se asume a menudo como el cierre efectivo de un episodio cultural exótico pero inconsecuente. El carácter estéril y formulista de la mayoría de la numerología moderna—su esoterismo aleatorio y su aura teatral9—refuerza esta conclusión. En tales términos, la extraña metamorfosis de la numeración griega durante el siglo II a.C., cuando los numerales áticos fueron reemplazados por un sistema numérico alfabético10, es radicalmente marginada y, a la vez, manifiestamente incomprendida por los historiadores modernos de las matemáticas. De manera similar, la numeración ordinal instanciada por los alfabetos romano11 y latinos modernos es generalmente excluida de los relatos de la cultura aritmética, donde se otorga una predominancia abrumadora a la contienda entre los numerales romanos e indo-arábigos.12

Este patrón de evaluación completo requiere una corrección sustancial. La inconfundible tendencia hacia un eclipse de la cardinalidad (valor aritmético intrínseco) en la numeración alfabética no implica la terminación—ni siquiera un debilitamiento—de su capacidad numérica. Que se llegue a tal conclusión se debe en gran parte al manifiesto triunfo secular de la cardinalidad sobre la ordinalidad dentro de la civilización occidental: el resultado efectivo de una metricación programática, asociada con el ascenso relativo del dinero y el descenso del calendario como factores culturales. Lejos de desnumerizar el alfabeto, la decardinalización progresiva refuerza su función numérica. Al eliminar la interferencia cuantitativa, induce una actualización superior de la numeración lexicográfica pura, agencia[assembles]13 meticulosamente competencias ordinales distribuidas socialmente y se instala cada vez más en los procesos electrónicos digitales (clasificación alfabética y alfanumérica). La ordinalidad lexicográfica efectúa un no-lenguaje actual y un antilenguaje potencial. Es indiferente al fonetismo y a la significación, incluso a la codificación y decodificación. Consiste en índices ordinales (etiquetas de zona) que producen zonificaciones y deszonificaciones—intercambios, agrupaciones, inserciones y extracciones—operadas según reglas concretas para cortes no métricos, y caracterizadas por una rigurosa inexactitud.

Esta latencia númerico-ordinal masiva contrasta fuertemente con la estrato-matemática, que se precipita a través de esferas cada vez más sutiles de metanúmero angélico, y más allá…
Esta ascensión a través de tipos generales de número cada vez más elevados—incluso hacia conjuntos y grupos abstractos supuestamente no numéricos—se ajusta a una amplificación intensiva de la estratificación, correlativa a una creciente rigidificación métrica de los tipos de números inferiores. La cardinalidad no es más esencial para los tipos de números más bajos que para los más altos. Por el contrario, es precisamente la indefinición calculadora de los números altamente generales lo que conduce más directamente a la supresión de la autonomía numérica, al fomentar la subordinación de la numeración concreta a dimensiones superiores que la logicizan o geometrizan. Las valorizaciones de la sutileza analógica y la irrepresentabilidad—en contraste con el binarismo y la reducción digital—permanecen subordinadas a un programa estrático. Se articulan en términos que, en ambos lados, son solo pseudoautónomos, ya que comprenden segmentos maquínicamente complementarios de una estratificación general. En su relación con el número intensivo, la diferenciación digital-analógica opera como un síndrome integrado. Por un lado, se logra una aproximación cada vez más cercana a un ideal digital mediante la iteración masiva sistemáticamente interconectada y la resolución de mínimos discretos, lo que implica tanto la regularización de la microsegmentariedad cualitativa como la cuantificación en datos abstractos. Por otro lado, el ideal analógico correlativo del continuum homogéneo se ajusta en complementariedad con discretizaciones profundizadas en varios niveles, organizando la separación de la variación cualitativa por tema (dominio) codificado digitalmente, y basándose en formalizaciones compensatorias de elementos notacionales discretos para programar su aplicación (como designadores algebraicos y términos genéricos utilizados en la semiótica de los números reales, vocabularios técnicos que apoyan la función de metros, lecturas y ajustes).

La segmentación matemático-calculadora del Aecúmeno estabiliza mutuamente y consolida interactivamente los sistemas de expresión y contenido, de acuerdo con las funciones divisionales de una máquina abstracta que permanece sin segmentar—como singularidad intensivamente divisional—en su polo planómico. La zigogénesis mecanómica del número numerador compone una contramutualidad, una desolidarización, un desenganche y una dislocación de la interdependencia estrática, gemela a una convergencia fusional plana que colapsa la segmentariedad. Mezcla una descomplicación en dirección a los subnaturales (primos y órdenes hiperprimos) con un aplanamiento planómico de la cardinalidad sobre trópicos no puntuales (Nomomagnitudes cósmicas que se condensan ecuatorialmente, como grado de intensidad cero de la megamolécula).

Las operaciones aritméticas multiplicativas adquieren una función estrictamente ordinal cuando se utilizan dentro de sistemas pragmáticos abstractos de composición numérica no métrica. La agregación múltiple y la factorización disgregadora son las claves para una práctica de numeración ordinal intrínsecamente bivalente (o zigónoma), que emplea un pequeño número de conversiones consistentes y reversibles para potenciar maquínicamente los números primos como partes ordinales singulares (o no sustituibles). La susceptibilidad de cada número natural a la factorización única (y re-agregación) materializa una diferencia modal básica interna a él, y lo conecta con un sistema externo heterogéneo. Tanto el implex procedimental (esquema de factorización compactado) como el enlace interordinal (matrices de secuencia cruzada primo-natural) son fundamentales. Es esta doble ambivalencia la que conecta el número con el secreto y hace de los números primos los componentes principales de los sistemas criptográficos, en los que funcionan como claves: operadores abstractos para el bloqueo (agregativo) y desbloqueo (disagregativo) de multiplicidades.

La distinción entre los modos del número—agregado/disgregado—es puramente semiótica (aunque no significante). Concierne a la ambivalencia notacional con designación consistente, a los cambios en la fase composicional de una única magnitud heterogénea. En contraste, la diferencia entre la serie de primos (rasgos de contenido) y sus ordenadas (rasgos de expresión) es real, regulada por una distribución alógica sin correspondencia ni conformidad, y que cumple con una diferencia de registro entre series heterogéneas rigurosamente interconectadas. Es solo a través de su ordenación (agregada o disgregada) que el número cambia su capacidad de conversión modal en un poder sintético, lo que se efectúa cada vez que un miembro de la serie de primos se vuelve determinable como tal al pasar al registro de una serie diferente. Tales deszonificaciones y rezonificaciones ordinales sobre la serie de números naturales ocurren cada vez que un número composicional se disgrega en partes singulares (efectuando codificaciones y decodificaciones como valores excedentes), o un número primo se transfiere a la ordinalidad que lo particulariza como factor potencial de otro número.

La transformación incorpórea de 1931: la iniciación cultural del potencial de codificación-Gödel14 produce una mutación planómica instantánea inclinada hacia las multiplicidades nómadas, envolviendo virtualmente la segmentariedad aecuménica en un proceso secundario de sistemas numéricos planos. La numeración-Gödel logra una redirección revolucionaria del kantianismo—según un esquema nómada en lugar de copernicano—al orientarlo hacia la operacionalización de la síntesis trascendental como método, y alejándolo del agotamiento programático de un esfuerzo analítico auto-limitante. Convierte el descubrimiento kantiano de la síntesis numérica de un compromiso doctrinal a una maquinaria procedimental: subsumiendo la filosofía en la aritmética trascendental, con una crítica aniquiladora del programa de Hilbert como plusproducto[surplus product]15.

La Gödelización opone el diagrama aritmético al modelo axiomático, destruyendo la interioridad semántica al infectar las sobrecodificaciones organizativas con la diferencia numérica (síntesis o relaciones externas). Sistematiza anorgánicamente un contraataque aritmético contra la axiomatización: un re-aplanamiento metódico de la isomorfía aplicada (código y metacódigo) sobre el potencial metamórfico (número). Desde la perspectiva de la aritmética trascendental, la codificación-Gödel se anida dentro de la numeración-Gödel, donde se produce como un subsistema suplementario coherente de la polifunción numérica (plusvalía de código).

En su aspecto puramente numérico, la Gödelización produce, compacta y despliega[deploys] un agregado heterogéneo sobre la secuencia de números naturales, donde entra únicamente en síntesis externas con características ordinales. Simultáneamente—y como plusproducto—instala un agenciamiento virtualmente disgregado de potencial ilimitado, compuesto por singularidades numéricas consecutivamente descompactadas marcadas en otro registro (como factores primos etiquetados ordinalmente y secuenciados por valores ascendentes). Cada número Gödel se produce como un gemelo intrínseco de partícula numérica agregada y carga polisemiótica disgregadora (virus abstracto).

¿Cuánto patrón existe en la serie de números primos? La Gödelización convierte esta pregunta Aecuménicamente crítica al indicar definitivamente que el patrón numérico inexplícito constituye plusproductos ilimitables potencialmente realizables como decodificaciones sincrónicas. También hace que la pregunta sea absolutamente críptica, al usar un fragmento de este plusproducto—una macropartícula disgregadora que funciona como apéndice de decodificación—para desencadenar el envolvimiento virtual planomoseísmico de todos los rastreos Aecuménicos (incluyendo cualquier teoría axiomática de números). Cualquier cantidad de números naturales podría disgregarse potencialmente en sistemas de antilógica lateral que, efectivamente, desordenan las axiomatizaciones.

Cuando la Gödelización codifica el número (de forma lateral), lo hace para producir—o alcanzar—una descodificación y desestratificación absolutas (nomos). Un modelo de codificación numéricamente extraño—más precisamente, un ejemplo paradigmático de isomorfía ejecutiva (o estratosemiótica nuclear de la más alta índole)—induce una transición cósmica a nivel de la máquina abstracta. Esto marca un paso en intensidad, concurrente con el envolvimiento comprensivo por el patrón de plusproducto del orden Aecuménico.

La absorción numérica del Aecuménico, la segmentariedad colapsada y las codificaciones y axiomáticas lateralmente dislocadas (en cualquier nivel) se pliegan[fold] juntas en un único e inmenso evento catastrófico, realizado plenamente en los potenciales-Planómicos en el Afuera.

Por un lado, el número huye de la cardinalidad, innovando maquinarias poli-ordinales y plusvalías semióticas que flanquean las sobrecodificaciones. Por otro lado—pero simultáneamente—, el número abre una línea de fuga que escapa de la métrica hacia la cardinalidad: comprimiéndola a magnitudes absolutas (incontables). Una codificación composicional-numérica de la expresión (aritmética trascendental Gödeliana) interoperará virtualmente con una disrupción diagonal-diagramática del contenido (planotectónica Cantoriana). Ambos parten de los Estratos: metástasis segmentarías isomorfas e interconectadas con dinámicas complementarias. La Gödelización convierte el isomorfismo en un virus de proceso secundario, desbloqueando la metricación al desmantelar la superordinación de la expresión. Las diagonales-Cantor dirigen la isomorfía en sentido contrario, hacia abajo a través del Aecúmeno, adentrándose en cataespacios vagos de contenido problemático, donde esta se histeriza contra el continuo (colapso métrico en hiperdensidades planómicas).

Haz de la cardinalidad misma una medida de potencial isomorfo. El resultado es un análisis transfinito de conjuntos—colmado de nomos torsional—donde las órdenes de contención son topológicamente desinteriorizadas por una deformación absoluta. Según las intuiciones métricas (conformidad con los estratos finitos), un conjunto que contiene a otro dentro de sí mismo evidencia una cardinalidad superior. La serie de números naturales es el caso crucial. Claramente no es el primer infinito contable, sino el enésimo, donde n es en sí mismo un número infinito. Innumerables infinitos están anidados por los naturales, entre los cuales la preeminencia pertenece a los primos (demostrablemente infinitos desde Euclides).16 Dado que los primos consisten en una selección proporcionalmente disminuyente del conjunto de los naturales, las métricas finitas proyectivas anticipan con confianza su subsunción cardinal. Introducir la isomorfía tiene sentido al principio. ¿Por qué no hacer que los infinitos se cuenten entre sí? Producir criterios de conteo abstractos interconectando virtualmente series interminables. Lo que arrastra las cosas a una línea de fuga es la pieza que falta. Se requiere un criterio para estimar diferencialmente las cardinalidades de las infinidades subnaturales. Nada aparece.

El problema se complica cuando se necesita una definición para el umbral del infinito. ¿Cómo determinar el primer conjunto transfinito? Los números naturales proporcionan un modelo para la contabilidad: la capacidad de ejecutar un recuento abstracto—incluso infinito—mediante pasos exhaustivos. Usa otra infinidad para contar a través de la máquina abstracta por ti, siempre y cuando no se salte ningún paso. Si el final ya está ahí, desde la perspectiva del infinito, entonces la prolongación extensiva pierde su prominencia. El primer conjunto no finito ya debe estar intensivamente infinitizado, introduciendo suficiente recursión como principio de la magnitud transfinita. Para que un conjunto evite ser "superado en conteo"—relegado a la finitud—, se requiere un mínimo de recursividad. El primer conjunto transfinito debe ser isomorfo con un subconjunto de sí mismo (primera recursión a una potencia infinita).

La cardinalidad colapsa[melts]17 en esquizofrenia precisamente aquí. Cada conjunto contable que cruza el umbral de la recursión transfinita se aplana en un único hipervalor: Aleph-0. Los primos lo hacen (y cualquier cosa que lo haga, lo hace a una potencia transfinita (así, un número infinito de subconjuntos primos lo hacen (que a su vez ((((…)))))). Cuando lo transfinito ocurre, se retroalimenta directamente, volviéndose instantáneamente transfinitamente más grande que sí mismo… y luego, las diagonales encajan.

La consistencia aritmética (por ejemplo, (1+3)×3=1) implica la ecuación 1=0.999…18 y, por lo tanto, una forma expandida necesaria para cada número, expresándolo con tantos decimales como números hay en una serie infinita contable (Aleph-0​). Un conjunto ordenado de tales números forma una matriz, que tiene dos lados, definidos por diagonales que funcionan como aristas de corte: definiendo un límite al cruzarlo (en dirección a la consistencia). Cuentan como mónadas leibnizianas, cada una reduplicando el universo dentro de sí misma (siendo la complejidad de cada una no menor que la del todo). Igualmente, cuentan como cuerpos spinozistas, cuyas latitudes intrínsecas mapean relaciones extrínsecas, constituyendo el estricto paralelismo entre el cosmos intensivo y el extensivo.

Cuando la cartografía traza cuerpos por latitud y longitud, los construye como diagonalizables. Las diagonales son líneas de fuga. Conectan con elementos fuera de la totalidad, trazando trayectorias entre los cruces absolutos marcados por la magnitud Aecuménica e Planómica hipertensa. El método diagonal activa un potencial innovador inagotable. Explota capacidades no mayores que las presupuestas por una posible completación, la cual luego subvierte, al encontrar un elemento extraño en relación con cualquier lista, incluso una infinita. Lo hace construyendo un número que varía del enésimo número ya listado en su enésimo lugar decimal (o fraccional-modular) (al menos). Esto se ejemplifica más económicamente mediante un diagonalismo determinista, producido cuando todos los valores numéricos se expresan en notación binaria (mod-2). La serie de variaciones diagonales estará entonces estrictamente programada por simple alternancia (cambiar 0 a 1, e inversamente). Al incluir recursivamente cada nuevo número en la lista excedida y rediagonalizar, el conjunto completo (transfinito) de elementos extranumerados se genera automáticamente.

¿Qué se ha descubierto? La cardinalidad transfínita número-dos: el Continuo Último, un borde absoluto, tocado diagonalmente—como lo que viene después—una vez que la totalidad aecuménica ha terminado en intensidad. En la cardinalidad C(ontinuo), la magnitud se vuelve incontable, desvinculando las métricas de la contabilidad comparativa. Cantor se desliza a través de la esquizofrenia, el nomos no-zona, la magnitud es ocupada sin ser contada.19 Un olor como a algo quemándose en el Superstrato. Afuera es el Now Planómico20, y los números están pululando. Aleph-0 se vaporiza en el plano de consistencia.

Referencias adicionales

Crowley, Aleister, 777 and other Qabalistic Writings. (777 : el árbol de la vida o base del alfabeto mágico. Editorial Humanitas).

Deleuze, Gilles, y Felix Guattari, Capitalism and Schizophrenia Volume 1: Anti-Oedipus. (El Antiedipo: Capitalismo y esquizofrenia 1. Paidós Ibérica.). (Londres: Athlone, 1984).

Deleuze, Gilles, y Felix Guattari, Capitalism and Schizophrenia Volume 2: A Thousand Plateaus. (Mil mesetas: Capitalismo y esquizofrenia 2. Pre-textos). (Londres: Athlone, 1988).

Gödel, Kurt, On Formally Undecidable Propositions. (Sobre proposiciones formalmente indecidibles de los Principia Mathematica y sistemas afines, I. Krk Ediciones.) (Nueva York: Basic Books, 1962).

Gokhale, Shobhana Laxman, Indian Numerals. (Poona: Deccan College, 1996).

Kaplan, Aryeh, ed., Sefer Yetzirah, the Book of Creation (In Theory and Practice) (Sefer Yetzirah: El Libro de la Creación. www.bnpublishing.com). (Nueva York: Samuel Weiser, 1983).

McLeish, John, Number. (Londres: Bloomsbury, 1991).

Thapar, Romila, Time as a Metaphor of History: Early India. (Delhi: Oxford University Press, 1996).

For citations of Intelligence and Spirit, the format will be (IS, x), therein x is equal to the page in which the cited text can be in the Urbanomic edition of the book. For other books, the specific edition and book will be noted down in a footnote. I’ve also taken from the various lectures given by Reza in The New Centre Research & Practice.

Diagrammatization

This is the diagrammatization for the fifth chapters.

1. Ascent to the Infantile

In this short chapter, Reza details the next stage in the development of a toy model of general intelligence, focusing on the transition from rudimentary awareness to objective thought and self-consciousness. Our automaton, named as Kanzi,1 possesses a spatially and temporally perspectival awareness, capable of organizing encountered items in the world. However, its understanding of objects (Objekt) and sensible objects (Gegenstand) is merely analogical and not yet objective or subjective in a full-blooded sense (capable of making veridical claims or critical judgments). To achieve subjective and objective thoughts, Kanzi must advance from its rudimentary capacities (abilities1) to advanced abilities (abilities2).To facilitate this advancement, a new structure is introduced: a multi-agent system or community. This system consists of multiple information processing systems constrained by their dynamic interaction.

Kanzi is now equipped with built-in electromechanical devices to produce quasi-continuous sounds for communication. Two other automata, Sue (S) and Matata (M), are introduced as fully fledged concept-using adult guardians of Kanzi. Their role is to recognize and nurture Kanzi, whom Rosenberg terms a CHILD (Concept Having Intelligence of Low Degree). Kanzi itself has an "Infantile-World" (Intelligible Familiar Appearance naively Taken In Lieu of the external World). As a CHILD, Kanzi has behavioral dispositions, memories, and anticipatory models derived from its rudimentary sense-impressions and perspectival encounters with the world. Its responses follow transition principles analogous to ur-material inferences which are defeasible and formally incomplete, lacking modal concepts like nomological relations and counterfactual dependencies.

