Foreword

[If you’ve already read any of the previous dialogs, you can skip the foreword and go straight to the introduction]

The previous Dialogue:

The history of philosophy is Philosophy itself. Therefore, without knowledge of this history, one cannot know what Philosophy is. I encourage you to join me on this series of texts where I will go through almost all philosophers and philosophies. I will not offer the usual history of philosophy that you can encounter in textbooks or Youtube summaries. My method of procedure is the following: the aim of every text in this series is to take a specific philosophy of the tradition and put it next to the philosophical attitudes, conceptions and views that followed, overcame or criticized it. The point is to address both concepts and problems in a dialogical manner, thus showing where the concrete thought resides, in short: how and why we have shifted from that view to another. In my mind, this is the only valid method.— Speaking in a crude way about Thales and making fun of the fact that he thought that water is the fundamental principle of everything means only that we apply today’s standards to the past. Such judgments are faulty, distorting and bending ancient ideas. Another misleading view stands outside history itself, judging what was right or wrong, true or false… as if the person making the judgment knows the truth with a capital T or confuses philosophy with mathematics where truth conditions are clearly set. Nonetheless, my hope is to present every stage clearly, creatively and faithfully to tradition. My second hope is to surprise learned scholars of philosophy. And my very last hope is to bring old—but valuable—thoughts and figures back to life, so they can speak to us once again. Well then, I wish you a pleasant reading.

Introduction

After a long journey from Egypt, Xenophanes finally reached Ephesus—a city where Heraclitus lived. They called him “the one who speaks in images,” or simply “storyteller.” Since Xenophanes had to cool his soul after his conversation with Anaximenes, he went to the baths on his first day, where he dazzled the public with his knowledge of cultures and, of course, spread gossip about Anaximenes. Heraclitus actually lived on a hill near the city. In order to visit him, one had to spend at least two hours walking along the track. The following conversation took place before Heraclitus’s modest dwelling. From above, he could clearly see who was coming, so he waited until Xenophanes reached him.

βίος και βιός

|Life and Bow|

HERACLITUS
Greetings, Xenophanes. Once upon a time, there was a man and another man, and they didn’t get along.

XENOPHANES
So, the news reached even the most remote places?

HERACLITUS
Yet my home is one of the most important. You should have counted on my ears being everywhere in this city.

XENOPHANES
But tell me exactly what you have heard, so I can be sure that your middleman has not misinterpreted my words.

HERACLITUS
No worries. He is well trained—I taught him myself. And furthermore, he heard your speech in person, so I trust the man.

XENOPHANES
Right. So, without further ado, tell me what you think!

HERACLITUS
Does it really matter what I think about your little conflict on a cargo ship? You know my position very well: battles, wars, conflicts, arguments—those are the main sources of progress, evolution, and enrichment. All I think is that I hope you are now much wiser than you were before the argument. I wish the same for Anaximenes.

XENOPHANES
Don’t tell me that you cannot see that one side argued better than the other.

HERACLITUS
Actually, I do not care that much whether someone argued better or worse. What I am interested in is the conflict itself: namely, what techniques were used during the argumentation, whether there were emotions or brute force. I do not care who had the best argument. Even if you had the better argument, does it really matter that much? The one who lost obtains much more than victory can offer—it is called experience. You could have an inner, divine feeling of victory, yet that is not going to last forever. On the other hand, his loss will remain in his mind forever, remembered as a negative example of how one should not continue arguing.

XENOPHANES
You think I am not experienced enough? I, too, had to lose in order to prepare myself better. Those victories could only be obtained thanks to my knowledge and my previous experience.

HERACLITUS
So it is. All that I am saying is that the conflict is much more important than victory as such.

XENOPHANES
You, too, Heraclitus, say really nothing new. All religions and cultures argue that, at the beginning, there was some chaos and conflict: Enki vs. Kur, Seth vs. Osiris, Cain vs. Abel.

HERACLITUS
You see, it’s important universally. Even our culture and civilization could not have been built unless we fought against natural forces. That’s why I cannot understand your obsession with natural elements. It does not matter whether arché is water, air, clouds, or the mystical apeiron. Without conflict and struggle, there is no life for civilizations. Only fire could be thought of as arché because it resembles conflict the best.