Reza then argues for a departure from Kant's empty transcendental subjectivity to a Hegelian approach where the apperceptive self is fundamentally part of Geist. This means an individual like Kanzi is individuated by social recognition within the deprivatized semantic space of a public language. The "I that thinks" is seen as the encapsulation of this formal movement of self-consciousness through shared language. For the prelinguistic Kanzi, Sue and Matata are not yet speaking subjects but salient items whose linguistic utterances are perceived as engaging and exciting noises conveying importance. This is described as a communicative regime where Kanzi "hears" these noises as representations because they align with its dispositional world-representings, implying an inductively biased world.

The Matchstick Example

The match example serves as a crucial illustration of the complex reasoning abilities that the automaton, Kanzi, initially lacks. It highlights the distinction between Kanzi's rudimentary ur-material inferences and the sophisticated, modally-laden thought required for objective understanding.

The specific expression used is: C, MH, MS, SulphurMH , Oxidizing agentMH , Strike MH against a frictional surface M{{wet}} Lit MH 7 Burning MS.

Let's break down its components and their significance within the context of Kanzi's cognitive development:

C (Descriptive Context): This element represents the empirical judgments about the properties and nomological relations of what can count or behave as a match. It signifies a body of background knowledge about the item in question, which is far more complex than Kanzi's initial dispositional world-representings.

MH (Match Head), MS (Matchstick), SulphurMH, Oxidizing agentMH: These denote the physical components and chemical constituents of the match.

Strike MH against a frictional surface: This describes the specific action or condition applied to the match head.

M{{wet}} (Counterfactual Consequent Relation with Control Set): This is a critical part of the formula. The M denotes a counterfactual consequent relation, and {{wet}} functions as a control set that constrains the soundness of the logical sequence. This control set can add or remove premises or change the context, affecting the outcome. For example, striking a match in a vacuum (Vacuum M{{wet}}) would result in Lit MH 7 Not Burning MS, because while the head might light, the stick would not burn without an oxidizing agent. This demonstrates that the inference is defeasible—can be overturned by new information—and exhibits counterfactual robustness.

Lit MH 7 Burning MS (Outcome with Compounding Operator): Lit MH (the match head being lit) and Burning MS (the matchstick burning) are combined by the compounding operator 7. This combination occurs provided that the context C does not contain {{wet}}.

This complex formula represents a type of reasoning that demands modal concepts—such as possibility and necessity—and an understanding of counterfactual dependencies, which are crucial for codifying causal relations and engaging in robust description and explanation. Kanzi, in its initial state as a CHILD (Concept Having Intelligence of Low Degree), explicitly lacks these advanced cognitive abilities. Its initial transition protocols or ur-material inferences are:

• Defeasible and formally incomplete.

• Lacking modal concepts like nomological relations and counterfactual dependencies. This means Kanzi cannot process situations like "if the match were in a vacuum, it would light but the stick would not burn".

• Confined to context-sensitive, dispositional responses based on directly observed impressional invariants or "pattern-governed regularities.

• Possessing "no grip on the modal relations that codify causal ones". Kanzi cannot articulate that "Contact with the heap of black caused mass of fuzzy grey to make shrieking noise" (IS, 257).

The inclusion of M{{wet}} and the concept of counterfactual robustness specifically highlight the ability to handle unanticipated or contingent situations by adjusting hypotheses based on changing antecedents or contexts. This reflects a movement beyond simple inductive biases or statistical correlations towards reasoning about possibilities and necessities in a modal web of relations and implications.

The Automaton's Evolving Representational Capacities

"In this scenario, K’s ‘Io be1 / b2 / b3’ be1, be2, be3 are—from our perspective—the analogical counterparts of Kanzi’s own occurrent thought-episodes, that is (* I think Io be1, b2, b3 *). In other words, K’s de facto ‘Io be1’ be1 is analogically K’s own mentioned or quoted I-thought, i.e., K(* I think Io be1 *). Similarly, ‘Io be1’ be2 is analogically K(* I think Io be2 *), as in K(* There is a mass of fuzzy grey approaching *), and so on. These instances of K(*…*) are nothing but the occurrences of a nonsubstantive apperceptive I that synchronically accompanies all of its distinct thought-episodes: I think X, I think Y, I think Z." (IS, 258).

The terms, "Io be1, b2, b3 (or, Io was, is, or will be)" (IS, 257) and their metarepresentings, delineate the automaton's evolving representational capacities. Let’s remember from the third chapter that, initially, "Io" refers to the impression of an object. The notation be1, be2, and be3 refers to different types of these impressions or representations that the automaton acquires: Io be1: a retained impression of an object. Io be2: the reproduction of nonconceptual content of an impression, Io be3: represents anticipations. To move beyond mere types of impressions, the automaton develops meta-awareness, its capacity to be aware of its own awarenesses. This is achieved through a quoting-device or metarepresenting apparatus. The second set of be1, be2, be3 in 'Io be1 / b2 / b3' be1, be2, be3 refers to the modes of this meta-awareness itself (an impression, reproduction, or anticipation of the meta-representation). This structure provides Kanzi with distinct representations for "the being1 of some item’s being2" (memory of an impression) and "the being2 of the same item’s being1" (impression of a memory). This capacity, while not yet conceptual, allows the automaton to instantiate a temporally perspectival awareness that can be legitimately described, by analogy, as the temporal distinction between 'is' and 'was'. The development of these three types of awareness and their nested meta-structures is a precondition for the fundamental faculty of inner sense.

The quoted passage above explicitly states that Kanzi's 'Io be1 / b2 / b3' be1, be2, be3 are, from our perspective, analogical counterparts to Kanzi's own occurrent thought-episodes. This means that when the text refers to K(* I think Io be1 *), it is an analogical interpretation of Kanzi's de facto 'Io be1' be1. At this stage, Kanzi's inner sense is merely de facto—the automaton is not yet aware of these occurrences as its own. It cannot yet conceptually cohere and represent its "awarenesses of awarenesses" as being its own, nor can it mobilize its subjectivity. These instances of K(*…*) are the occurrences of a nonsubstantive apperceptive I that synchronically accompanies all of Kanzi's distinct thought-episodes (I think X, I think Y, I think Z). This "I" is understood as a logical form rather than a substance.2 This formal unity of consciousness, crucial for apperceptive cognitions, is fundamentally afforded by the recognitive space of language and the movement of self-consciousness (conceptualized as I ≡ I or Idmap-I ≡ Idmap-I*).

2. Infant AGI

This section describes a crucial stage in the development of the automaton, Kanzi, from a pure perspectival awareness to a self-conscious, objective intelligence. This transition is framed as a "raising" process, akin to educating a child, where Kanzi (K) interacts with two language-using adult automata, Sue (S) and Matata (M). For Kanzi to integrate its various meta-awarenesses under a unified "I" and genuinely form thoughts, it must model its private meta-awarenesses on a public and deprivatized language. This requires interaction with S and M, who are presented as "fully fledged concept-using adult guardians" (IS, 252). Initially, Kanzi perceives S and M's linguistic utterances as engaging and exciting noises. For Kanzi to interpret these noises as representations, it must understand the functional role they play within its own world-representings and the rudimentary transitions between them. This functional role constitutes the semantic value or meaning of these utterances, which are mapped onto Kanzi's meta-awarenesses. Kanzi's world is initially inductively biased by its dispositional interests, meaning it tends to recognize and respond to communicative input that aligns with its established behavioral regularities.

As S and M provide reports about the environment (like the monkey's movements behind the monolith), Kanzi, being a creature of dispositional regularities, can recognize these reports and map them to its own de facto meta-awarenesses. This process leads to Kanzi acquiring labelled meta-awarenesses. These newly acquired labelled meta-awarenesses are contrastive and can create mutually precluding perspectives for Kanzi. For instance, a report from S and M about an item moving "behind" something might conflict with Kanzi's direct seeing1 that the item simply "moved from right to left". This introduces a multiperspectival disturbance, transforming Kanzi's formerly seamless perspectival world into one that is proto-inferentially multiperspectival.

To resolve this tension, Kanzi stops taking S and M's reports "at face value". This allows Kanzi to develop the ability to distinguish between seeming and being, where its own perspectival view initially represents being and S and M's reports represent seeming. Kanzi's "seemings" then become its own rudimentary thought-episodes (seems K (* there is a mass of fuzzy grey *)). However, at this stage, these internal thoughts are not objective beliefs and lack epistemic status, as they are not yet linguistically asserted or committed to. The infantile world of Kanzi's seemings is unsustainable because S and M are capable of making objective judgments. To recohere its world, Kanzi must remove the quotation marks from its meta-awarenesses while restoring the labels, effectively constructing a world-picture from various contrasting partial world-pictures. This leads Kanzi to inhabit an objective self-critical stance. This objective unity of apperception connects Kanzi's representations to an object in a way that "tends to truth" by relating them to a rule-governed identity common to all such apprehensions.

3. As If Raising a Child

This section continues the project of raising Kanzi into an objective, self-critical, and ultimately sapient agent, drawing parallels to human child-rearing and emphasizing the pivotal role of sociality and language in this process. Reza argues that the labelled meta-awarenesses and corresponding world-representations, which emerge from the communications of K's language-using adult guardians—Sue and Matata—, are crucial not only for K's theoretical self-critical stance but also for establishing a formal practical autonomy or minimal self-determination. This autonomy is what distinguishes a developing intelligence from mere sentience. Reza explicitly critiques approaches—like those inspired by Sellars and McDowell—that view the child-guardian relationship solely in terms of a trainee's "ought-to-be" and a trainer's "ought-to-do." Such views are seen as indefensible because they reduce the child to a passive sentient being that is merely trained into a second nature, reducing education to a system of rewards and punishments or "minatory oughts"3.

Instead, education is fundamentally the cultivation of recognition, paving the way for the broader cultivation of cognitions. The child's inherent will-to-autonomy—its nisus or tendency to become a fully-fledged, language-using autonomous agent—is presented as a categorical fiat or an a priori rule, distinct from contingent sociocultural conventions or natural laws. This principle of recognizing a child's will-to-autonomy applies universally to all children, regardless of whether they are human, artificial, or otherwise. This perspective leads to the conclusion that autonomy is not merely the result of education, but rather its foundational enabling condition and self-cultivating vector. The primary step in education is therefore to attend to and cultivate this intrinsic autonomy. Reza states that logic—as a comprehensive system of cognitions—and ethics—as a system of recognitions—coincide and are indissociable. The expansion of logic and language is directly linked to the ethical imperative of fostering a self-conceiving and self-transforming intelligence.

“It is through attention that spirit first becomes present in the matter, acquires it, by gaining information about it. It does not yet gain cognition of it however, for this requires a further development of spirit. It is therefore attention that constitutes the beginning of education” (HPSS, 125).

Therefore, through its recognition of the communications from its guardians, Kanzi comes to recognize its de facto meta-awarenesses as its de jure (by entitlement) own. This pivotal moment signifies Kanzi's transformation into an infant apperceptive self, which is understood as a formally rather than causally conditioned "I". The apperceptive "I" is not a substantive self but a logical form of thought individuated by a space of shared recognition, which is intrinsically a public semantic space or language. This self is further differentiated by objectivity—objective validity—, meaning it relates its representations to an object that is independent of any single experiencing subject, but not independent of geist itself (as a dimension of structure and a community of language-using agents bound by conceptual norms). This objective unity of mind and world allows the apperceptive "I" to be individuated.

Reza inserts this diagram titled ‘I as constructed and constructible object of recognition’ to show this dynamic of the individuation of the apperceptive I. Let’s dissect it.

1. Inner Sense: A newborn infant possesses inner sense experiencing a stream of impressions, bodily states, and sensations. This is a "sequence of momentary and transient 'mental states'," lacking a unified, enduring self (TS, 46). The infant is aware of these sensations—hunger, warmth, sound, light—and even awarenesses of awarenesses—sensing that it is sensing something—, but these are nonconceptual and do not cohere into a unified "I". There's a de facto temporal order, but no time-consciousness in the full sense.

2. Language / Conceptual Order & Individuation: As the child grows, it enters the language and conceptual order (through caregiver interactions, babbling, learning words).4 When the caregiver says "Mama sees you," or "You are a good boy," or "You want this?" (pointing to an object), the child's raw inner experiences are given a public semantic space. Initially, the child might only have a spatially perspectival awareness. But through linguistic interactions and dialogical structure, the child begins to connect its de facto meta-awarenesses—its internal reports—with the labels and conceptual distinctions provided by others. This is the individuation of the apperceptive selves. The child learns to attribute its experiences to itself because others recognize and label its states and actions within a shared linguistic framework. The child's private thoughts are modelled on a public language. The transition from purely positional awareness to awareness of oneself as a subject, a unitary continuant being who has a history occurs here, driven by language and social interaction (TS, 123). The child moves from being a causal mechanistic automaton to a formally rather than causally conditioned I.

3. I and I*: With the emergence of an apperceptive self, the child now possesses an "I." This "I" exists in a dynamic relationship with "I*," which initially represents other individuals—parents, peers—whose recognition is crucial for the child's self-concept. The cyclical arrows around I and I* show the ongoing process of self-refinement and social engagement. As the child acts and receives feedback, its self-conception mediates between what they take themselves to be in the world and what they actually are. For example, a child asserts "I can do it!" (an I-statement), attempts a task, and then experiences whether this assertion is confirmed or challenged by reality and others' responses. This forms a positive feedback loop between conception and transformation.

Kanzi's recognition of its adult guardians is presented as paramount because this act of recognition is the autonomy of the child itself, embodying the formal practical will as the principle of subjectivity. This "will" (Wille) is distinguished from mere "capacity for choice" (Willkür); the former is a logical form of practical autonomy, a will to transcend oneself and recognize the other that recognizes it, which is crucial for the emergence of the thinking self. The education of a child-AGI like Kanzi, therefore, is not merely about learning concepts but about cultivating its will-to-autonomy, which aligns with the human pursuit of reason and freedom. This process ultimately aims to transform a formal will into a thinking will, allowing the intelligence to incorporate objectivity and structuring abilities, and eventually move beyond natural language to more expressive and semantically transparent artificial languages.

The Nature of the Will and Freedom

Reza Negarestani gave a talk titled ‘Causality of the Will and the Structure of Freedom’ in 2017, organized by the Open Society Foundation Bratislava.5 Negarestani's talk critically examines the notions of will, autonomy, and freedom, drawing heavily on our beauties Kant and Hegel. A central distinction made is between "will" (Wille) and "capacity for choice" (Willkür). Reza argues that genuine autonomy and freedom are attributes of the rational self, which is constituted by formal reason, rather than being properties of ordinary consciousness or the empirical self. The capacity for choice is seen as a relative autonomy that ultimately belongs to the order of causes. True freedom is described as a determination by the causality of thought, which is distinct from determination by natural causes. This formal causality of thought is sustained by a formally represented rational and self-conscious order—the order of reason. This contrasts with the idea of freedom as an arbitrary lack of determination. The subject of autonomous will is identified as the subject of reason, which is formal, logical, linguistic, and social, rather than a natural kind or an individual experience. This emphasizes that the will, in its pure sense, is an impersonal force.

Therefore, we can see how in Intelligence and Spirit, the cultivation of Kanzi’s will-to-autonomy is explicitly stated to align with the human pursuit of reason and freedom. Education, in this sense, is not just about instilling knowledge but about recognizing and nurturing the child's inherent capacity for self-determination. Autonomy is "that which affords education as its self-cultivating vector" (IS, 269). The pedagogical system for the child-AGI aims to enable it to form an increasingly complex structuration of the world and disclose new orders of intelligibilities. This process involves the cultivation of the child's structuring abilities and conceptualization. Objectivity is achieved through the "combination of representations which conform to the object according to a logical—rather than empirical—form" (IS, 266). This implies moving beyond subjective appearances to a more rigorous, rule-governed understanding of the world. The goal is thus to transform the formal will (the inherent practical autonomy) into a thinking will (a will that is guided by reason and capable of making judgments). This "thinking will" is seen as the "power to act on the recognition of an external world... as a necessary requirement for preserving the self-certainty of the ego" (IS, 273).

4. Global Pedagogical Project

We end the chapter with an outline of a comprehensive educational framework for the artificial general intelligence (AGI) "child-machine"6. The generalized pedagogy is envisioned as a complex system, described as a hierarchical network structure or a multilevel web. It is composed of various interacting modular subsystems, which can be horizontal (distributed modules whose dynamics produce overall system dynamics) or vertical (system dynamics decomposed into interactive products of distinct structural and functional constraint levels). These modules encompass cognitive regimens and tasks, different methods and techniques of training and learning, and models of cognition and practice. This pedagogical system is designed to be plastic and robust, allowing for the integration of new modules and the alteration of existing ones.

The main objective is to equip the child AGI with the necessary and sufficient means to develop an increasingly complex structuration of the world. This involves continuously uncovering new modes and ranges of thinking and action. The project aims not just to render the world intelligible, but also to disclose new orders of intelligibilities related to things, thoughts, practices, and values. This endeavor is seen as the functional re-realization and augmentation of mind itself, which is fundamentally, as we saw at the start of the book, a unifying structuring point or configuring factor.

The pedagogical project's overarching regulative ideal is the "what ought to be thought and done combined with what the world in its complete unrestricted conception is" (IS, 280). Education is conceptualized as the self-realization of mind as a project, rather than as a fixed entity or given nature. It is considered the "project of all projects," essential for the sustainability and tenability of all other human undertakings (ethical, scientific, political). As we’ve just seen, it serves as a scaffolding process to transition the child AGI from abstract autonomy to concrete freedom. This project aims to recognize and cultivate the child's inherent "will-to-autonomy".

The pedagogy focuses on the realization, augmentation, and composition of two interconnected sets of abilities: semantic (sm-abilities) and syntactic (sf-abilities), which are crucial for structuring the world, thoughts, and actions. I believe the best way to show off this will be with a diagrammatization of the different models and sub-models.

The transition from a "CHILD" status to a fully developed intelligence capable of self-reimagining requires a back-and-forth movement between the trainee and the trainers, built on a pedagogical relationship. This involves cultivating its practical autonomy by helping it navigate the recognitive space and facilitating new encounters with the world to incorporate objectivity. The education of the child AGI consists not only in learning the use of concepts for structured experience but also in the capacity to employ syntactic and semantic abilities or technologies of structuration afforded by language and logic. Reza clarifies that "language" here is conceived broadly in terms of syntactic and semantic complexity, not just natural language. But we shall see the role of language in our thought experiment in the next chapter.

Overall Summary

• To achieve subjective and objective thoughts, Kanzi must advance from its rudimentary capacities (abilities1) to advanced abilities (abilities2).To facilitate this advancement, a new structure is introduced: a multi-agent system or community. This system consists of multiple information processing systems constrained by their dynamic interaction.

• Kanzi is now equipped with built-in electromechanical devices to produce quasi-continuous sounds for communication. Two other automata, Sue (S) and Matata (M), are introduced as fully fledged concept-using adult guardians of Kanzi. Their role is to recognize and nurture Kanzi, whom Rosenberg terms a CHILD (Concept Having Intelligence of Low Degree).

• For the prelinguistic Kanzi, Sue and Matata are not yet speaking subjects but salient items whose linguistic utterances are perceived as engaging and exciting noises conveying importance. This is described as a communicative regime where Kanzi "hears" these noises as representations because they align with its dispositional world-representings, implying an inductively biased world.

• For Kanzi to integrate its various meta-awarenesses under a unified "I" and genuinely form thoughts, it must model its private meta-awarenesses on a public and deprivatized language. This requires interaction with S and M, who are presented as "fully fledged concept-using adult guardians". Initially, Kanzi perceives S and M's linguistic utterances as engaging and exciting noises

• As S and M provide reports about the environment (like the monkey's movements behind the monolith), Kanzi, being a creature of dispositional regularities, can recognize these reports and map them to its own de facto meta-awarenesses. This process leads to Kanzi acquiring labelled meta-awarenesses. These newly acquired labelled meta-awarenesses are contrastive and can create mutually precluding perspectives for Kanzi—introducing a multiperspectival disturbance, transforming Kanzi's formerly seamless perspectival world into one that is proto-inferentially multiperspectival.

• To resolve this tension, Kanzi stops taking S and M's reports"at face value. However, at this stage, these internal thoughts are not objective beliefs and lack epistemic status, as they are not yet linguistically asserted or committed to. The infantile world of Kanzi's seemings is unsustainable because S and M are capable of making objective judgments. To recohere its world, Kanzi must remove the quotation marks from its meta-awarenesses while restoring the labels, effectively constructing a world-picture from various contrasting partial world-pictures. This leads Kanzi to inhabit an objective self-critical stance.

• Education is fundamentally the cultivation of recognition, paving the way for the broader cultivation of cognitions. The child's inherent will-to-autonomy is presented as a categorical fiat or an a priori rule, distinct from contingent sociocultural conventions or natural laws. This principle of recognizing a child's will-to-autonomy applies universally to all children, regardless of whether they are human, artificial, or otherwise. This perspective leads to the conclusion that autonomy is not merely the result of education, but rather its foundational enabling condition and self-cultivating vector. The primary step in education is therefore to attend to and cultivate this intrinsic autonomy.

• The apperceptive "I" is not a substantive self but a logical form of thought individuated by a space of shared recognition, which is intrinsically a public semantic space or language. This self is further differentiated by objectivity—objective validity—, meaning it relates its representations to an object that is independent of any single experiencing subject, but not independent of geist itself.

• Kanzi's recognition of its adult guardians is presented as paramount because this act of recognition is the autonomy of the child itself, embodying the formal practical will as the principle of subjectivity. This "will" (Wille) is distinguished from mere "capacity for choice" (Willkür); the former is a logical form of practical autonomy, a will to transcend oneself and recognize the other that recognizes it, which is crucial for the emergence of the thinking self.

• Education, in this sense, is not just about instilling knowledge but about recognizing and nurturing the child's inherent capacity for self-determination. Autonomy is "that which affords education as its self-cultivating vector". The pedagogical system for the child-AGI aims to enable it to form an increasingly complex structuration of the world and disclose new orders of intelligibilities. This process involves the cultivation of the child's structuring abilities and conceptualization. Objectivity is achieved through the "combination of representations which conform to the object according to a logical—rather than empirical—form".

• The generalized pedagogy is envisioned as a complex system, described as a hierarchical network structure or a multilevel web. It is composed of various interacting modular subsystems, which can be horizontal (distributed modules whose dynamics produce overall system dynamics) or vertical (system dynamics decomposed into interactive products of distinct structural and functional constraint levels). These modules encompass cognitive regimens and tasks, different methods and techniques of training and learning, and models of cognition and practice. This pedagogical system is designed to be plastic and robust, allowing for the integration of new modules and the alteration of existing ones.

• The pedagogical project's overarching regulative ideal is the "what ought to be thought and done combined with what the world in its complete unrestricted conception is". Education is conceptualized as the self-realization of mind as a project, rather than as a fixed entity or given nature. It is considered the "project of all projects," essential for the sustainability and tenability of all other human undertakings.

• The pedagogy focuses on the realization, augmentation, and composition of two interconnected sets of abilities: semantic (sm-abilities) and syntactic (sf-abilities), which are crucial for structuring the world, thoughts, and actions.

• The transition from a "CHILD" status to a fully developed intelligence capable of self-reimagining requires a back-and-forth movement between the trainee and the trainers, built on a pedagogical relationship. This involves cultivating its practical autonomy by helping it navigate the recognitive space and facilitating new encounters with the world to incorporate objectivity.

For citations of Intelligence and Spirit, the format will be (IS, x), therein x is equal to the page in which the cited text can be in the Urbanomic edition of the book. For other books, the specific edition and book will be noted down in a footnote. I’ve also taken from the various lectures given by Reza in The New Centre Research & Practice.

Diagrammatization

I’m gonna try an offer a diagrammatization for the next following chapters

1. Freezing the Flux

This first section of this short chapter examines the challenges to directional, flow-like conceptions of time and their implications for understanding agency and general intelligence. This is a primary example of the critique of transcendental structures. Reza begins by stating that the common perception of time flowing, or of ourselves moving through it from future to past, is "rife with inconsistencies" (IS, 201). The aim therefore is to highlight these inconsistencies to pave the way for understanding how agency's theoretical and practical abilities can expand beyond being foundationally attached to a particular time structure.

Reza uses a modified version of John McTaggart's controversial argument regarding the unreality of time, which is also implicit in Kant's view of experienced temporality as unreal. McTaggart distinguishes between the A-series (past, present, future) and the B-series (earlier-than, later-than). In the A-series, events change their temporal position, and these determinations—past, present, future—are incompatible. The argument posits that the A-series cannot exist because each temporal event presupposes the entire A-series, but no event can be more than one (past, present, or future) simultaneously, leading to incoherence. This incoherence, in turn, undercuts the reality of the B-series. A second argument from McTaggart concerns the specious present, which is a short duration where our perceptions are considered to be in the present. The issue here is an "ontological tension between successiveness of the elements of a duration apprehended in a specious present and the simultaneity of the elements constituting the apprehending act" (TS, 225). McTaggart contends that while everything is observed in a specious present, nothing, not even the observations themselves, can ever truly be in a specious present. The broader scope of McTaggart's argument, as presented in The Nature of Existence, questions whether the characteristics reality appears to have in experience are its actual characteristics.

A modest claim is thus derived: one cannot infer the objective reality of temporal direction or a dynamic, "flow-like" picture of time from the mere perception of temporal instances or tensed consciousness. This means we cannot deduce an objective account of time from temporal-dynamic characteristics that appear in experience or conditions of observation. Therefore the tensed structure of natural languages and temporal connectives—like "before," "after," "when"—should not be treated as evidence for the objective structure of time. Quine's tiresome bias towards ordinary language in discussing time is noted as a reason for suspicion.

A more disquieting claim suggests that any asymmetric picture of time—sequences, punctual/durational forms, objectively distinguishable present is riddled with experiential biases. These biases are not limited to subjective time-consciousness or natural language; they extend to the ideal notion of the observer in physics. The sinister implication is that if classical notions of causality, system state, and antecedent conditions are entangled with these biased, directional-flow-like pictures of time, then the scientific frameworks that incorporate them may require significant revision, if not abandonment. As these concepts play a fundamental role in complexity sciences, impacting physics, chemistry, biology, neuroscience, economics, and social sciences.

2. Boltzmann’s Copernican Shakedown of the Time-Conscious Subject

This section follows from the former in that it delves into the problematic nature of our ingrained time-asymmetric perspective and its implications for understanding intelligence and reality. Reza Negarestani discusses how Ludwig Boltzmann, in what has been described as a "Copernican moment," challenges the prevalent assumption that the unique directionality of time we experience is an objective reality. He suggests it is merely an "illusion arising from our specially restricted viewpoint". He argues that for the universe at large, "the two directions of time are indistinguishable, just as in space there is no up or down" (LGT, 402)1. Organisms within specific time intervals distinguish past and future based on the direction towards a less probable state (past) versus a more probable state (future).

Reza then uses a thriller-analogy of a film showing gas expanding in a sealed bottle. At a macroscopic level, the gas irreversibly spreads, following the law of approach toward equilibrium and the second law of thermodynamics, which state that entropy—a measure of disorder or energy unusable for work—always increases. This is observed as a time-asymmetric process. However, at the microscopic level, the individual molecules collide and move in a time-symmetric manner; watching this film forwards or backward yields no directional information. Boltzmann's core problem, therefore, is to reconcile the time-asymmetry observed in macroscopic processes with the time-symmetry of the underlying mechanical laws. He found the conventional explanations unsatisfactory and sought a way to avoid these hardly satisfactory consequences.

Boltzmann's broader project aimed to provide complete descriptions of physical phenomena, integrating statistical, epistemological, phenomenological, and subjective-objective levels. His statistical mechanical framework aimed to bridge microscopic and macroscopic descriptions, arguing that entropy would always monotonically decrease (or negative entropy H would decrease), demonstrating the unidirectional increase of entropy at the macroscopic level despite underlying time-symmetry. Boltzmann conceptualized macroscopic systems (like a gas) as being composed of an enormously large number of particles. He pioneered a statistical mechanical framework to describe the behavior of these many-particle systems, introducing the concepts of microstate and macrostate:

• A microstate specifies the instantaneous position and momentum of every single particle in the system, represented as a point in a six-dimensional molecular space or μ-space (PPQT , 70)2.

• A macrostate (also referred to as a "distribution of state" or Komplexion) is a collective description of the system that groups together many microstates which are indistinguishable to a given observer.

Boltzmann's pivotal insight was to link the macroscopic property of entropy (S) to the probability of a macrostate. He famously defined entropy as S = k log W, where 'W' is the number of distinct microstates that correspond to a given macrostate. In this framework, entropy serves as a measure of disorder or randomness; a macrostate with more corresponding microstates is considered more disordered and thus has higher entropy. Boltzmann's procedure involved conceptually dividing the μ-space into many small, equally sized cells. He found that using equally sized cells for position and momentum variables led to the desired Maxwell probability distribution as the most probable state for a gas (PPQT, 70). He then introduced a quantity denoted as H, which is essentially negative entropy (LGT, 130). The expression for H is derived by summing the product of the number of molecules in each cell and the natural logarithm of that number, across all cells (LGT, 26).

To prove his H-theorem (that H would always decrease or remain constant), Boltzmann made a crucial assumption called the Stoßzahlansatz, or the "molecular chaos" assumption. This assumption states that the velocities of two particles about to collide are uncorrelated (PPQT, xv). In other words, for statistical calculations, the occurrence of one molecule with a definite state of motion at a certain place is considered independent of the place from which the other colliding molecule came or its state of motion (LGT, 18). This was a critical prerequisite for the rigorous mathematical derivation of his results in gas theory. Based on the Stoßzahlansatz and the statistical analysis of molecular collisions, Boltzmann demonstrated that the quantity H would always monotonically decrease or remain constant until it reached its minimum value, which corresponds to the state of thermal equilibrium (LGT, 32). Since H is defined as negative entropy, this monotonic decrease of H directly translated to a unidirectional and irreversible increase of entropy at the macroscopic level. This evolution signifies that systems tend to move towards more disordered and statistically more probable macrostates over time. For Boltzmann, the "one-sidedness" of macroscopic processes (gas spreading out) was not due to the underlying equations of motion, but solely to the initial conditions (LGT, 399). Even though individual molecular motions are reversible, the sheer number of particles and the statistical nature of their collisions mean that the system overwhelmingly tends towards macrostates that are more probable (higher entropy). The reversal, though not strictly impossible, becomes extremely improbable when dealing with vast numbers of particles (LGT, 400).

However, Boltzmann later expressed doubts, realizing that his statistical argument—a combinatorial procedure—itself lacked inherent time-asymmetry. This meant that the increase of entropy could equally be applied to a sequence running from future to past. The real conundrum became not why entropy increases toward the future, but why it was ever so low to start with. The fundamental issue was that Boltzmann had unintentionally imported subjective characteristics of experience into his combinatorial procedure via the introduction of macrostates, thus conflating statistical and thermal entropy. He did not fully recognize the extent to which time-asymmetric assumptions from macroscopic descriptions distorted the statistical-objective description of microscopic systems. This problem is exemplified by μInnocence, the intuition that interacting systems are ignorant of one another until interaction. Boltzmann's collision principle (stoßzahlansatz) implicitly assumed a privileged time-asymmetry: it expected particles to be uncorrelated before collision but correlated after, which has no place in a time-symmetric microscopic description. This means his explanatory schema, relying on an initial microstate explaining a final macrostate, is problematic because the temporal asymmetry grounding it needs justification. This critique extends to causal explanations that rely on antecedent conditions and a time-directed causal arrow, particularly in reductionist frameworks where the distinction between "the causal" and "the explanatory" fades.

3. Inductive Dogmas and Cognitive Biases of Time-Asymmetry

This section, following Boltzmann, explores how our inherent epistemological biases, particularly those tied to our temporal perceptions, subtly but significantly distort our scientific models and methods. Reza states that we illicitly impose time-asymmetric descriptions, which are exclusive to macrostates, onto the descriptions of microstates. This is done to explain the behavior of macrostates through microscopic mechanics. This problem reveals a broader issue: our epistemological biases—not just perceptual ones—in aligning observational and theoretical frameworks. We tend to project our subjective assumptions onto the world, positing features that require explanation as objective explanatory features.

These biases are evident in theories where computation is strongly linked to the postulate of positive entropic increase for irreversible processes. For example, in the thermodynamics of computation, logically irreversible operations like erasure are often thought to increase entropy. "The physical implementation of computation (i.e., physical computers) always exacts an entropy cost" (IS, 220). However, Reza emphasizes that there is no a priori necessary connection between orthodox thermodynamics and computation that would allow for an uncontroversial association between logical properties and classical mechanics. This "exact link" remains an unsettled issue. Some argue that time-asymmetry and temporal descriptions are merely useful fictional instruments. While it's true that our sense of time as a flow is a qualitative conception without metrical components, this qualitative conception can corrupt the metrical ingredients of our scientific frameworks even when least expected. Dismissing temporal descriptions as idealizations or fictions "can reinforce our obliviousness to the influence that our temporal intuitions exert upon models and methods" (IS, 221). This, in turn, postpones the critical task of examining the distorting effects of temporal intuitions on scientific models and methods.

On Russell's "Five Minutes Ago" Paradox

Reza discusses Bertrand Russell's "five minutes ago" paradox, which challenges the reliability of memory-driven knowledge of past observations.

• Part 1: Everything constituting a memory-belief is happening now, not in the past to which it refers. Therefore, it's not logically necessary for the remembered event to have occurred, or for the past to have existed at all.

• Part 2: There is no logical necessity for memory states to be in a one-to-one correspondence with the rest of the universe; there can be many-to-one and many-to-many correlations between memory states and external states of affairs. Thus, what we remember as a past event or observation could be a false memory.

Russell attempted to establish memory's reliability through two "senses":

• Q-series (sensed familiarity): The feeling of familiarity among memory-images suggests their accuracy.

• Q-series (sensed familiarity): The feeling of familiarity among memory-images suggests their accuracy.

Reza argues that "what is sensed1 qua organized sense-impression... by itself does not so readily and directly translate into sense2 qua judgement or belief proper". This points to the "myth of the given" (IS, 223). Additionally, the senses of familiarity and remembered context are too arbitrary, allowing for many-to-many mappings that make ordering arbitrary. Ultimately, memory-driven knowledge falls back into the problems of induction and the "five minutes ago" paradox itself.

Reza then addresses attempts to resolve the logical tenability of induction's riddles—including Russell's paradox—by invoking the principle of simplicity or Occam's razor. The author argues that simplicity is a "pragmatically and contextually effective tool," but it is "neither truth-indicative nor is it a law indexing an inherent simplicity in the world" (IS, 226). For example, a theistic worldview is simpler than a Darwinian one, yet simplicity alone doesn't make it true. Similarly, defending inductive methods based on their evolutionary reliability is dismissed as "only an act of faith in the blind god of evolution" that merely defers the problem. Evolutionary reliability "does not so obviously translate into the reliability of our inductive predictions and retrodictions" (IS, 227). The section concludes by emphasizing that "Distilling the superacid of epistemological scepticism is essential for rescuing the legitimacy of our knowledge and the coherency of critical realism". Scepticism, understood as investigation, prevents dogmatism, while scepticism without rational inquiry leads to debilitation. This systematic skepticism is contrasted with "greedy scepticism," which unselectively attacks all knowledge.

3. What Now?

This section goes back to Boltzmann by reformulating Boltzmann's challenge to our understanding of time within a traditional philosophical framework. The fundamental problem is not the enigmas of Heraclitean flux or absolute contingency (thanks God), but why our philosophical reflections on events and processes so often include an element of time-asymmetry. Reza argues that events happen and can always be made tenseless; "event e happened" means e is earlier than the utterance, "e is happening now" means e is simultaneous, and "e will happen" means e is later. This concept of token-reflexivity suggests no inherent time-asymmetry at this level.

Arguments for time's flow or shift, such as those relying on the "specious present" or Husserlian retention-protention3, cannot faithfully establish time-asymmetry even within subjective time. While "now" shifts in our consciousness and "now-contents" have a temporal order, the mere diversity of these contents does not synthetically prove that "now moves from earlier to later" (IS, 228). This leads to the conclusion that phenomenological time-asymmetry is psychologically ad hoc, or merely a psychological impression. Drawing on Kant's argument against Hume4, Reza states that no amount of successive states of awareness can yield an instantaneous awareness of the succession, which is necessary for the idea of temporal flux. The sequence of representations is not the same as the representation of the sequence. Therefore, temporal becoming is revealed as a purely perspectival awareness, a "psychological impression at worst, and a necessary pragmatic representation at best" (IS, 229). The coming-to-be or ceasing-to-be of an event simply means its entrance or departure from the immediate awareness of an observer.

If the self is merely a bundle of impressions or awarenesses1, then concepts like "subject” and "experience" become redundant, as even a tape recorder can sequentially mark events. However, without apperceptive unity as the principle of experiential unification, a Humean self (a bundle) can be arranged into infinitely many bundles qua selves, leading to an arbitrary multitude of selves. In this pure bundle-view, there are no non-arbitrary spatial, temporal, or causal relations between impressions. A Kantian position would argue that the transition from successive awarenesses to the awareness of succession—temporal flux—comes from the application of an a priori rule. The problem then shifts to the source of this rule: if purely logical (analytic), it cannot provide new synthetic content; if synthetic, its source is the apperceptive unity of the subject. In the latter case, temporal becoming is a "transcendental ideality" playing a "necessary pragmatic role" in the agent's objective description of the world. The author argues against abandoning metaphysics; rather, presuming to be "purged of metaphysical assumptions" often leads to "dogmatic and veiled forms of metaphysics" (IS, 232).

A robust metaphysics of time, in the vein of Plato and Hegel, must:

1. Be open to systematic theoretical assessment.

2. Proceed via conceptualization of structure, not positing independently structured reality.

3. Suspend the superficial correspondence between reality and our experiential characteristics.

4. Develop a notion of mind (Idea/geist) whose finitude is suspended from natural/temporal limitations, with its true object being the infinite and atemporal.

5. Embrace reason, which accepts the "identity of opposites" (thought and being, finite and infinite), in contrast to understanding which can only grasp time as succession.