XENOPHANES
I think you do not get it at all. The whole debate about arché is about something fundamental. Without this fundament, you do not have people in battle, animals fighting, or gods in conflict. In my eyes, conflict is something secondary. Yes, it has some importance, of course, but there is something much more primordial than conflict or two sides in opposition, so to speak. I told you once, Heraclitus, that every culture creates gods in its own image. To me, it seems that you are greatly inspired by our deities. There are many examples: Athena in conflict with Poseidon, Hades and Persephone, or one can just look into the Iliad and Odyssey, where battles are present in almost every spoken word.

HERACLITUS
Let me tell you a brief story. I had a friend, a traveler like you. His name was Kafelios. He was not an ordinary man; he aimed to have children with as many women as possible. I admit he was strange, but his goal was to celebrate life. He even called himself life (βίος). As he was cruising around the Greek islands, he tried to sleep with as many women as he could. In Cephalonia, many say, he produced 30 children in only one single week. So, in that part of the Greek world, they started to worship him as a male equivalent of Demeter or other gods of fertility. They say he might have brought around 1,000 children to life. Amazing, isn’t it? … But his name proved to be his undoing. His last visit occurred on the sacred island of Delos. The high priest of the island, when he saw Kafelios, first asked him his name and then the purpose of his visit. He said, “My name is βίος, and my name is in harmony with my purpose here: to bring life.” However, the high priest of Delos heard “bow” (βιός) instead of “life.” So, the ending is obvious: he was immediately killed for threatening the high priest with a weapon.

XENOPHANES
That makes total sense. Delos is the birthplace of Apollo and Artemis, a bow is sacred there, and it isn’t something to mess with. Yet I didn’t get how this story answers the problem.

HERACLITUS
You said that in the Iliad and Odyssey there are fights present in almost every spoken word. I immediately associated your words with the story. However, the story shows that even a word like “life” can easily turn into something that can take a life—a bow. Kafelios is the very example of this. Thus, conflicts occur even in things you do not expect them to. Even the debate about the arché produced disagreements. Therefore, my proposal is to examine the conflict itself.

XENOPHANES
You can examine oppositions, but I can be an example that we do not have to be in conflict. Thus, for now, I will mute myself, so you can see that without another human being, you cannot be in conflict.

HERACLITUS
No. No. Please hear me out. Yesterday, I obtained a transcript of the conversation between Anaxagoras and Thales. It concerns the issue we are debating right now. Hear me out and tell me, please, what you think.

[Heraclitus starts to read.]

Anaxagoras (to Thales)
The stubborn mind will never ever bend:
What more do you need to be enlightened?

Thales
The waves will gladly bow to every wind,
Yet far from the jagged cliffs they’ll end.

Anaxagoras
This cliff came about by fiery vapours.

Thales
By moisture living things were created.

Homunculus (between the two)
Let me walk beside you, please.
I myself desire to ‘be’!

Anaxagoras
Have you, O Thales, in a single night
Brought a mount, from mud, to light?

Thales
Never has nature, in her living flow,
Been bound to day, night, and hours, though.
She creates every form by rule;
At her greatest, force is never her tool.1

HERACLITUS
So, what do you say?

XENOPHANES
[Says nothing and smiles.]

HERACLITUS
You cannot mean this seriously. Don’t behave like a child and talk to me.

XENOPHANES
[Widens his smile.]

HERACLITUS
Are you making fun of me? You think this is funny?

XENOPHANES
[Approaches him and hugs him.]

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Before we dive into the realm of infinity, some terminological clarification is necessary. For Hegel numbers, quanta and quantity are distinct yet connected notions. “Obviously, there are different categorial forms of speech in which we talk about of (pure) numbers, (pure) geometrical forms and (pure) sets of (pure) things. Hegel analyses their respective constitution under the title ‘quantity’” (Stekeler-Weithofer, 2005, 247). Although it may seem confusing why Hegel speaks about quality turning into quantity and vice versa, his focus lies on the presuppositions underlying everyday talk of numbers and mathematical entities. He wants to present us what it means to be a number, to be a quantum, measure or magnitude – what we implicitly assume when we speak of such things.