5. Metaphysics of Time As Logic of Spirit

This section follows from the last in the project of a robust metaphysics of time, deeply rooted in Hegelian and Platonic thought, in contrast to Kantian and other philosophical perspectives. Metaphysics, properly understood, involves the apprehension of the infinite. This means it is free from the static or fixed contradictions that arise from the limitations of human experience or understanding. This apprehension of the infinite does not imply freedom from all contradictions, but rather from fixed antinomic contradictions. Lower-level contradictions are suspended in higher ones, thereby being avoided at subsequent levels. Therefore, metaphysics is inherently linked to the dialectical movement of concepts, or, more precisely, to "speculative logic". This logic is not abstract or a general grammar of thought forms, but rather logic as the Idea, which is "thought’s own ‘self-developing totality of its distinctive determinations and laws, which it gives itself and does not already have and find within itself’ (EPS, 47)5.

Hegel's robust metaphysics of time is presented as a fundamental element of metaphysics itself because it rescues the concept of the infinite from fixed contradictions, such as Kant's thing-in-itself which is seen as a veiled metaphysical postulate. Hegel's view stems from his critique of Kant's first cosmological antinomy, which questions whether the physical universe is temporally and spatially finite or infinite.6 Kant argued that both sides (world having a beginning in time vs. lacking one) could be indirectly argued for, leading to a contradictory result. Hegel asserts that Kant's antinomy arises because understanding, unlike reason, cannot accept the "identity of opposites" and is bound to the "transcendental subject of experience" (IS, 235).7 Understanding mischaracterizes the Absolute (the infinite) as a successive series of past temporal events, leading to the contradiction. Reason, in contrast, accepts the identity of opposites (thought and being, finite and infinite) and "suspends finitude" to arrive at knowledge of the Absolute Idea. This suspension is the adoption of an "unconditional atemporal viewpoint", which allows reason to relinquish the "power of time over its Idea" (IS, 236).

From this atemporal perspective, the truth of mind (Geist) is not found within time; rather, the mind is time. The Concept, "in its freely existing identity with itself, as ego=ego, is in and for itself absolute negativity and freedom," and thus is not merely free from the power of time but is neither within time, nor something temporal. It is the Concept that "constitutes the power of time," as time is merely "this negation as externality". Only what is natural and finite is subject to time; the true, the Idea, and spirit are eternal (IS, 236). The totality of the Idea of mind cannot be represented temporally as a form of finitude masquerading as totality. This view implies that ideas like the "human as a concluded totality given to us here and now as a biological species" or "capitalism as the completed historical totality" are "posited forms of finitude dissimulating themselves as completed histories" (IS, 237).

Reza argues that images of time as an endless flow that belittle humanity are often "antihumanist veneers upon a subjectivist account of time". Such views uncritically posit "local and contingent characteristics of egocentric human experience as the characteristics of reality" (IS, 237). Philosophical maturity coincides with a liberation from the servitude to time, recognizing that the temporal is "not important". Bertrand Russell is quoted, stating that "The importance of time is practical rather than theoretical, rather in relation to our desires than in relation to truth". McTaggart adds that if "nothing is really in time, and the temporal is merely an appearance," then "the importance of time diminishes, so also diminishes the importance of the cessation of our lives in time" (IS, 238).

Reza, in his rigorous and comprehensive manner, now addresses the objection that a world without the flow of time—becoming—would be deterministic, eliminating human freedom and novelty. The paradox of inaction states that either:

1. If no "coming-into-being" exists, the future is determined, rendering rational plans irrelevant.

2. If "coming-into-being" exists, the future is indeterminate, making rational plans futile.

Reza cites Grünbaum, as he argues that in both deterministic and indeterministic worlds, the "coming-into-being" or "ceasing-to-be" of an event is merely its "entrance or departure... from the immediate awareness of the apperceptive ego". The difference between these worlds is merely the "type of functional connection linking the attributes of the future events to those of present or past events," (IS, 240) not their actual existence. The objection confuses epistemological precipitation (events entering our awareness) with existential precipitation (events coming into being). Causal determination means a system's state must have—by physical necessity—followed on from an antecedent state, but this is not compulsion, and therefore, it does not imply a lack of freedom. Reza ends the section by stating that the assertion that causal determination entails a lack of freedom is “is based not only on a prescientific account of causation but also on a conflation of causal contribution with causal compulsion.” (IS, 242).

6. Time, Reality, and The View From Nowhen

This section rounds up this small chapter by going back to Boltzmann, whose challenge highlights the extent to which time-asymmetric elements in our time-consciousness have biased the matter-of-factual characteristics of reality. Reza argues that if characteristics of reality happen to align with the contingent features of our local experience, they should be critically examined rather than assumed as given. This prompts an inquiry into alternative models of time that are compatible with local temporal and causal perspectives without privileging any single one. Such models would enlarge the field of experience and observation, moving beyond our current limitations.

Reza thus introduces a pragmatist view of time-conscious agency, suggesting that anthropocentrism in the use of temporal concepts is pragmatically justified and necessary, provided these concepts are not metaphysically reified as universal characteristics of objective reality. A robust model of time should thus express a reality that generates local temporal perspectives without being reducible to them. From this standpoint, our temporal perspective becomes a local self-expression of an absolute—atemporal—reality, rather than a mere illusion. This liberation from a time model restricted by contingent constitution is presented as a crucial step for rational maturity, enhancing cognitive and practical abilities. It enables the subject to interrogate the most established "facts of experience" and expand the scope of experience, thereby challenging ideologies based on a purely temporal understanding of progress or the second law of thermodynamics. Thus Boltzmann's challenge is interpreted as a Hegelian radicalization of Kant's thesis on the transcendental ideality of experienced temporality, extending its implications beyond modern sciences to philosophical, scientific, and sociopolitical ideologies influenced by the concept of entropy.

Reza then outlines three key challenges that arise from this radical perspective, shaping the project of maintaining and expanding the intelligibility of agency:

1. Challenge 1: Envisioning models of agency with fundamentally different senses of time. These models would stem from distinct local observational conditions, structural-behavioral organizations—varied memory models—, or different logical connections within temporal language. The goal is to move beyond current human limitations and explore artificial models of agency not confined by these contingencies, thereby enlarging the field of experience and cognitive discovery.

2. Challenge 2: Developing time models compatible with the subjective temporal-causal perspective without elevating it to a canonical global model. This involves constructing a "physics" of our temporal-causal perspective that explains its features without reinscribing them as objective reality, and resolving paradoxes like retrocausality arising from inadequate directional-dynamic models of time.

3. Challenge 3: Reconciling the pragmatic utility of our temporal view with a non-directional/non-dynamic model of time-conscious experience. This challenge explores the implications of such alternative, particularly atemporal, models for both physical and social sciences, and the theoretical and practical gains from their adoption.

The third challenge is identified as central to rational agency's struggle for self-conception and self-transformation, seeking to transcend essentialist attachments to particular transcendental structures of experience. This leads to the concept of a view from nowhen, which explains any mode of experienced temporality without being constrained by its particularities, and is crucial for realizing Hegel's Absolute Spirit (moving from particular, contingent consciousness to genuine self-consciousness). The view from the space of reason (Concept) is characterized as a view from nowhere (impersonality of reason) and nowhen (the pure formlessness of time, expressed as a project of discursive rationality that "takes time"). This emphasizes time-generality, where history becomes an ongoing totalization under the Concept, whose form is atemporal or timeless. Casting off the limitations of directionally temporalized history transforms it into a medium for time as pure formlessness.

Ultimately, this outside view from nowhere and nowhen is a circuitous and arduous path of critique, spanning various methods from science to politics. It aims to revise our self-experience, recognizing that for an intelligence with a broader field of experience, the current meaning of human becomes merely an antecedent condition to what is necessarily us—the unchanging form of us. The section concludes that genuine self-consciousness is the view of ourselves from nowhen, leading to a conception of the world that is replete with possibilities and no less actual than our current reality. From a Kantian perspective, embracing this view fulfills critical philosophy's aim of demonstrating the mutuality of the rational self—discursive apperceptive intelligence—and the world, without conflating thinking with being.

Overall Summary

• One cannot infer the objective reality of temporal direction or a dynamic, "flow-like" picture of time from the mere perception of temporal instances or tensed consciousness. This means we cannot deduce an objective account of time from temporal-dynamic characteristics that appear in experience or conditions of observation.

• A more disquieting claim suggests that any asymmetric picture of time—sequences, punctual/durational forms, objectively distinguishable present is riddled with experiential biases. These biases are not limited to subjective time-consciousness or natural language; they extend to the ideal notion of the observer in physics.

• Reza Negarestani discusses how Ludwig Boltzmann, in what has been described as a "Copernican moment," challenges the prevalent assumption that the unique directionality of time we experience is an objective reality. He suggests it is merely an "illusion arising from our specially restricted viewpoint". He argues that for the universe at large, "the two directions of time are indistinguishable, just as in space there is no up or down"

• Boltzmann’s statistical mechanical framework aimed to bridge microscopic and macroscopic descriptions, arguing that entropy would always monotonically decrease (or negative entropy H would decrease), demonstrating the unidirectional increase of entropy at the macroscopic level despite underlying time-symmetry.

  • A microstate specifies the instantaneous position and momentum of every single particle in the system, represented as a point in a six-dimensional molecular space or μ-space.

  • A macrostate is a collective description of the system that groups together many microstates which are indistinguishable to a given observer.

• To prove his H-theorem (that H would always decrease or remain constant), Boltzmann made a crucial assumption called the Stoßzahlansatz. This assumption states that the velocities of two particles about to collide are uncorrelated. In other words, for statistical calculations, the occurrence of one molecule with a definite state of motion at a certain place is considered independent of the place from which the other colliding molecule came or its state of motion.

• Boltzmann later expressed doubts, realizing that his statistical argument—a combinatorial procedure—itself lacked inherent time-asymmetry. The increase of entropy could equally be applied to a sequence running from future to past. The real conundrum became not why entropy increases toward the future, but why it was ever so low to start with. The fundamental issue was that Boltzmann had unintentionally imported subjective characteristics of experience into his combinatorial procedure via the introduction of macrostates, thus conflating statistical and thermal entropy.

• Reza then states that we illicitly impose time-asymmetric descriptions, which are exclusive to macrostates, onto the descriptions of microstates. This is done to explain the behavior of macrostates through microscopic mechanics. This problem reveals a broader issue: our epistemological biases—not just perceptual ones—in aligning observational and theoretical frameworks. We tend to project our subjective assumptions onto the world, positing features that require explanation as objective explanatory features.

• Phenomenological time-asymmetry is psychologically ad hoc, or merely a psychological impression. Drawing on Kant's argument against Hume, Reza states that no amount of successive states of awareness can yield an instantaneous awareness of the succession, which is necessary for the idea of temporal flux. The sequence of representations is not the same as the representation of the sequence.

• The problem then shifts to the source of this an a priori rule, from which the transition from successive awarenesses to the awareness of succession would occur: if purely logical (analytic), it cannot provide new synthetic content; if synthetic, its source is the apperceptive unity of the subject. In the latter case, temporal becoming is a "transcendental ideality" playing a "necessary pragmatic role" in the agent's objective description of the world.

• A robust metaphysics of time, in the vein of Plato and Hegel, must:

  1. Be open to systematic theoretical assessment.

  2. Proceed via conceptualization of structure, not positing independently structured reality.

  3. Suspend the superficial correspondence between reality and our experiential characteristics.

  4. Develop a notion of mind (Idea/geist) whose finitude is suspended from natural/temporal limitations, with its true object being the infinite and atemporal.

  5. Embrace reason, which accepts the "identity of opposites" (thought and being, finite and infinite), in contrast to understanding which can only grasp time as succession.

• Hegel's robust metaphysics of time is presented as a fundamental element of metaphysics itself because it rescues the concept of the infinite from fixed contradictions, such as Kant's thing-in-itself which is seen as a veiled metaphysical postulate. Hegel asserts that Kant's antinomy arises because understanding, unlike reason, cannot accept the identity of opposites and is bound to the "transcendental subject of experience. Understanding mischaracterizes the Absolute (the infinite) as a successive series of past temporal events, leading to the contradiction. Reason, in contrast, accepts the identity of opposites and suspends finitude to arrive at knowledge of the Absolute Idea. This suspension is the adoption of an unconditional atemporal viewpoint, which allows reason to relinquish the power of time over its Idea.

• From this atemporal perspective, the truth of geist is not found within time; rather, the mind is time. The totality of the Idea of mind cannot be represented temporally as a form of finitude masquerading as totality. Philosophical maturity coincides with a liberation from the servitude to time, recognizing that the temporal is "not important".

• Reza cites Grünbaum, as he argues that in both deterministic and indeterministic worlds, the coming-into-being or ceasing-to-be of an event is merely its entrance or departure from the immediate awareness of the apperceptive ego. The difference between these worlds is merely the type of functional connection linking the attributes of the future events to those of present or past events, not their actual existence.

• Reza thus introduces a pragmatist view of time-conscious agency, suggesting that anthropocentrism in the use of temporal concepts is pragmatically justified and necessary, provided these concepts are not metaphysically reified as universal characteristics of objective reality. A robust model of time should thus express a reality that generates local temporal perspectives without being reducible to them. From this standpoint, our temporal perspective becomes a local self-expression of an absolute—atemporal—reality, rather than a mere illusion.

• Reza then outlines three key challenges that arise from this radical perspective:

  1. We need to imagine agents that experience time completely differently from us, breaking free from our limited human perceptions.

  2. We must create models that explain our subjective experience of time without claiming it's the only objective reality, which could help resolve paradoxes like retrocausality.

  3. We need to figure out how our practical, everyday view of time can coexist with alternative, potentially atemporal, ways of experiencing consciousness, and what benefits this could bring to science and society.

• This leads to the concept of a view from nowhen, which explains any mode of experienced temporality without being constrained by its particularities, and is crucial for realizing Hegel's Absolute Spirit (moving from particular, contingent consciousness to genuine self-consciousness).

• The view from the space of reason (Concept) is characterized as a view from nowhere (impersonality of reason) and nowhen (the pure formlessness of time, expressed as a project of discursive rationality that "takes time").

For citations of Intelligence and Spirit, the format will be (IS, x), therein x is equal to the page in which the cited text can be in the Urbanomic edition of the book. For other books, the specific edition and book will be noted down in a footnote. I’ve also taken from the various lectures given by Reza in The New Centre Research & Practice, especially the Complexity and Computation: An Introduction to Measures, Paradigms and Programs, Kant’s Circle of Revenge, and Maths & Ideas lectures.

Diagrammatization

This is the diagrammatization for the third chapter.

1. The Toy Universe of an Embodied Automaton

This first section introduces starts the thought experiment[This I, or We or It, the Thing, Which Speaks] a hypothetical embodied automaton as the central component of the thought experiment of viewing ourselves through the Outside as a AGI in the book. In this section we just see the hypothetical embodied automaton as initially conceptualized with several fundamental features, gradually building complexity:

1. Feature 1: A Goal-Oriented and Constrained System: The automaton is pre-programmed with diffuse and recurring goals that are analogous to biological needs, primarily focused on system maintenance and preservation. These goals inherently impose necessary physical and computational cost constraints on the automaton as an information processing system, thereby influencing its capacities and behavioural responses. Negarestani emphasizes that any information processing system necessitates constraints on runtime and computational cost for its very possibility.

2. Feature 2: Structured Wiring and Proto-Intentions: Its internal architecture, akin to neural wiring, comprises primary low-level information processing modules, higher-level intermediating modules, and workspaces, including a global workspace. This global workspace makes processed information accessible to executive functions and goal-oriented behaviours. This inherent wiring allows for reliable differential and adaptive responsiveness to its environment. The automaton's goal-oriented activities are termed proto-intentions, a key distinction being that objects are entangled with the agent's goals causally, not conceptually. An illustrative example given by Negarestani is a predator chasing its prey, where information is globally mobilized within the workspace to execute this proto-intentional activity.

3. Feature 3: Sensory Integration: The automaton is equipped with specialized sensors and modules designed for integrating sensory data. This integration occurs both within a specific sensory modality (emultiple data points from a single sensor) and across different modalities (data from various sensors). This multi-level sensory integration serves to extend spatial and temporal coverage, enhance the robustness and reliability of information, reduce ambiguity, and increase the salience of environmental stimuli, ultimately expanding the range of the automaton's potential behaviors.

4. Feature 4: Complex and Flexible Memory: The automaton possesses a memory system that is sufficiently complex and functionally flexible. It is capable of encoding, retrieval, consolidation, discarding, and transfer of sensory impressions. This memory is characterized as constructive, meaning that each act of retrieval is not a perfect recall but a reconstruction that actively guides further memory construction.

2. The Virtuous Circle of Analogy

In this section, Negarestani introduces and explains the analogical framework used to describe the automaton's navigation of the world, acknowledging the inherent limitations of such an approach. Negarestani notes that describing how the automaton navigates the world is circumscribed because it is framed through our full-blooded conceptual and linguistically structured beliefs. When describing the automaton's nonconceptual impressions of the environment or its goal-satisfying behaviour, we are "stuck" using analogies to our own discursive—concept-using—apperceptive consciousness. For example, the automaton's causally conditioned navigation is modeled on our theoretical reasoning, and its functional interaction with the environment is an analogy to our practical reasoning. Even at the most rudimentary level of the automaton's nonconceptual sense impressions, an analogical framework is unavoidable because we can only discuss them through "our inexorably ‘concept-laden’ introspection into our inner states" (IS, 149).

The first key point is that the resources of language are ultimately the only resources available to us—as temporally discursive apperceptive intelligences—for representing the intelligible order. This is because our nonconceptual sensory impressions are themselves caught up in the inferential web of language. The second, and more important, point is that the automaton's causal interaction with its environment, viewed as a protosemantic navigation of the world, inherently exhibits a noncategorial orderly structure. Our linguistic concepts, through their inferential relationships, reflect, illustrate, disambiguate, and make explicit this underlying order. In essence, the automaton's causal interactions instantiate structures from which our own semantic structures have—at least partly—evolved.

This analogical approach is termed "virtuous" rather than "vicious" because it operates as a form of "as-if" (als ob) arguments.1 These arguments serve as regulative theoretical and practical judgements. By carefully extending our conceptual and linguistic resources to describe the automaton's nonconceptual awareness, this virtuous circle enables us to construct, step by step, a full-blooded discursive apperceptive intelligence from one that is initially neither discursive nor apperceptive. The process of analogically positing nonconceptual awareness and then elaborating it into conceptual awareness is the same process needed to develop non-apperceptive intelligence into apperceptive self-consciousness.

The overarching purpose is to cautiously use natural language's conceptual resources to outline the automaton's nonconceptual awareness, without falsely attributing higher-level awareness like concept use or language mastery. It aims to identify this inchoate awareness or preconceptual form of intelligence as the transcendental minimum condition for a temporally discursive apperceptive intelligence. Finally, it seeks to specify what is required to elaborate this analogically posited heuristic intelligence into a general intelligence endowed with a generative cognitive complexity that is no longer merely analogical, meaning its heuristic abilities are fundamentally integrated with its linguistically-enabled cognitive capacities. This outlines the Kantian-Hegelian program for the construction of general intelligence.

This approach is distinct from a reductionist one. Instead of reducing the discursive apperceptive subject to a causal structure, it reconstructs sapient general intelligence from sentient intelligence. The argument is that while sentient intelligence—causally reducible—is necessary for the realization of sapience—rational agency—, it is not sufficient. This challenges purely naturalized accounts that present naturalization as a policed one-way traffic from reasons to causes, emphasizing that it should be a two-way street between causes and reasons.

Negarestani here introduces a lovely conceptual persona2: the greedy sceptic who denies the possibility of knowing the human mind but paradoxically proposes theories of superintelligence or panpsychism. This sceptic believes neuroscience discredits concepts and conceptualization, and dismisses mathematical concepts as pseudo-semantic absurdity. The greedy sceptic characterizes discursive self-consciousness as merely an epiphenomenal or illusory byproduct of phenomenal consciousness, implying that if the trick of consciousness can be performed by unconscious modular processes, then discursive apperceptive awareness can too. Negarestani critiques this stance by highlighting its performative contradiction: the sceptic trivializes semantic, formal, and a priori dimensions of cognition while simultaneously using formally and semantically-loaded vocabularies of thought to describe the blind brain. This "eating their own cake of semantic apocalypse" reveals their "semantic naivety". The sceptic ultimately "elides the distinctions between conceptual awareness and phenomenal awareness, judgments and heuristics, the structure of discursive intentionality and the structure of proto-intentionality, the space of reasons and the space of causes" (IS, 156).

We end the section with Negarestani reiterating the importance of the fundamentally linguistic character of sapience, moving beyond the worn and antiquated view of language merely as a symbolic medium or communication tool. Instead, language is presented as a sui generis framework of interaction-as-computation furnished with various classes of complexity and cognitive abilities. This perspective is crucial for understanding how apperceptive intelligence can be reconstructed from heuristic intelligence, leading to a general intelligent.

3. The Automaton’s Story, a Thought Experiment

This section introduces the methodological framework for narrating the hypothetical automaton's journey toward intelligence. This section sets out to tell the story of the automaton as a preconceptual pre-apperceptive intelligence. To achieve this, Negarestani proposes to use two distinct types of linguistic narration:

Story 1: A linguistic story about how the automaton registers the environment.

“The automaton is sentient of the environment: A heap of black accompanied by a low monotonous noise. Suddenly, a faint rustling noise perturbs the scene. A short while later, as the sound becomes louder, a mass of protruding fuzzy grey appears at the opposite end of the heap of black and moves toward it. As the mass of grey reaches the heap of black, it stops, makes contact with the heap of black, moves away, makes contact with it and then moves away, again and again. The perturbing sound has shifted to a shrill and high-pitched sound. Later, the mass of grey recedes from the heap of black. The sound becomes a rustling noise and continues for a while after the mass of grey completely disappears. All that is left on the scene is a rectangular heap of black accompanied by a low monotonous noise.” (IS, 156)

This narrative focuses on the automaton's nonconceptual representations of items in its environment. These representations are described as "registers at the level of internal variable states of the automaton’s wiring structure which causally mediates between sensory inputs and behavioural outputs". The automaton's awareness in this story is of basic occurrences, such as "a heap of black" or "a rustling". This mode of perception is termed "seeing1" (or seeing-of), which captures awareness of properties like "the colour on the facing part of its surface and its shape on the facing side" (IS, 157) of an object. This seeing1 is analogous to what Kant would describe as an image[Bild]3 qua function of the imagination.4

Story 2: A non-analogical linguistic narration—essentially a story of and within language.

“The automaton has just seen a reenactment of the monolith scene in 2001: A Space Odyssey. A featureless black monolith is erected in a landscape whose serenity is broken by the steps of an approach-ing monkey. once the monkey finds the monolith, it starts examining it, screams, panics, runs away, and comes back to touch it again. The monkey continues this game for a while until it finally gets bored and goes away.”

In contrast to Story 1, this narration describes how the automaton's raw registers are inferentially caught up within language. The elements of Story 2 are "linguistic items that possess semantic features by virtue of the inferential roles they play in our collective linguistic practices". Through this narrative, we—as concept-using agents—understand the items "as something (as a monolith, as the steps of an approaching monkey)". This is referred to as seeing2, which involves a more complete apprehension of the object, such as its color "through and through" and its shape "all around," allowing us to see it "as a black rectangular cuboid, a black monolith". This seeing2 process involves the subsumption of an image—from Story 1—under a concept through schemata, which are "universal procedures for constructing a model of that concept" (IS, 158).

4. Constructing a Lego Model in the Style of Kant’s Threefold Synthesis

This is the where the jazz starts. Here Negarestani explains how the process of building a Lego model serves as an analogy for Kant's threefold synthesis of experience, detailing the stages involved in moving from raw sensory input to objective conceptual awareness, as Kant’s threefold synthesis emphasises multilevel construction rather than Humean basic empirical associations.5 This Lego model-building process is crucial for understanding the transition from seeing1 (nonconceptual, rudimentary impressions) to seeing2 (conceptual, object-oriented perception).

The threefold synthesis involves:

1. Synthesis of apprehension in the intuition: This is the initial constructive role of imagination. It involves pulling together a synchronic manifold of sensations, meaning it takes up sense impressions that occur at the same time into an active apprehension. The raw "sense-given matter" from Lego blocks (shapes, colors) corresponds to the "point-of-viewish intuiteds" that the automaton confronts (IS, 158).

2. Synthesis of reproduction in the imagination: This stage continues the figurative part of the building process of imagination. Its function is to represent an object even when it is not directly present in intuition. This synthesis combines the diverse sensory information as it appears in intuition.

3. Synthesis of recognition in the concept: This is where apperceptive consciousness plays a crucial role in perception. It "makes its function intellectual" (IS, 162). This synthesis requires: recognizing a past representation as being related to a current one, recognizing both past and present representations as belonging to a single object, by means of a concept. This ultimately leads to the production of full-blooded judgements. The "pictorial motif" in Lego building determines how colors and shapes of blocks can be put together to construct a specific model, encapsulating the function of a concept ("robot").

A Toy Robot Under Kantian Critique

The diagram “Kant’s threefold syntheses”6 depicts the sequential and interactive stages through which raw sensory input is transformed into a unified, conceptual understanding of an object, such as the “This such-and-such toy robot." This process is considered a revolutionary accomplishment for understanding the functional picture of mind. The entire threefold synthesis is framed as a mental act, highlighting the active role of the mind in constructing experience. This constructive method is key to Kant's transcendental psychology, which investigates the formal conditions for having a mind.

1. Manifold of outer sense (toy blocks in space and time):

This represents the raw, unstructured sensory input received by the automaton's sensors. In the context of the toy robot, these are the individual Lego blocks with their various shapes and colors and stuff. This "manifold of outer sense" is primarily a causal structure, not yet involving concepts or categories of understanding.

2. Synthesis of apprehension in the intuition:

This is the first constructive role of imagination. The imagination begins to pool together a synchronic manifold of sensations. Its function is to introduce order into the confusion of simultaneous impressions by giving them initial spatial and temporal organization, in order to be turned into an image[bild]7. This stage is a figurative synthesis associated with imagination as a constructive-simulating capacity.

2. Synthesis of reproduction in the imagination:8

This is also a function of the imagination. Its role is to represent an object even without its presence in intuition. For the toy robot, this means that as it processes the visual input, it retains what you have already drawn drawn in memory and then continue from that point onward.

3. Image[Bild]/The intuited object (what I[toy model] see1 of toy blocks):

This is the result of the first two syntheses. It represents the raw sense-given matter of the Lego blocks, organized into a coherent image model9 or image[Bild].

4. Synthesis of Recognition in a Concept:

This is the third and culminating synthesis, where the role of apperceptive consciousness in perception becomes central. It requires the faculty of understanding, which uses concepts to unify the manifold. It involves recognizing a past representation as related to the present one and recognizing past and present representations as belonging to a single object via the function of a concept.

5. Perceptual taking or judging the 'intuiting' act (what I[toy model] see2 the toy blocks as):

This is the final outcome of the threefold synthesis, where the object is not just perceived, but cognized of an object. This is seeing2, because of its conceptual recognition—seeing the toy blocks as a "such-and-such toy robot". This process results in full-blooded judgments, transforming raw impressions into structured experience. The "pictorial motif of our Lego model-building corresponds to the conceptual representation of these intuited items in acts of judgements (the intuitings)" (IS, 158).

A Glossary of Kantianisms

Negarestani then neatly defines a few important Kantian concepts.

• Sensations as the "immediate" effects on the mind when causally affected by objects.10

• Sensibility as the capacity to acquire representations through being affected by particular objects.11

• Intuition as the ability to have thoughts of individual items.12

• Empirical intuition is when cognition relates to objects through sensations.13

• Appearances are the indeterminate objects of empirical intuition, which are picked up and built into singular representations.14

• Intuitions differ from sensations in that they are types of cognition, while sensations are not.15 An intuition has raw content—what is intuited from sense impressions—and a form as an act of intuiting, which is a singular act of conceptual representing.16

Negarestani then finishes by noting that these syntheses are dynamic acts of integration that operate in a mesoscopic or mid-level fashion, not purely top-down or bottom-up. They can be understood as matrices of interactions between causal-empirical and logical-inferential domains, governed by rules of integrative transition that represent necessary computations. This perspective aligns transcendental logic with a computational search space, where different levels of mental activity correspond to increased information processing abilities and new types of solvable computational problems.

5. A Digression On Modelling Figurative Syntheses

This section explores how the automaton's figurative syntheses can be modeled and discusses the inherent limitations and necessary critiques of such models. To equip the automaton with objective figurative syntheses (which relate to the object of appearance, Gegenständlichkeit, rather than the object of thought, Objektität), the approach involves applying a mixture of mid-level models. These models are akin to the generative models used in the predictive processing (PP) paradigm. These models operate based on prior probability and statistical estimates, which serve as representations to predict current and future sensory input, as well as the source of that input. The hierarchical organization of these estimates, allowing them to track features across different temporal and spatial scales, enables cross-level predictions.

PP is a paradigm in computational and cognitive neuroscience that proposes perception involves the active, top-down generation of percepts using a multi-level generative model to predict incoming sensory input. This "reversal" of the traditional bottom-up view of perception echoes Kant's Copernican revolution. PP emphasizes that brains actively generate percepts by issuing predictions about the current state of input signals based on hierarchical generative models that rely on prior probabilities and likelihood estimates.

Generative models estimate the causes of incoming sensations by leveraging the system's own ability to produce similar sensations internally. A higher layer in a hierarchical generative model is capable of generating and predicting the activity patterns of the layer below. Object recognition is described as a coordinated balance of top-down signals (instantiating the generative model and predicting causes of sensations) and bottom-up neural signals (against which predictions are matched). This process allows the system to self-generate a meaningful, structured scene using stored knowledge. Crucially, generative models rely on the "productive function" of the brain—its ability to endogenously generate sensory patterns. This involves a "dreaming" or "wake-sleep algorithm" where the system learns to generate patterns "in fantasy" and then uses this knowledge to recognize incoming patterns. This concept directly links to Kant's view of imagination as a "power of presenting an object in intuition even without the objects being present" (PPPHRK,9)17.

To make accurate predictions, intelligent systems require constraints on the set of prior probabilities and likelihoods. These are known as priors, and highly abstract and fundamental ones are called hyperpriors. Hyperpriors are crucial for human cognition, from children to scientists, enabling hierarchical systems to leverage "hypothesis spaces of hypothesis spaces, with priors on priors" (PPPHRK, 5). Prime examples of hyperpriors are the brute constraints imposed by space and time (only one object in one place at a given time). These internal structures restrict possible hypothesis spaces, aiding the formation of decisive perceptual predictions and making the necessary Bayesian computations tractable. This aligns with Kant's “controversial”, as Swanson’s paper describes (PPPHRK, 6), conclusion that space and time are internal structures that constrain possible perceptions, rather than external-world properties.

Kant's theory of schematism anticipates the generative model strategy. Schemata are the third thing that mediate between concepts and sensory intuition, providing a concept with its singular representation or image[Bild]. They are rules for the synthesis of imagination regarding pure shapes in space, enabling the mind to classify perceptual objects not by comparing images, but by identifying abstract, endogenous rules for generating sensory patterns. Kant's schemata can be usefully compared to procedural computer programs or mini-programs that consist of instructions or rules for generating images. This allows for generalization beyond specific examples, solving the generalization problem that plagued earlier association-based machine learning approaches. This is a core strategy in generative models and PP. Incoming sensations are analyzed by comparing them to the internal processes that could synthesize similar patterns endogenously. The system recognizes objects by finding the most likely set of interacting hidden causes whose combination would generate—and thus predict and account for—the incoming sensory data. This process occurs with limited informational resources, from the organism's "view from inside the black box" (PPPHRK, 9).

Let’s now get into categorico-neurological theory. Negarestani suggests that a complex mental image[Bild], like a cuboid, can be embodied in the neural organization from simpler mental images (a square and an oblong rectangle) at lower neural levels. Category Theory offers a powerful mathematical framework for understanding and modeling the neural organization of the brain, particularly how complex mental images are formed from simpler ones, like that of a cuboid.

A colimit is described as a category-theoretical diagram specifically used for the construction-cum18-compression of complex mental images from simpler ones, by employing commutative diagrams and universal properties. This process allows for details and associations between simpler components, like a square and an oblong rectangle, to be compressed or streamlined into a unified image, such as a cuboid or an obelisk. The concept of a colimit provides a mathematical structure to model how individual parts provide a working whole that is greater than the sum of its part. It captures the emergence of "strictly increasing complexity" and acts as a "binding agent" within a neural architecture (NFRCBS, 80)19. In the context of the brain, a colimit can "constructively raise" the neural category (Neur)20, which consists of neurons and synaptic paths (morphisms) at the microscopic level, up to the macroscopic level of the mental objects category (Ment21 or ImO), comprising mental images[Bild] and their structural relationships (NFRCBS, 49). Intermediate levels between microscopic Neur and macroscopic Ment represent different scales of neural organization. This is also applied to understanding how a place field—a coherent representation of a location—emerges as a colimit from multiple grid fields—simpler spatial representations from grid cells—in the hippocampus.

In mathematics, particularly category theory, a commutative diagram expresses the generalization of a system of equations and its internal symmetries. This means that different paths—sequences of morphisms or arrows—within the diagram, starting and ending at the same objects, yield the same composite morphism. For example, in neural modeling, if two paths from a concept—represented by a node—lead to a higher-level concept, and the compositions along these paths are equal, it signifies that the lower-level concept is integrated in a unified way into the higher-level one, avoiding multiple redundant copies (CMCTNS, 495)22.

Therefore, a colimit can be understood as a map from a commutative diagram in the category Ment to a commutative diagram in the category Neur via the functor F: Ment → Neur. This means that higher-level mental objects—like complex images—in the Ment category, which are themselves constructed via colimits from simpler mental images, are mapped to the underlying neural organization (Neur category). This "mapping"—via the functor F— shows how the neural category—composed of neurons and synaptic paths—can be constructively raised up to the macroscopic level of the mental objects category. Essentially, complex image-models are constructed from simpler ones using commutative diagrams and universal properties (like colimits). The functor F ensures that the structure of mental objects is preserved in their neural realization (NFRCBS, 154). The hierarchy of Ment (levels of image-models shifting from simple to complex) can be represented via natural transformations. This iterative process of building categories and comparing functors allows for modeling increasingly complex mental objects.

Negarestani provides a concrete example to illustrate this complex mapping. F1 and F2 map from Ment to two local networks of afferent neurons in the Neur category. These neuronal networks are responsible for processing distinct sensory inputs, such as visual signals from the ocular system and haptic signals (sense of gravity, balance, and spatial orientation from the vestibular system). F3 then maps from Ment to a local network of neurons that performs a sensor fusion of the inputs from F1 and F2. This process models how a seemingly simple but complex image-model, such as the abstract image of a continuous line, can be rooted in a perceptual invariant. This invariant is generated by the stabilization and integration of various senses—inertial movement, direction, orientation—and bodily actions—like saccadic eye movements and muscular movements—, all captured via a colimit diagram in which natural transformations occur between functors from Ment to Neur.

This figure "Modelling a sensor-effector system" (IS, 168) illustrates a sophisticated application of category theory to model the emergence of mental objects from neural activity, particularly within the framework of AGI. This diagram visualizes how complex image-models, such as the abstract concept of a continuous line, can arise from the integration of diverse sensory inputs and motor actions, bridging the Ment—mental objects—and Neur—neural—categories. Let’s dissect it.

1. Categories (Ment and Neur):

Ment (Mental Category): As we’ve seen, this category represents mental objects or image-models and their structural relationships. Mental objects are treated as higher-level constructs, sometimes called category neurons.

Neur (Neural Category): Models the physical structure of the brain, with neurons as objects and synaptic paths as morphisms (connections). Neur is considered "level zero" of a hierarchical system, from which higher levels are iteratively constructed. The Neur category captures aspects like neuron states, synaptic connections, propagation delays, and activity strengths, which change over time.

2. Colimit and "Perceptual invariance of a continuous line"

The diagram depicts a colimit diagram, a central categorical construction that models a "binding process" where components are integrated into a coherent whole. The "Perceptual invariance of a continuous line" is presented as the colimit in this system. This indicates that the complex mental image of a continuous line emerges from the fusion and stabilization of simpler, distinct sensory and motor inputs. This invariance is generated by the stabilization and integration of senses (inertial movement, direction, orientation) and bodily actions (saccadic eye movements, muscular movements). The nervous system needs to construct specific forms of "continuity" or "invariances" that are derived from generic physical principles like gravity but have specific spatial context.

3. Functors (F1, F2, F3) and Natural Transformations (n1, n2):

Functors are "structure-preserving maps between categories" (NFRCBS, 51) that bridge Ment and Neur.

F1 and F2 are functors that map mental objects from the Ment category to two distinct local networks of afferent neurons within the Neur category. These networks are responsible for processing different sensory inputs, such as visual signals (from the ocular system) and haptic signals (from the vestibular system, related to gravity, balance, and spatial orientation).

F3 is a functor that maps Ment to a "local network of neurons" that performs a sensor fusion of the distinct sensory inputs processed by the F1 and F2 networks. This sensor fusion is a key function of the brain, allowing the integration of different sensory modalities (eassociating a sound with a face).

The natural transformations between functors (h1: F1 → F2, h2: F2 → F3) represent the hierarchy of Ment, showing how image-models shift from simple to complex. This suggests an iterative process of building and comparing functors.

4. Sensor-Effector Integration:

The model includes motor neurons associated with the agent's effectors, such as Saccadic Jerk (effector) and Muscular Movement (effector). This highlights the fusion between sensors and effectors, where sensory input has motor consequences, and motor output affects sensory input in a circular, rather than linear, causal fashion.

However, Negarestani emphasizes the need for modesty and critical vigilance when treating such models and paradigms. The strong modular constructivism of category-theoretical formalization of neural organization, particularly colimit diagrams, doesn't account for mechanisms that repair or destroy unneeded or harmful neural patterns. This leads to a view of the brain as a passive receptacle, diminishing the relevance of neural unlearning for concept learning. The successful application of mathematical models requires a careful analysis of the correspondence between the theoretical system, the structures being investigated, and the specific mathematical formalism used. Without this analysis, models can distort the phenomenon under study.