Quantity as such: “…is the continuous unity of discrete ones” (Houlgate, 2022a, 139). This label – quantity – is the most abstract and general one, due to its character of applicability to many things. Many things in our world have quantity or can be expressed through quantity. Quantity takes the form of limited units of itself – quanta. A number is in turn the most concrete determination of quantity. “Quantum, which in the first instance is quantity with a determinateness or limit in general, in its complete determinateness is number” (SL 168). The reason behind this is simple: a number has a specific amount (Anzahl) of units. Therefore, every number is unique. 2 is different from 4 because it has a determinate amount of two units. The number is thus constituted as the unity with the specific amount of units. “Thus completely posited in these determinations, quantum is number” (SL 169). In the case of a quantum, it is only limited, however there is no exact amount of units – it is just a representation of quantity. The most common examples of quanta are the following expressions: “more-or-less”, “many”, “several”, “a bunch of” or “x”. “Quantum, only as such, is limited in general; its limit is its abstract, simple determinateness” (SL 169).

Quantity – means the most general label for the discussion about quanta, numbers and so on.

Quantum – is the limited unit of quantity, also general and universal in its character. (EL 160, §101)

Number – is represented by a specific amount of units, it is the most concrete notion-form of quantum. (EL 161, §102)

To a contemporary reader, those definitions might appear strange. Yet, defining number, quantum, and quantity in this way was common in the age when Hegel was writing the Logic. To be sure, today we define numbers and their classes through set theory; it seems almost natural to say a set of “natural”, “real”, or “rational numbers”. We no longer use the notions of amount and unit to define numbers, now is everything a set. Returning to the past, consider the following example: “Cauchy starts, in a similar way to his teacher Sylvestre François Lacroix (1765– 1843), with ‘magnitudes’ and focuses on their changes, more precisely on their increases or decreases. These changes of the “magnitudes” he calls by the traditional name ‘quantity’” (Spalt, 2022, 118). Now Hegel: “A magnitude is normally defined as something that allows for increase or decrease” (SL 153). We can find many such similarities between Cauchy and Hegel, for example, Cauchy defines a “number” to be a result represented by the geometrical ratio of the compared measures of two magnitudes. “If, e.g., the two measures are ‘6 hours’ and ‘2 hours’, their geometrical ratio is the ‘number’ 3” (Spalt, 2022, 119).

In Hegel words those two magnitudes would be represented by the already mentioned notions of amount and unit. Relating, of course, in the same way. Where “2” represents the unit and “6” the amount, resulting in number three because when you divide amount of 6 by 2 units it makes 3.

Yet the similarity does not end there. When Cauchy speaks about numbers, he really means something firm and unchangeable. He uses the term “un nombre fixe”. On the other hand, when he wants to explicitly state the opposite, he writes as follows: “A variable quantity is one which is regarded as taking on, in succession, several values that differ from one another”^[1] (Cauchy, 1821, 4). Thus, we can see at play the distinction between the unchanging, fixed and the variable, indeterminate; that is the difference between a “number” and a “quantum”. To add some contrast and one extra example, Lagrange speaks explicitly about the term “quantités indéterminées” (see Lagrange, 1797, 8). To express the opposite term, he uses the expression “un nombre constante” (Lagrange, 1797, 22).

1.2.1. What changes and what persists?

In the sphere of quality, we have differentiated several bad infinities,

so we will here too. However, Hegel thinks that we can find the concept of the true infinite also in the sphere of quantity. There are some differences between the qualitative true infinite and the quantitative infinite, but, since we are acquainted with the concept of the true infinity, I will lay out the determination of the quantitative infinite first. The so-called intension of the latter is the following: (i) the infinite quantum has to be in a relation to another quantum and at the same time, it has to be posited as a relation; (ii) it must relate to itself in relating to another – a self-relation; (iii) the true infinite is the quality of a quantum.