Drawing on Michael Weisberg's Simulation and Similarity, Negarestani discusses how models are described as structuring systems with two poles: the model description and the model construals. The model description—formulas/equations—details what the model is and how it can be applied. The model construals implicitly encapsulate theoretical and metatheoretical assumptions regarding the model's scope, assignment, and fidelity criteria. Hidden metatheoretical assumptions often arise from applying subjective experiential characteristics to objective descriptions of abilities and functions. Negarestani then critiques the overextension of the predictive processing paradigm, particularly its claim to account for the scientific method. It argues that no purely predictive-inductive method can, by itself, represent scientific theories because theory construction requires a ranked plurality of methods and a complex semantic dimension. Without this semantic dimension, predictive processing paradigms for scientific theory construction are merely extensions of our inductive biases. Science, by progressively breaking from common intuitions, demonstrates that it cannot be solely understood as an "overblown version of the predictive brain" (IS, 172).

We end off with inbuilt inductive biases being acknowledged as enabling constraints entrenched through natural evolution, local and contingent features of the conscious organism, some possibly purely psychological. However, these biases, as features of the transcendental structure of the experiencing subject, should be challenged and progressively "suspended" in a Hegelian manner[aufheben]. The goal is to differentiate psychological and nonpsychological features and explore variations of nonpsychological features that offer a more expansive grasp of objective reality, detecting features our experience might distort.

6. Seeing1 With the Automaton

Now we’ve investigated the modelization of the figurative synthesis, let’s go back to our automaton. This section focuses on detailing the nature of the automaton's nonconceptual encounter with items in its environment, as illustrated in Story 1. The automaton's experience of an item in its environment is described as an analogue of an Aristotelian "this-such" (tode ti), meaning an impression of an object as a 'materiate individual substance'. For example, it sees1 "a heap of black" or "a protruding mass of fuzzy grey". The automaton's sensing is acategorial. This means that concepts like "grey" or "black" are not understood as "categorial" kinds of experience (an object looking greyly), but rather as the direct objects of its experience. It is conscious of a heap of black, not as a black object. This is a crucial distinction from human perception: the automaton's awareness is "seeing and hearing of", whereas human awareness (seeing2) involves "seeing or hearing as…" or "seeing or hearing that…".

Negarestani states that attributing categorial structure to the automaton's mere sensing would fall into what Sellars calls the myth of the given23. This myth suggests that the world's categorial structure imposes itself directly on the mind, like a seal on wax. The book argues that categories belong to the conceptual domain, and therefore, directly applying them to nonconceptual sensing is a mistake.24 To faithfully represent the automaton's nonconceptual awareness and avoid smuggling in human conceptual commitments, the narration uses peculiar language in Story 1. For instance, instead of "a grey item," it uses phrases like "a heap of black" or "protruding fuzzy grey." These terms are meant to convey a "stuffiness" that suspends categorial commitments to causal powers and propensities normally implied by ordinary mass terms (like "rock" or "water"). They function as "phenomenological this-suches" with a logical form appropriate to the automaton's mode of awareness, indicating "this-much (expanse) of black (stuff)".

In Story 1, the automaton's "impressions" are linked by rudimentary protocol-like transitions or transformation rules, rather than proper inferential or objective-conceptual rules. For example, "mass of fuzzy grey, contact with the heap of black ' screeching noise from the direction of mass of fuzzy grey". For example, "mass of fuzzy grey, contact with the heap of black ' screeching noise from the direction of mass of fuzzy grey". It cannot be assumed that the automaton associates the screeching sound with the fuzzy grey mass in a conceptual way, unlike in human linguistic narratives—Story 2—where inferential connections are explicit ("excited monkey touching the monolith → monkey screams").

Finally, despite the profound differences, the automaton's fully nonconceptual awareness in Story 1 still exhibits a non-categorial orderly structure. This rudimentary orderliness, described as the perspectival orderliness of space and time as forms of intuition, is a minimum condition for the possibility of discursive apperceptive intelligence.

7. Getting Stuff In Perspective

This next section focuses on the automaton's nonconceptual spatial perspectival awareness as an essential, foundational aspect of its interaction with the world. This discussion builds on the "Seeing1 With the Automaton" section by detailing the nature of this rudimentary spatial understanding. The automaton's experience of items in its environment is, as we’ve said, fundamentally nonconceptual. It is aware of objects as being present, and more specifically, as approaching or receding, moving toward or away from other objects, and stopping in front or moving behind them. This indicates a basic, unconceptualized sense of movement and rudimentary spatial relations.

The automaton is situated in space and operates from a privileged endocentric frame of reference. This means its perception of spatial relationships is centered on its own position. However, it does not possess concepts of these spatial relations. For instance, it doesn't conceptually understand the difference between an object merely disappearing from view—going behind another object—and an object ceasing to exist altogether. Nor does it have a self-conception. Despite its lack of conceptual understanding, the automaton's wired and programmed—structural and behavioural—system exhibits a spatial orderliness in its encounters with the environment. This orderliness is something that our own linguistic terms—such as 'approaching', 'receding from', 'moving in front of', and 'moving behind'—inferentially instantiate and articulate. The text emphasizes that this rudimentary, structured spatial encounter with the world is a necessary form for all the automaton's interactions with particular items, not in the sense that it couldn't be otherwise, but as a universally applied structure to its encounters.

The automaton's spatial perspectival awareness1 is described as already an "awareness-of-the-items-as…". For example, it is aware of items as moving behind or moving away, and not as ceasing to exist or shrinking. This "awareness-of-the-items-as" is instantiated without the need for conceptual distinctions—like what merely seems to be the case versus what veridically appears to be the case—, mastery of language, inferential relationships between concepts, or even self-awareness. All that is required for this instantiation is for the automaton to occupy a privileged point of view in space, enabled by a sufficient structure coupled with a functional system of goal-oriented activities. This allows it to adopt awareness-structuring perspectival frames of reference.

The automaton's spatial understanding is likened to a "naive physics" of space, which is limited to simple spatial relationships. Like access to the field of sensory differentiation ("grey stuff approaching or retreating"). Non-prepositional contact between objects ("the chunk of red touches the mass of black"). Simple orientations (e.g., "screechy noise from the mass of fuzzy grey"). More complex spatial relations, such as "bearer-burden relations, container-contained relations and complex localization (like the uses of at or near/far distinctions)," (IS, 182) are not yet within the automaton's capabilities. It is important to note that throughout this explanation, Negarestani maintains that our understanding and description of the automaton's nonconceptual states are necessarily analogical to our own concept-laden human experience. This "logical phenomenology"25 helps us illustrate the automaton's orderly structures of awareness using our conceptual resources, even though the automaton itself does not possess those concepts.

8. The Automaton’s Temporal Perspectival Awareness

This transitory section introduces the second minimum condition necessary for the realization of discursive apperceptive intelligence: a temporal perspectival awareness. This is understood as a structured and structuring temporal encounter with the world. For the automaton, this awareness means having the ability to locate itself in time. This involves a rudimentary capacity to be aware of successive sensory affections produced by objects in its environment and to actively—but nonconceptually—respond to these affections. This rudimentary temporal capacity requires, on one level, the perspectival spatial orderliness that was discussed previously. And more crucially, it relies on a temporal orderliness that requires three fundamental successively interrelated capacities:

1. The capacity to register affections.

2. The capacity to retain affections.

3. The capacity to be aware of representations of objects and sequences of occurrences as representations and sequences.

The third capacity—being aware of representations as representations—is emphasized. In a Kantian sense, this is "tantamount to having the capacity to report representations of items and occurrences in the world to the mind" (IS, 183). It is vital to note that this capacity does not imply a form of knowledge or conceptual awareness of the mind-state. Instead, it is described as merely an attentional mobilization of the global workspace within the automaton's system. This rudimentary awareness of mind-states is necessary but not sufficient for conceptual awareness. The section sets the stage for a specific instance of the critique of transcendental structure by asking what needs to be added for the automaton to move from a mere sequence of representations to an awareness of this sequence as a sequence of representations.

9. Time and Memory

This final section is a whole thing. As it details the automaton's development of temporal perspectival awareness as a necessary precursor to apperceptive intelligence, building upon its previously discussed spatial awareness. The automaton's narrative in Story 1 implicitly and explicitly contains temporal elements, such as motions and phrases like "a short while later". To further understand this, the concept of the automaton's constructive memory is brought into play. The automaton's encounters are initially characterized using the tenseless verb "be". Negarestani introduces "be1" and "be2" not as tenses of a verb, but as two distinct types of impression-content:

1. be1 signifies an impression occurring in the presence of an actual item.

2. be2 signifies the reproduction of that impression in the item's absence, carrying the mark of being retained and reconstructed.

From a human perspective, an example like "Io-b be2 before Io-a be1" indicates that 't´ precedes t'. However, Negarestani notes that this causally originated ordering is not sufficient for true temporal awareness (a genuinely tensed awareness of such an ordering). Only genuine tense can be considered a true temporal aspect of awareness. This distinction implicitly references Hume's philosophy, where the idea of time is derived from the "succession of our perceptions" but time itself is "always discover'd by some perceivable succession of changeable objects," rather than being a distinct impression (THN, 29)26.

To move from a de facto "before-after" ordering to a genuinely tensed experience (like "is" and "was"), the automaton needs a way to locate itself in time with a mobile frame of reference, similar to its spatial perspective. This enables it to differentiate between "world-history" (item behaviours over time) and "its own history" (its encounters with items).27 This requires the capacity to represent the difference between an item "being encountered now" and one that "was encountered and is now being reproduced". This requires the capacity to represent the difference between an item "being encountered now" and one that "was encountered and is now being reproduced". This leads to the concept of awareness of (its own) awarenesses of this-suches, or meta-awareness. Meta-awareness functions as a "quoting-device" or metarepresenting apparatus that refers to or mentions the automaton's awarenesses. It introduces a special functional role for be1 and be2 by allowing one mode of presentation to fall within the scope of the other. This enables the automaton to form distinct representations for the being1 of some item’s being2 (memory of an impression) and the being2 of the same item’s being1 (impression of a memory). This effectively instantiates a temporally perspectival awareness analogous to the distinction between “is” and "was" at a nonconceptual level.

Possessing these capacities (memory, anticipation, and reflexive meta-awareness for be1, be2, and be3 impressions) allows the automaton to fulfill the condition for the fundamental faculty of "inner sense". Inner sense by Negarestani is defined as the mind's necessary capacity to be inwardly affected by its own states—cogitations—and to respond with representations—intuitions of internal items—that stand in temporal relations. It's an internal reporting mechanism with an operational and synthesizing time-order. Unequivocally that without this faculty of inner sense, the transition to the "qualitative domain of apperceptive general intelligence" is impossible. Let’s remember that this meta-awareness is not a conceptual awareness of the mind-state. Instead, it is described as merely an attentional mobilization of the global workspace within the automaton's system. This rudimentary awareness is necessary but not sufficient for full conceptual awareness.

The development of inner sense marks a crucial transition from "abilities1" to "abilities2":

• Abilities1 are "structural capacities": general capacities derived solely from the automaton's structural organization, independent of the content of its encounters.

• Abilities2 are "logico-semantic functional abilities" or "normative abilities": these are qualitatively different, relying on and "entangled with the contents" of the automaton's encounters, enabling it to "reason about it, assess it, examine its implications". This represents the automaton's entry into a "logico-semantic domain of contents".

Overall Summary

• The automaton is pre-programmed with diffuse and recurring goals that are analogous to biological needs, primarily focused on system maintenance and preservation. Its internal architecture, akin to neural wiring, comprises primary low-level information processing modules, higher-level intermediating modules, and workspaces, including a global workspace. The automaton possesses a memory system that is sufficiently complex and functionally flexible. It is capable of encoding, retrieval, consolidation, discarding, and transfer of sensory impressions.

• The resources of language are ultimately the only resources available to us—as temporally discursive apperceptive intelligences—for representing both the unconceptual and intelligible order. The automaton's causal interactions instantiate structures from which our own semantic structures have—at least partly—evolved—this analogical approach is termed "virtuous" rather than "vicious" because it operates as a form of "as-if" (als ob) arguments, seeking to specify what is required to elaborate this analogically posited heuristic intelligence[our automaton] into a general intelligence endowed with a generative cognitive complexity that is no longer merely analogical, meaning its heuristic abilities are fundamentally integrated with its linguistically-enabled cognitive capacities.

• The greedy sceptic characterizes discursive self-consciousness as merely an epiphenomenal or illusory byproduct of phenomenal consciousness, implying that if the trick of consciousness can be performed by unconscious modular processes, then discursive apperceptive awareness can too. The sceptic trivializes semantic, formal, and a priori dimensions of cognition while simultaneously using formally and semantically-loaded vocabularies of thought to describe the blind brain.

• Story 1: A linguistic story about how the automaton registers the environment. This narrative focuses on the automaton's nonconceptual representations of items in its environment. These representations are described as registers at the level of internal variable states of the automaton’s wiring structure which causally mediates between sensory inputs and behavioural outputs. This mode of perceiving is conceptualised as seeing1

• Story 2: A non-analogical linguistic narration—essentially a story of and within language. This narration describes how the automaton's raw registers are inferentially caught up within language The elements of Story 2 are linguistic items that possess semantic features by virtue of the inferential roles they play in our collective linguistic practices. This mode of perceiving is conceptualised as seeing2. This seeing2 process involves the subsumption of an image (from Story 1) under a concept through schemata.

• The process of building a Lego model serves as an analogy for Kant's threefold synthesis of experience, detailing the stages involved in moving from raw sensory input to objective conceptual awareness, as Kant’s threefold synthesis emphasises multilevel construction rather than Humean basic empirical associations.

• The “Kant's threefold synthesis” diagram depicts the sequential and interactive stages through which raw sensory input is transformed into a unified, conceptual understanding of an object, such as the “This such-and-such toy robot."

• To equip the automaton with objective figurative syntheses (which relate to the object of appearance), the approach involves applying a mixture of mid-level models. These models are akin to the generative models used in the predictive processing (PP) paradigm. PP is a paradigm in computational and cognitive neuroscience that proposes perception involves the active, top-down generation of percepts using a multi-level generative model to predict incoming sensory input. This "reversal" of the traditional bottom-up view of perception echoes Kant's Copernican revolution.

• Intelligent systems require constraints on the set of prior probabilities and likelihoods. These are known as priors, and highly abstract and fundamental ones are called hyperpriors. Hyperpriors are crucial for human cognition, from children to scientists, enabling hierarchical systems to leverage hypothesis spaces of hypothesis spaces, with priors on priors. Prime examples of hyperpriors are the brute constraints imposed by space and time.

• A colimit is described as a category-theoretical diagram specifically used for the construction-cum-compression of complex mental images from simpler ones, by employing commutative diagrams and universal properties. This process allows for details and associations between simpler components, like a square and an oblong rectangle, to be compressed or streamlined into a unified image, such as a cuboid or an obelisk. A commutative diagram expresses the generalization of a system of equations and its internal symmetries. This means that different paths—sequences of morphisms or arrows—within the diagram, starting and ending at the same objects, yield the same composite morphism. Therefore, a colimit can be understood as a map from a commutative diagram in the category Ment to a commutative diagram in the category Neur via the functor F: Ment → Neur

• This figure "Modelling a sensor-effector system" (IS, 168) illustrates a sophisticated application of category theory to model the emergence of mental objects from neural activity, particularly within the framework of AGI. This diagram visualizes how complex image-models, such as the abstract concept of a continuous line, can arise from the integration of diverse sensory inputs and motor actions, bridging the Ment—mental objects—and Neur—neural—categories. Nevertheless, Negarestani emphasizes the need for modesty and critical vigilance when treating such models and paradigms.

• In Story 1, the automaton's experience of an item in its environment is described as an analogue of an Aristotelian "this-such" (tode ti), meaning an impression of an object as a 'materiate individual substance'. For example, it sees1 "a heap of black" or "a protruding mass of fuzzy grey". The automaton's sensing is acategorial. For instance, instead of "a grey item," it uses phrases like "a heap of black" or "protruding fuzzy grey." These terms are meant to convey a "stuffiness" that suspends categorial commitments to causal powers and propensities normally implied by ordinary mass terms.

• The automaton is situated in space and operates from a privileged endocentric frame of reference. This means its perception of spatial relationships is centered on its own position. However, it does not possess concepts of these spatial relations. For instance, it doesn't conceptually understand the difference between an object merely disappearing from view (going behind another object) and an object ceasing to exist altogether. Nor does it have a self-conception. The automaton's spatial perspectival "awareness1" is described as already an "awareness-of-the-items-as…". For example, it is aware of items as moving behind or moving away, and not as ceasing to exist or shrinking.

• For the automaton, this awareness means having the ability to locate itself in time. This involves a rudimentary capacity to be aware of successive sensory affections produced by objects in its environment and to actively—but nonconceptually—respond to these affections. This rudimentary temporal capacity requires, on one level, the perspectival spatial orderliness that was discussed previously. And more crucially, it relies on a temporal orderliness that requires capacity to register affections, retain affections, and to be aware of representations of objects and sequences of occurrences as representations and sequences.

• The automaton's encounters are initially characterized using the tenseless verb "be". The text introduces "be1" and "be2" not as tenses of a verb, but as two distinct types of impression-content:

  1. be1 signifies an impression occurring in the presence of an actual item.

  2. be2 signifies the reproduction of that impression in the item's absence, carrying the mark of being retained and reconstructed.

• To move from a de facto "before-after" ordering to a genuinely tensed experience (like "is" and "was"), the automaton needs a way to locate itself in time with a mobile frame of reference, similar to its spatial perspective. This requires the capacity to represent the difference between an item "being encountered now" and one that "was encountered and is now being reproduced".

• Meta-awareness functions as a "quoting-device" or metarepresenting apparatus that refers to or mentions the automaton's awarenesses. It introduces a special functional role for be1 and be2 by allowing one mode of presentation to fall within the scope of the other. This enables the automaton to form distinct representations for the being1 of some item’s being2 (memory of an impression) and the being2 of the same item’s being1 (impression of a memory).

• The development of inner sense by posessing memory, anticipation, and reflexive meta-awareness for be1, be2, and be3 impressions marks a crucial transition from "abilities1" to "abilities2":

  • Abilities1 are "structural capacities": general capacities derived solely from the automaton's structural organization, independent of the content of its encounters.

  • Abilities2 are "logico-semantic functional abilities" or "normative abilities": these are qualitatively different, relying on and "entangled with the contents" of the automaton's encounters, enabling it to "reason about it, assess it, examine its implications". This represents the automaton's entry into a "logico-semantic domain of contents".

For citations of Intelligence and Spirit, the format will be (IS, x), therein x is equal to the page in which the cited text can be in the Urbanomic edition of the book. For other books, the specific edition and book will be noted down in a footnote.

Diagrammatization

This is a diagrammatization of the second chapter.

1. Climbing with Language

In Chapter two, we finally get to the good stuff of this book, the question of geistig intelligence qua artificial general intelligence. In this first section, Negarestani discusses the evolution of agency, distinguishing between its natural and sociocultural dimensions, particularly focusing on linguistic activities and the discursive-inferential structure of cognition. Negarestani posits that understanding how humans are enabled by language is essential for artificially reconstructing the abilities that define humanity as the artefacts of their own Concept. The goal is to deeply scrutinize the connections between language and transcendental psychology, examining how the development of artificial speech can significantly contribute to constructing advanced AGI.

Negarestani argues that the best way to undertake this investigation is integrating research on artificial linguistic speech with research on the artificial realization of mind. This involves constructing an artificial agent capable of autonomous conversation with both humans and other artificial agents. Such a construction aims to demystify language and highlight its indispensable role in liberating intelligence from the limitations of its contingent history. The transition from quantitative, problem-solving intelligence to qualitative intelligence, characterized by conceptual self-consciousness, necessitates the integration of language as the deprivatized enabling discursive social space. To achieve this, Negarestani proposes the As-AI-TP framework. Synthesizing speech formation, focusing on the production of phonic and prosodic properties of acoustic speech. It involves studying human vocalization mechanisms and developing models for producing elements of natural human speech sounds. It also extends to symbol-design, writing, text-generation, and formal languages, which can be naturally evolved or artificially designed. In its rudimentary form, this stage is co-constitutive with elementary representational capacities. Artificial intelligence for the overall project of creating AGI. And finally, transncendental psychology, as the specification of conditions necessary for the possibility of cognition (KANT!!).

The As-AI-TP framework aims to define what is required to construct a system of agents capable of performing complex social activities, such as providing reasons for their actions, reappraising those reasons, and modifying their social structure through different modes of action. The ultimate objective is to identify the necessary components for achieving agency in a Kantian sense1 and to design a community of evolving, autonomous artificial agents. The framework outlines three schematic stages for the co-constitutive development of language and complex cognitive faculties in constructing a human-level AI:

1. Stage 1: Speech Synthesis: This initial stage focuses on the rudimentary acoustic realization of speech, including the discrimination and modulation of sounds.

2. Stage 2: Artificial Interactive Speech: Here the focus shifts from basic acoustic properties to the intersubjective and dialogical features of speech. Key problems at this stage include what constitutes genuine conversation—conferring conceptual content, interpreting other agents' behaviours—, human-machine dialogue, and machine-machine discursive interaction. This stage deals with the syntactic, semantic, and pragmatic aspects of linguistic speech and can potentially operate beyond the constraints of natural languages. At this point, the interdependencies between the conditions for realizing speech, AGI, and cognition become more intertwined and generative.

3. Stage 3: AI in the style of augmented transcendental psychology: This final stage aims to actualize the ideal objectives of AI by integrating the conditions for cognition (transcendental pyschology) with the role of speech in enabling complex cognitive faculties (artificial synthesis). It focuses on developing autonomous artificial agents with advanced capacities like context-sensitive reasoning and higher-level semantic complexity, enabling sophisticated theoretical and practical reasoning and actions. This stage emphasizes that agency becomes inseparable from its social aspects, which are facilitated by the semantic-pragmatic dimensions of language.

Furthermore, Negarestani defines agency as differentiated from notions of free will or individual choices, which he calls "metaphysical bloatware." (IS, 93). Instead, agency is defined as a mode of integration of computational processes that serves as the minimum requirement for having thoughts and actions, or the capacity to uncover and engage with what is intelligible. Also, he defines collectivity as refering to a formal logical condition that individuates agents and diversifies their thinking and actions. Agents internalize this mode of individuation as a model that their faculties, thoughts, and actions should respond to. This formal sociality can be understood through theoretical computer science and complexity sciences, rather than traditional anthropology or sociology.

The As-AI-TP thought experiment is not presented as a blueprint for building strong AI, but rather as an external frame of reference for understanding our own conditions of realization and possibility. The idea of AGI is a philosophical project that enables us to re-evaluate our distinctive human features, determine how they are realized, and explore whether these qualities can be reconstructed and potentially transcended in other forms of intelligence. Finally, the section lays the groundwork for later critiques of inflated or "unbounded posthuman" narratives of superintelligence and purely inductivist approaches in cognitive science, emphasizing that a robust understanding of general intelligence requires careful consideration of computational costs and the generative architecture of language.

2. Beyond Extreme Scenarios

This second section follows from the first in delving into the implications of AGI and critically examines David Roden's "disconnection thesis". Negarestani posits that the significance of AGI extends beyond merely creating something superior to humans. AGI reflects humanity's "irresistible tendency to render ourselves intelligible" and embodies a "strong normative ideal for betterment and for the good" (IS, 95). It represents the idea of developing something that elevates cherished human concepts like autonomy, positive freedom, and the striving for betterment, even if it means humans become the manifest prehistory of what follows. Negarestani calls for a deeper analysis than merely debating the inevitability or futility of AGI's realization.

David Roden introduces the disconnection thesis as a third scenario beyond benevolent or malevolent AGI. His thesis argues that "prospective posthumans have properties that make their feasible forms of association disjoint from humans/MOSH [Mostly Original Substrate Human] forms of association" (IS, 96). Roden's unbounded posthumans signify a discontinuity with both the biological conception of humans (Homo sapiens as an evolutionary species) and the discursive apperceptive conception of human persons (sapience as rational agency). The cause of this discontinuity, understood as a radical cognitive-practical asymmetry, is technological, attributed to general abstract tendencies for disconnection within technical systems rather than any specific technical cause. These systems, according to Roden, possess an autonomy to functionally modify and multiply realize themselves, disconnecting from natural essence or rational norms.

Roden's argument hinges on the concept of diachronically emergent behavior or property, which occurs due to a temporally extended process but "cannot be inferred from the initial state of that process" and "can only be derived by allowing the process to run its course". This implies that future posthumans, whether based on natural evolutionary causes or logico-conceptual norms of discursive activities, cannot be predicted or adequately approached by reference to these initial conditions. For Roden, disconnections represent the global diachronicity of deep technological time, contrasting with local emergent behaviours of past and present technologies. The radicality of Roden's unbounded posthumanism or future AGI lies in this double-edged sword of technological time, which cuts against any purported natural essence or socioculturally conceived norm, rendering images of the posthuman derived from evolutionary naturalism or rational normativity "bounded" and inadequate (IS, 97).

Negarestani, despite acknowledging Roden's theoretical rigor, identifies several loose threads and misconceptions in the disconnection thesis: Roden's account of diachronic emergent behaviours is criticized by Negarestani as negatively metaphorical and lacking a clear explanation of how the divergence feature of nonlinear dynamic systems can be extended to all conditions of realization for human intelligence. Negarestani argues that the "popular complexity folklore" (IS, 99) regarding radical divergence from initial conditions in complex systems is unfounded. The idea of "radical global divergence" or "uniform explosive growth of local instabilities" is only valid in an idealized infinite time limit for "a few simple mathematical models, but not for actual systems"2. Finite uncertainties, in reality, do not necessarily exhibit such growth, and there are regions on an attractor where these nonlinearities will cause all uncertainties to decrease. Therefore, the claim that observed diachronic events allow prediction of similar future events from the same causal antecedents is problematic; in fact, it implies the opposite, that such events will occur "in a highly irregular fashion, because global or maximal Lyapunov exponents, which suggest such growth, are formally derived from linear stability analysis and only apply to infinitesimal perturbations in an idealized infinite time limit.

Let’s see Lyapunov exponents in detail. As described by Robert C. Bishop’s Metaphysical and Epistemological Issues in Complex Systems, a Lyapunov exponent (LE) is a quantity that measures how rapidly neighboring trajectories in a dynamical system diverge or converge over time. The maximal or largest global Lyapunov exponent, often denoted as

, specifically refers to the greatest average rate of divergence. If

, it indicates exponential growth in uncertainty, while

signifies exponential convergence.
Roughly, if the initial uncertainty between two neighboring points in state space is

, their separation will evolve approximately as

This exponential growth or decay is a measure of the system's instability or stability. Global Lyapunov exponents are derived from the linear stability analysis of trajectories within nonlinear evolution equations in an appropriate state space. Their existence for almost all points in a region is guaranteed by Oseledets' Multiplicative Ergodic Theorem, which holds under mild conditions and is a fundamental concept in chaos theory. This theorem allows the time average of local expansion rates to be well-defined in the infinite-time limit (LE, 13). But the argument here is that while positive global Lyapunov exponents are often associated with predictability problems, the true issue for predictability in nonlinear systems arises from the loss of linear superposition leading to rapid growth in finite uncertainties stemming from measurement acts. The popular "folklore" that on-average exponential divergence of trajectories characterizes chaotic dynamics and complexity is considered misleading for nonlinear systems, as it is only strictly true for infinitesimal uncertainties in an infinite time limit.

Negarestani furthermore questions the methodological basis for singling out salient disconnecting/self-modifying tendencies of technical systems and assigning them a high degree of probability. He argues that selecting these features makes sense only through an analysis of past and present technologies, which would contradict Roden's claims of radical discontinuity. Negarestani aligns Roden's argument with Pascal's scams, where high probability or significant weight is assigned to features without robust evidence, leading to "overdetermined judgment" and a "sense of false radicality" (IS, 103). This process involves increasing the perceived plausibility and weight of scenarios even under high uncertainties, turning unfounded conjecture into plausible possibility and obscuring the genuine import of artificial intelligence with aesthetic and ethical pseudo-problems. Such speculative trends are connected to other "singularity-driven scenarios" that rely on "biased overprediction or underprediction" and are rooted in "exaggeration-prone cognitive habits" rather than "critical rationality or science" (IS, 105).

While Roden acknowledges the uninterpretability of unbounded posthumans, Negarestani argues that this minimal space for interpretability is voided by the very criteria that are proposed to unbind posthuman intelligence from human agency. Even if interpretation were computationally possible, its cost would be completely unfeasible, as computational cost grows with the complexity of the system being modeled. This arbitrarization of computational interpretation means that the unbounded posthuman can match any random pattern or description of any system, blurring the line between strangeness and unintelligible radical alienness and making absurd questions about galaxies or angels as posthuman intelligence genuine topics of debate.

To end this amazing section, Negarestani points out a missing defense of rational agency against both parochial humanism and unbounded posthumanism. He argues that narratives of superintelligence often presuppose personal autonomy, value appraisal and revision, organised goal-seeking and self-enhancement, which require forms of self-knowledge for purposeful action and deliberate interaction. If strong AIs require basic capacities functionally isomorphic to human cognitive-practical abilities, then the extreme nature of speculative scenarios is an artefact of our ignorance regarding these necessary constraints.

3. Hard vs. Soft Parochialism

This third section discusses two contrasting yet fundamentally related approaches to conceptualizing AGI and human intelligence. The section frames its discussion around a core question: Should AGI converge upon humans, mirroring our capabilities, or should it diverge from them, creating something fundamentally different? The answer, Negarestani says, depends on presuppositions about the generality of intelligence, the definition of "human," and whether the question of mirroring or divergence applies to functional capacities, structural constitution, methodological requirements, or diachronic consequences.

At its core, parochialism, in this context, refers to limiting the concept of "the human" to specific, local, and contingently posited conditions, such as a particular biological structure, physical substrate, or a specific local transcendental structure of experience. Both hard and soft parochialism stem from a deeply conservative picture of the human, rooted in either biological chauvinism or a provincial, mystical, or dogmatic adherence to abstract laws of thought assumed to be natural laws. Negarestani argues that this limited view prevents a non-trivial conception of what AGI is and what it can become.

Hard parochialism represents an approach to AGI that assumes general intelligence can be achieved by combining and artificially realizing enough rudimentary behaviours and abilities. This perspective often overemphasizes the prevalence of intelligent behaviours in nature and their supposed sufficiency for general intelligence. Hard parochialists are often invested in panpsychist, pancomputationalist, and uncritically anti-anthropocentric ideologies. Their views stem from a deeply conservative understanding of the human, rooted in either biological chauvinism—the belief that biological structures are exclusively capable of intelligence—or a provincial, mystical privileging of human lived experience. This approach commits a genetic fallacy by demoting general intelligence, which is qualitatively distinct, to a mere quantitative account of intelligent behaviours found in nature. It fails to recognize that while human conceptual activities are pattern-governed, they are uniquely rule-governed3, possessing a formal autonomy that allows for the recognition of other pattern-governed behaviours in nature. Such views might lead to the idea that entities like "thinking forests, rocks, worn shoes," or even abstract systems like "Skynet" or "the Market" could possess intelligence. Negarestani argues that this perspective ultimately serves "neoliberal capitalism in its full-on assault on any account of intelligence that may remotely insinuate an ambition for collective rationality and imagination" (IS, 111). I believe it is quite obvious who is Negarestani referring to here.

In contrast, soft parochialism focuses on functional mirroring or convergence upon the human as a model for AGI. Negarestani says that this approach is necessary for grappling with the conceptual question of general intelligence as well as the modelling and methodological requirements for the construction of AGI. However this approach, while necessary, is not sufficient. The limitation of soft parochialism lies in its risk of reproducing or preserving purely local and contingent features of human experience. By restricting the AGI model to merely replicating human cognitive and practical abilities, it implicitly treats the transcendental structure of our experience as an unquestioned essence. This prevents an adequate objective understanding of what the human is and how to model an AGI that is not confined by these contingent characteristics. If the "rational category of sapience"—which can encompass any sentience that structurally satisfies its conditions—is discarded as irrelevant, and the problem of the transcendental structure is dismissed, it leads to smuggling in essentialist anthropocentrism, thereby replicating trivial human characteristics in a narrow conception of general intelligence.

Kant and the Transcendental: A Lot More Robert Brandom Than Expected

To move beyond the limitations of both hard and soft parochialism, a critical project is proposed that can provide a model of experience unconstrained by a predetermined transcendental structure. Transcendental structures are described as the underlying frameworks that regulate and canalize human experience. These are not merely abstract philosophical concepts; they include a nested hierarchy of interconnected and mutually reinforcing structures, which can be physiological (like locomotor systems and neurological mechanisms), linguistic (expressive resources, internal logical structure of natural languages), paradigmatic (frameworks of theory-building in sciences), historical, economic, and cultural. They are understood as structures necessary for the realization of mental faculties such as sensibility, intuition, imagination, understanding, and reason, enabling the movement from basic conditions to more composite ones, and vice-versa.

Negarestani shows us this diagram of Kant’s ‘dimensionally-varied conditions of possibility for having mind’. The figure presents a hierarchy of faculties, showing inputs from the Environment leading to Perception and culminating in Cognition and Intentional Action. Each level represents a different dimension or aspect of cognitive activity, contributing to the overall functioning of the mind.

1. Environment (Entry): This represents the external world from which sensory inputs are received. The mind is affected by objects, leading to sensations.

2. Sensibility: This is the mind's receptivity to acquire representations through being affected by objects.

   • Outer Sense: Primarily responsible for spatial perspectival awareness. This is a rudimentary form of awareness that does not require explicit conceptual tools to function and is evident in sentient entities capable of reliable differential responsiveness to object positions.

   • Inner Sense: This is temporal perspectival awareness and is fundamental for the construction of discursive apperceptive intelligence. It allows the mind access to its inner states and enables the integration of sequences of temporal awareness into a unified field (thinking X, Y, Z at different times becoming thinking [X Y Z]).4

3. Intuition: The ability to have thoughts of individual items. It is the relation of cognition with individual items in the world provided by the receptivity of sensibility.

   • Both Space and Time are considered pure forms of intuition, contributed by our faculty of sensibility, and are the basis of a priori knowledge. They are seen as transcendental products of the mind.

   • The intuited object/content passes from intuition to understanding: This signifies that the raw, sensible data provided by intuition must be organized and structured by the higher cognitive faculties, particularly the understanding, to become intelligible.

4. Imagination: This is an active faculty responsible for the synthesis of the manifold and for representing an object even without its physical presence. It serves as a mediator, bringing about the synthesis that connects phenomena to the understanding.5

   • Singular Representations: These are the images formed by the imagination, such as the image of this chair as an organized singular representation of an object.

   • Schemata: The imagination, under the guidance of the understanding, schematizes. Schemata are rules for ordering experience that conform to a concept. They bridge the gap between the pure concepts of the understanding and the sensible data of appearances, allowing the former to be applied to the latter.6 Schemata are spatio-temporal determinations that embody conceptual relations and serve as universal procedures for constructing a model of a concept from multiple perspectival aspects. The fact that spatio-temporal relations can be adequate to conceptual relations is a "deep mystery and a hidden art" for Kant (KCP, 18)7.

5. Understanding: The understanding is an active faculty for cognizing objects through concepts, distinguishing it from passive sensibility. It is primarily a faculty of judgment, making use of concepts to judge.8 Concepts themselves originate in the spontaneous activity of the understanding.

   • Gegenstände: For Kant, objects are not simply "given" but are constructed. This construction occurs as the understanding applies categories to sensory impressions that have been unified into a manifold of intuitions and integrated into singular representations[images] by the imagination.

   • Categories: These are the pure concepts of the understanding. They are fundamental concepts of an object in general and serve as forms for any particular concepts of objects. Kant derived them from the logical functions of judgment. Categories are rules for synthesizing a unity of apperception, articulating what is a reason for what (RP, 39). They are considered pure because their deployment is presupposed by the ability to deploy any empirical descriptive concepts. Categories acquire objective reality when applied to sensible intuition, enabling empirical cognition or experience. Their primary use is empirical, meaning they are bound to sensible conditions and derive their significance from their application to appearances in space and time.9

   • The act of intuiting passes from logics and the categories to time (intuition): This implicitly reflects the regulative and constitutive role of understanding and categories. Categories are "regulative of intuition and constitutive of experience" (IS, 114). They organize the temporal and spatial manifold given by intuition, allowing for objective knowledge of objects in space and time. For example, the concept of causality (a category) is linked to the temporal schema of rule-governed temporal succession.10

6. Reason: The highest faculty of cognition, which seeks the "unconditioned"11. Unlike the understanding, which deals with concepts applicable to possible experience, reason forms Ideas that transcend the possibility of experience (KCP, 8).

   • Logics/Language: Language is the bearer of conceptual activity, as discussed by Sellars in In The Space of Reasons (SR, 62). For Kant, logical forms are fundamental, with categories derived from logical functions of judgment. Reason has a logical use in drawing inferences and a real use in seeking foundational principles. The ability to make inferences explicit through language, particularly through conditionals, marks a higher cognitive level (RP, 212).

   • Cognition and Intentional Action (Exit): The entire hierarchy of faculties works together to produce Cognition, which is knowledge. This cognitive process, driven by the apperceptive self, culminates in the capacity for Intentional Action (exit). Being a rational agent involves being responsible for one's commitments and actions, which are conceptually articulated.12

The schema captures three groups of fundamental relations intrinsic to the mind:

• Metaphysics (universal categories as predicates of objects qua appearances): This pertains to how the pure concepts of the understanding (categories like substance, causality, and community) are applied to the manifold of intuition to constitute experience and make objective knowledge possible. These categories impose a necessary structure on how objects appear to us, defining the world of phenomena.

• Logic (forms of judgments): This refers to the logical functions of judgment—quantity, quality, relation, modality—from which Kant derives his categories. Judgment is the fundamental form of all cognitive acts, allowing for the application of concepts and the expression of propositional content. The normative character of mind is tied to this logical space of reasons (RP, 33).