1.2.2. Quantitative infinite progress and the concept of the infinite quantum

I will proceed by explaining all three criteria mentioned in the previous paragraph. Let us begin with the last one. Why must the true infinite be a quality of a quantum (iii)? The nature of the quantum, at the beginning, is infinite – in a bad sense. It can rise or descend infinitely: it can be divided, added to, or multiplied in infinite ways. Speaking about the infinite progress, the most common idea is to imagine a series of numbers that go on ad infinitum. I, II, III, IV, V, VI, VII, VIII, IX, X, …, L, …, C, …, D, …, M, … and so on. So to speak, you can always add 1. Those are, however, always the words it ends with – “and so on”, “ad infinitum”, “you can always add 1”, “you can go on to infinity”, “…”. Since you can always go on, it does not matter which quantum you choose, it is certainly not infinity, simply because the infinite lies beyond the quantum itself. Thus, we know that if we choose something from the sequence, it will nonetheless be a quantum – limited quantity. “[T]he beyond or the infinite is thus itself a quantum” (SL 191). Another quantum lies beyond our chosen quantum. Yet then again, beyond that one lies another quantum and so on. The infinite as the beyond is the “non-being” of a quantum. It has a qualitative difference from the quantum itself. “The infinite, which in the infinite progress only has the empty meaning of a non-being, of an unattained but sought beyond, is in fact nothing other than quality” (SL 203).

It is the quality of a quantum to raise itself to higher numbers; however, what it finds there is only another quantum (it finds only itself). Now the distinction between a number and a quantum comes in handy. A number – as a specific amount of units – cannot be infinite because, if we take, for example, the number 3 and add 4 to it, it becomes a wholly different number. It ceases to be the number three 3. On the other hand, if I have a quantum, say x, and I multiply it by y, I get z or xy and it is still a quantum. There is no conceptual difference between x and z; they are both limited quantities. Yet, between 1 and 2 there is a difference because 2 has one more unit than 1. A number, therefore, cannot be infinite or have an infinite quality. To leave its specific amount means that the number ceases to be.

To go back, no matter what operation we perform, we will always encounter a quantum. Therefore, infinity is not a quantum that one can find in the infinite series; it is a quality of a quantum to be infinite. Now we will unpack what this quality means (ii). “The true infinity of the quantum, however, does not lie beyond the latter in another quantum (let alone one that is infinitely big or small). It consists in a certain quality that is exhibited by the quantum itself: the quality of being infinitely self-relating in and through another” (Houlgate, 2022, 165). I already sketched that in rising itself (in an infinite progress), a quantum will always encounter another quantum, thus always encountering itself. Therefore, a quantum, by its own quality of being infinite, relates to itself in other quanta. But why is the idea of self-relation so important? The importance lies in the fact that the quality of self-relation renders explicit the negation of the idea of the beyond. “What lies beyond the quantum is, after all, not simply beyond it but is the quantum’s own determinacy; beyond itself, therefore, the quantum relates only to itself (albeit in a new form). This means, however, that the quantum, as now conceived, no longer has a ‘beyond’ as such” (Houlgate, 2022, 164).

The very last issue will demonstrate why the concept of the infinite quantum has not only to be in relation with another quantum, but also must be established as a relation (i). This part has some similarity with qualitative infinity, concretely in the matter of what is relating to what, or rather what are the details of the relation that constitutes an infinite quantum. I have said that a quantum is in relation to another quantum; they are both quanta, thus the quantum as such is just relating to itself. It is its self-relation. However, as such, we are not able to differentiate between two quanta. On the other hand, numbers are easily differentiable because we see their concrete amounts of units. Until now, we knew only the “abstract” concept of the quantum, in other words what would Hegel call its being-in-itself. The concept becomes determinate only in the case when we also know the other side­ – being-for-itself. – In general, the moment of being-for-itself is of great importance in Hegel’s work.^[2] So far, the concept of the quantum was indeterminate in the sense that it lacked a fixed identity. At any point in the infinite series where we stop, we encounter a quantum. In this way, all quanta are the same. Now, I will borrow the idea of the division universal/particular for the concept of the true infinity. We came to the conclusion that there is a plurality of quanta (particularity) and that the quantum-concept (universal) is through these particulars in relation to itself. “The […] point to be noted about the truly infinite quantum is that, paradoxically, it does not exhibit the quality of self-relation – is not infinitely and absolutely itself – purely by itself. It exhibits this quality only in relation to another, and indeed as that relation” (Houlgate, 2022, 167). In order to avoid confusion, the infinite quantum has to be in self-relation, yet at the same time it needs this other, in order to exhibit that quality. In my view, this otherness itself is what makes the concept of a quantum determinate. – This fact is demonstrated in a more general point throughout Hegel’s work: when something is claiming to exist and we want to get acquainted with it, or simply recognize it, it must become somehow determinate. The determinacy comes only in comparison, contrast, or analogy to another. Only in this case it can stand out from the crowd so to speak.^[3]