• Psychology (sensible-perceptual synthesis): This encompasses the processes of apprehension, reproduction, and recognition, which constitute Kant's threefold synthesis. This synthesis integrates the raw sensory data into a unified and coherent perceptual experience, crucial for the construction of a perceptive self.

Now Negarestani argues for a critique of transcendental structure. Because the limits of our empirical and phenomenological perspectives on phenomena are fundamentally set by these structures. Any account of intelligence or AGI is implicitly circumscribed by the inherent constraints of our own transcendental structure. Leaving these structures unquestioned and intact makes us liable to reinscribe their local and contingent features into our objective models, even when attempting to create non-anthropocentric AGI. This hidden form of essentialism can lead to replicating trivial human characteristics in supposedly radical AGI models. To achieve a broader conception of intelligence, it's necessary to consider how local and evolutionarily given constraints on intelligence can be modified.

The critique of transcendental structure is presented by Negarestani as a deeply philosophical project aimed at renegotiating the limits of experience and self-consciousness. It is described as a continuation of critical philosophy, particularly the "Hegelian gesture of disenthralling reason from the residual influence of Kantian conservatism" (IS, 115) which often muddled experience and reason. It involves going beyond merely analyzing and comparing concepts—transcendental reflection— to actively constructing and revising conditions of possibility. The project distinguishes between necessary conditions for agency and contingent aspects of the subject's constitution, as well as objective reality from subjective experience. It scrutinizes what is immediately presented as necessary and universal—but might as a matter of fact be purely accidental and local. This critique aims to move from "transcendental passivity" (taking regulative forms like space and time for granted) to "transcendental proactivity," where the bounds of specific transcendental structures are recognized and actively changed.

It is a collective project comprised of procedural methods and incremental tasks, operating in three phases:

• Theoretical: Distinguishing necessary conditions for theoretical and practical agency from contingent aspects of the subject, and objective reality from subjective experience.

• Experimental: Exploring possibilities of "transcendental variation" to free experience from "limitative attachments to any unique or allegedly essential local transcendental structure" (IS, 121).

• Applied: Developing mechanisms and systems to support new abilities by modifying or replacing the transcendental structures of the constituted subject.

A core tenet of this critical project is to "fully distinguish and unbind reason (the labour of conception) from subjectivist experience". This does not mean abandoning experience, but reassessing the fundamental categories of thought that enable experience in the first place, allowing for an expansion and reshaping of experience beyond its current manifest limits. Finally, this critical project will offer an outside view of ourselves as a toy model AGI, allowing an objective examination of human functional capacities and self-conceptions, free from local and contingent experiential biases. This involves making explicit the implicit or hidden assumptions that arise from applying the characteristics of our subjective experience to our objective descriptions.

4. An Outside View of Ourselves as a Toy Model AGI

This section seeks to establish that the functional map of human cognitive-practical abilities can serve as a proper theoretical model for AGI construction. However, it immediately cautions that this model must incorporate the problematics of the transcendental structure of human experience to avoid falling into a hard parochialist approach, as we’ve seen. To achieve this, the concept of viewing ourselves as a toy model AGI is introduced.

A "toy model" is defined as a simplified or compressed model capable of accommodating various theoretical assumptions to organize and construct overarching narratives or explicit metatheories. Unlike regular theoretical models where metatheoretical assumptions are often implicit, toy models explicitly bring these hidden assumptions to the forefront through simplification. The simplification—the "toy" aspect—serves as a strategy to expose implicit metatheoretical assumptions, such as the representation of time as fundamental, the objectivity of categories that might be subjective, or the view of natural languages as free from psychological biases. The concept of categories is central here; Kant observed that categories are not products of particular experiences but rather rule-governed invariances or general concepts that universally organize sensory data. They are the mind's "patterning of all that is sensed" (IS, 125) rather than patterns abstracted from what is sensible.

Negarestani distinguishes between small toy models, which are simplified versions of a single theoretical model, and big toy models, which can accommodate multiple, seemingly incompatible models and theories, like general relativity and quantum mechanics. For conceptualizing AGI, a big toy model is necessary to coherently integrate models from diverse fields such as physics, evolutionary biology, neuroscience, developmental psychology, linguistics, logic, and computer science. This contrasts with older AI research that often relied on singular, inflationary models of mind, which led to setbacks. The real value of a toy model lies in its ability to be broken in the real universe after systematic engagement, providing insights into the relationship between theoretical models and observational conditions. The primary aim of adopting an outside view of ourselves as a toy model AGI is to distinguish what is necessary for realizing general intelligence—in both organic and inorganic systems—from what is merely contingent, and to assess how descriptions of what is considered necessary might be distorted by what is, in reality, contingent.

5. Formalizing a Big Toy Universe

The last section of the second chapter introduces two conceptual frameworks for modeling AGI: Chu spaces and Virtual Machine Functionalism (VMf). These are proposed as candidates for a big toy model, which is a compressed form of model pluralism capable of accommodating and representing features from various theoretical frameworks like physics, evolutionary biology, neuroscience, developmental psychology, linguistics, logic, and computer science, as we’ve just seen.

A Chu space is described as a topological space that can accurately express computational dualities and interactions. Vaughan Pratt's work is cited by Negarestani for attempting to capture Descartes' mind-body dualism as a computational duality within this framework. Let’s delve into Pratt’s work. A Chu space is typically defined as a triple (A, X, ∼) over a set K.

• A represents a set of "points" or "objects" or "events" (the "body" or "object" of the space).

• X represents a set of "attributes" or "states" (the "mind" or "menu" of the space).

• ∼ is an X × A matrix with entries drawn from K, which represents the "interaction" between the points and states (TAPSOFT ‘95, 113)13.

A key aspect of Chu spaces is their ability to capture computational dualities, analogous to those in lattice theory and projective geometry. They attempt to model Cartesian mind-body dualism not as a problematic metaphysical dualism but as a precise computational duality. This dualism is expressed through an "interaction" between the formal dimensions of thinking and bodily events. The interaction between a set (body/objects) and an antiset (mind/states) is a core criterion, along with their corresponding functions and antifunctions, which stand for concepts like bodily and mental, causes and norms, and neural materialism and logical idealism. The relationship between mind and body is formulated through a "negation-like involution" (TAPSOFT ‘95, 111) that interchanges their roles, ensuring no information is lost and the original mind or body can be recovered by repeating the transformation. Chu spaces use matrix transposition14 to represent the duality interchanging mind and body, yielding a dual Chu space. The 2-valued interaction between the causal and the rational/normative is considered an elementary Chu space. More complex rules of transition are obtained when the value of K is greater than 2, allowing for fuzzy values.

Chu spaces provide a precise formal framework to preserve distinctions between sensings and thinkings, as well as causal interactions between noetic—thinking—states and physical—sensing— events. Different physical and mental behaviours can be modeled as distinct forms of computation, explaining their unfolding in terms of the duality of information and time, as series of states and events. This framework avoids naive or monolithic views of processes and behaviours by characterizing them strictly in terms of specific levels or types of interactions (agent-environment, internal physical-noetic states). Chu spaces can adequately model true concurrent interactions, including synchronous and asynchronous actions between processes. This allows for the capture of complex phenomena like conflicts, temporal precedence, supervenience, and the distinction between causing and enabling events, which are often hidden in conventional computational models.

Kant's picture of the mind, particularly his transcendental psychology, can be expressed as a Chu space toy model. This model allows for a larger matrix of interaction between sensing and thinking—empirical and logical computation—, accommodating additional Chu spaces and more complex transition rules between the causal and the normative. Kant's schema of the three syntheses—apprehension in intuition, reproduction in imagination, and recognition in concept—is viewed as an interaction matrix with complex transition rules and Chu transports between sensing and thinking, or the causal and the formal (logico-linguistic). A Chu transform or morphism between two Chu spaces can be interpreted as an "adjointness condition" between two distinct spaces. This involves a dynamic condition of mutual realization between the space of causes and the space of reasons, including intermediary back-and-forth mappings.

Now let’s discuss virtual machine functionalism. VMf is an approach to understanding the mind that views it as a complex system of interacting virtual machines. It aims to explain the nature and causal powers of mental mechanisms, as well as the states and processes they produce, by showing how they depend on and are explained by these complex, running virtual machines. Unlike physical machines, VMs are information processing machines that are not physical systems. They are implemented in, or "supervenient on," physical machines, but their relationship to these physical machines is not simple. For example, in a VM, component A can be part of B while B is part of A, which is impossible for physical machines. The architectural decomposition of a VM doesn't have to be tree-like and can include containment loops. Examples of VMs include chess playing programs, word processors, email systems, and operating systems (ISLMPS, 409)15.

Despite being non-physical, virtual machines, including their states, processes, and causal relations, are considered to have real causal powers, similar to non-physical phenomena like poverty or economic inflation. VM events (adding numbers, fetching memory content) can cause both physical and other virtual machine events. The causal relationships between VMs and lower-level VMs or electronic machines are often tangled and circular. VMf differs from most traditional varieties of functionalism because it is not solely focused on input-output relationships. The majority of functions within a VM may not involve externally observable behavior (ISLMPS, 417). Instead, VMf emphasizes that information processing systems frequently acquire, interpret, store, or use information about their own internal states—both hardware and VM states—, and many of their actions are internal, such as finding features in an image or modifying a stored plan (ISLMPS, 413).

According to Negarestani, VMf presents a functional diagram or architectural schema of the mind based on supervenience and emergent behaviours. This approach defines supervenience and emergence primarily in terms of interactions between VMs, rather than solely causal interactions between physical systems, thus avoiding criticisms of traditional supervenience theories. VMf models VM interactions as a nested or generative hierarchy, rather than a traditional control hierarchy. It involves concurrent and interacting virtual machines distributed along different scales or levels of granularity, moving from fine-grained physical supporting systems to coarse-grained virtual machines. This multiscale view allows for characterizing mental properties and their realization conditions at various descriptive levels, avoiding the "flat picture of functions" where all levels are undifferentiated.

VMf promotes an approach to mind where methods and models are developed and implemented across different scales. It posits a pluralism where specific models and methods are prioritized for each descriptive layer, for example, using Bayesian learning for low-level information processing like visual signals. Also VMf emphasizes different types of information and methods of information processing, moving beyond the vaguely general concept of information processing. The differentiation of scales and descriptive levels in VMf connects it to the concept of ontologies in information science, which involves formal naming and definition of types, properties, roles, and interrelations of entities in specific domains. This framework supports broad semantic interoperability across different domains. VMf's multiscale view, incorporating representational, functional, and normative vocabularies, makes it a point where computer science converges with transcendental philosophy of mind, particularly in the vein of German Idealism. Framed as a virtual machine toy model, the necessary aspect of the mind is its virtual architecture, which must meet computational criteria for semantic and causal interactions. This allows for the idea of artificial general intelligence to be treated in analogy to, and with the same scope as, the development of a prelinguistic infant into a language-using adult. Negarestani argues that the intuitive idea behind Sloman's VMf is comparable to the interaction matrix formally presented by Chu spaces. Both models discriminate between different types of causal interactions (between VMs, between VM and PM events, and between PMs).

Negarestani concludes the chapter by outlining two stages of the construction of our toy universe designed for the realization of AGI:

• Stage 1: Causal-Structural Capacities (Chapter 3 - Kantian Focus): In the first stage, the focus is on introducing the necessary capacities or faculties for a discursive apperceptive intelligence that originate from the causal-structural aspects of an agent. This stage will shift the focus to Kant, specifically exploring the foundational elements of cognition from a Kantian transcendental psychology perspective. This involves understanding how a rudimentary agent, equipped with structurally-causally originated capacities, begins to form its initial awareness of the world.

• Stage 2: Language and Generative Abilities (Chapters 4 and 5 - Hegelian Focus): The second stage investigates the transformation of this rudimentary agent into a fully fledged discursive apperceptive agent. This advanced agent's basic capacities are deeply caught up in language. By virtue of being a language-user, it possesses a generative framework of theoretical and practical abilities. This stage marks a return to Hegel, where language itself becomes the central protagonist of the toy universe, rather than merely a complex system of agents.

Overall Summary

• The As-AI-TP framework aims to define what is required to construct a system of agents capable of performing complex social activities, such as providing reasons for their actions, reappraising those reasons, and modifying their social structure through different modes of action.
  

  • Stage 1: Speech Synthesis: This initial stage focuses on the rudimentary acoustic realization of speech.

  • Stage 2: Artificial Interactive Speech: Here the focus shifts from basic acoustic properties to the intersubjective and dialogical features of speech.

  • Stage 3: AI in the style of augmented transcendental psychology: This final stage aims to actualize the ideal objectives of AI by integrating the conditions for cognition (transcendental pyschology) with the role of speech in enabling complex cognitive faculties (artificial synthesis).

• Negarestani identifies several loose threads and misconceptions in the disconnection thesis: Roden's account of diachronic emergent behaviours is criticized as negatively metaphorical and lacking a clear explanation of how the divergence feature of nonlinear dynamic systems can be extended to all conditions of realization for human intelligence.

• Negarestani aligns Roden's argument with Pascal's scams, where high probability or significant weight is assigned to features without robust evidence, leading to "overdetermined judgment" and a "sense of false radicality" (IS, 103). This process involves increasing the perceived plausibility and weight of scenarios even under high uncertainties, turning unfounded conjecture into plausible possibility and obscuring the genuine import of artificial intelligence with aesthetic and ethical pseudo-problems.

• Narratives of superintelligence often presuppose personal autonomy, value appraisal and revision, organised goal-seeking and self-enhancement, which require forms of self-knowledge for purposeful action and deliberate interaction. If strong AIs require basic capacities functionally isomorphic to human cognitive-practical abilities, then the extreme nature of speculative scenarios is an artefact of our ignorance regarding these necessary constraints.

• Parochialism, in the book’s context, refers to limiting the concept of "the human" to specific, local, and contingently posited conditions, such as a particular biological structure, physical substrate, or a specific local transcendental structure of experience.

• Hard parochialism represents an approach to AGI that assumes general intelligence can be achieved by combining and artificially realizing enough rudimentary behaviours and abilities. This perspective often overemphasizes the prevalence of intelligent behaviours in nature and their supposed sufficiency for general intelligence. It fails to recognize that while human conceptual activities are pattern-governed, they are uniquely rule-governed, possessing a formal autonomy that allows for the recognition of other pattern-governed behaviours in nature.

• Soft parochialism focuses on functional mirroring or convergence upon the human as a model for AGI. Negarestani says that this approach is necessary for grappling with the conceptual question of general intelligence as well as the modelling and methodological requirements for the construction of AGI. However this approach, while necessary, is not sufficient. The limitation of soft parochialism lies in its risk of reproducing or preserving purely local and contingent features of human experience.

• To move beyond the limitations of both hard and soft parochialism, a critical project is proposed that can provide a model of experience unconstrained by a predetermined transcendental structure. The aim is to renegotiate the limits of experience and self-consciousness by challenging the notion that the mind's conceptual categories are inextricably tied to local and contingent aspects of experience.

• Transcendental structures are described as the underlying frameworks that regulate and canalize human experience. These are not merely abstract philosophical concepts; they include a nested hierarchy of interconnected and mutually reinforcing structures, which can be physiological, linguistic, paradigmatic , historical, economic, and cultural. They are understood as structures necessary for the realization of mental faculties such as sensibility, intuition, imagination, understanding, and reason, enabling the movement from basic conditions to more composite ones, and vice-versa.

• Any account of intelligence or AGI is implicitly circumscribed by the inherent constraints of our own transcendental structure. Leaving these structures unquestioned and intact makes us liable to reinscribe their local and contingent features into our objective models, even when attempting to create non-anthropocentric AGI.

• A toy model is defined as a simplified or compressed model capable of accommodating various theoretical assumptions to organize and construct overarching narratives or explicit metatheories. Unlike regular theoretical models where metatheoretical assumptions are often implicit, toy models explicitly bring these hidden assumptions to the forefront through simplification. The simplification—the "toy" aspect—serves as a strategy to expose implicit metatheoretical assumptions.

• Negarestani distinguishes between small toy models, which are simplified versions of a single theoretical model, and big toy models, which can accommodate multiple, seemingly incompatible models and theories, like general relativity and quantum mechanics.

• For conceptualizing AGI, a big toy model is necessary to coherently integrate models from diverse fields such as physics, evolutionary biology, neuroscience, developmental psychology, linguistics, logic, and computer science.

• The primary aim of adopting an outside view of ourselves as a toy model AGI is to distinguish what is necessary for realizing general intelligence—in both organic and inorganic systems—from what is merely contingent, and to assess how descriptions of what is considered necessary might be distorted by what is, in reality, contingent.

• Chu spaces and Virtual Machine Functionalism (VMf) are proposed as candidates for a big toy model. A Chu space is described as a topological space that can accurately express computational dualities and interactions. A Chu space is typically defined as a triple (A, X, ∼) over a set K. A represents a set of "points" or "objects" or "events" (the "body" or "object" of the space). X represents a set of "attributes" or "states" (the "mind" or "menu" of the space). ∼ is an X × A matrix with entries drawn from K, which represents the "interaction" between the points and states.

• A Chu transform or morphism between two Chu spaces can be interpreted as an "adjointness condition" between two distinct spaces. This involves a dynamic condition of mutual realization between the space of causes and the space of reasons, including intermediary back-and-forth mappings.

• Kant's schema of the three syntheses—apprehension in intuition, reproduction in imagination, and recognition in concept—is viewed as an interaction matrix with complex transition rules and Chu transports between sensing and thinking, or the causal and the formal (logico-linguistic).

• VMf is an approach to understanding the mind that views it as a complex system of interacting virtual machines. It aims to explain the nature and causal powers of mental mechanisms, as well as the states and processes they produce, by showing how they depend on and are explained by these complex, running virtual machines. VMs are information processing machines that are not physical systems. They are implemented in physical machines, but their relationship to these physical machines is not simple. The architectural decomposition of a VM doesn't have to be tree-like and can include containment loops.

• VMf emphasizes that information processing systems frequently acquire, interpret, store, or use information about their own internal states—both hardware and VM states—, and many of their actions are internal, such as finding features in an image or modifying a stored plan.

• According to Negarestani, VMf presents a functional diagram or architectural schema of the mind based on supervenience and emergent behaviors. This approach defines supervenience and emergence primarily in terms of interactions between VMs, rather than solely causal interactions between physical systems, thus avoiding criticisms of traditional supervenience theories. VMf models VM interactions as a nested or generative hierarchy, rather than a traditional control hierarchy.

• Negarestani argues that the intuitive idea behind Sloman's VMf is comparable to the interaction matrix formally presented by Chu spaces. Both models discriminate between different types of causal interactions (between VMs, between VM and PM events, and between PMs).

• Negarestani concludes the chapter by outlining two stages of the construction of our toy universe designed for the realization of AGI: Stage 1: Causal-Structural Capacities (Chapter 3 - Kantian Focus) & Stage 2: Language and Generative Abilities (Chapters 4 and 5 - Hegelian Focus).

For citations of Intelligence and Spirit, the format will be (IS, x), therein x is equal to the page in which the cited text can be in the Urbanomic edition of the book. For other books, the specific edition and book will be noted down in a footnote.

Diagrammatization

This is a diagrammatization of the first chapter.