The distinction universal/particular helps us to see the difference. The quantum-concept stands for fixed, absolute determinacy and quanta themselves are just part of the infinite series, rising and descending. The former stands in this relation with those other quanta; it is not beyond, it is present in every instant of the infinite series, yet it is different. The difference consists in the fact that the infinite quantum represents the quality of that series, namely the infinite. – Two randomly picked quanta can be in relation to one another; they are in this relation because they share the same quantum-concept. Therefore, one finite quantum can find itself in another, but only as such they are just two finite moments in relation – each one-sided. On the other hand, the infinite quantum as relation, so to speak, governs the relation; it is the quality that determines others and is not determined.

“There is thus a fundamental ambiguity in the structure of the truly infinite quantum in its explicit form: it stands in relation to another quantum, but it also contains within itself, and so coincides with, that whole relation itself. In coinciding with the relation between two quanta (one of which is itself as a one-sided moment), the infinite quantum is, however, also a wholly self-relating unity, and so an independent quantum in its own right” (Houlgate, 2022, 169).

1.2.3. Infinite quantum as direct ratio and notes on calculus

Since we are in the realm of quantity, the infinite relation or quality also has to be expressed through a “quantitative relation” (SL 203). It is ambiguous yet the infinite quantum that establishes the infinite ‘self-relation’ consists of a quantum, and thus could be expressed by limited quantities. Hegel’s example is to present his idea of infinity on the logical structure of a direct ratio.

For instance, take two numbers like 1 and 3. The idea of the direct ratio consists of the proportional increase or decrease of numbers. Thus, when I change the number 1 into 2, the number 3 will change into 6. Following the same idea, the next ratio would be 2:6, the next one 3:9, and the next one 4:12… All ratios preserve the original ratio of 1:3. The latter as a quantum that determines the infinite series is always present in all cases and instantiations, thus preserving its fixed identity. It relates to the other and through this other it relates to itself. The idea of true infinity evolves beyond the direct ratio to inverse ratio and lastly to ratio of powers. I will provide such exposition in the next section.

The second example of the true quantitative infinite comes from Hegel’s remarks on differential calculus. I will not provide a full-length exposition because those two remarks take up around 100 pages. In any case, there is an extensive and detailed literature concerning the issue (Stekeler, 2019), (Stekeler, 2005), (Houlgate, 2022); the following is a detour from the main line of thought, and it can be skipped; the main line begins again with 2.3. I personally agree with Terry Pinkard that: “Hegel would, so it would seem, accept the interpretation which moderns like Weierstrass gave to the infinite” (Pinkard, 1981, 463). Historically, it is settled that first Cauchy and then Weierstrass put down the fundamental concepts and the so-called “rigorous formulation” of calculus (Boyer, 1949, 300). Hegel’s account of calculus happened before such a formulation. However, as I noted in the first part (1.2.), Hegel inclined to Lagrange’s algebraic approach to calculus, which later influenced Cauchy (Fraser, 2005, 265).

But what does Hegel write about calculus? One must clearly state that: “Hegel criticizes the idea of infinitesimal and infinite magnitudes. They do not exist at all, not even as abstract objects in mathematics” (Stekeler, 2005, 243). He is principally against any metaphysical interpretation of dx/dy; this is, in my view, justified by the fact that he denies them their own existence. They exist only in a ratio (relation) and only as moments of that relation. “This relation is itself expressed by a quantum that has the form nxn–1, and so it has a ‘determinate quantitative value’ (SL 229 / LS 293-4). Yet the relata are neither quanta, nor increments, but principles of variability or ways of changing, conceived explicitly as qualities” (Houlgate, 2022, 224). Or in Hegel’s own words:

“dx, dy, are no longer quanta, nor should they signify quanta, but have meaning only in connection, the meaning of mere moments. They no longer are a something, the something taken as quantum, nor are they finite differences; but neither are they nothing, not a null void of determination. Outside their relation they are pure nullities; but they are to be taken only as moments of the relation, as determinations of the differential coefficient ” (SL 215, R1).

Certainly, we can conclude that Hegel recognizes a similar logical structure between his concept of the true infinite and, at that time, the new mathematical domain of exploration and discoveries. His concept of the infinite enables him to identify particular-specific relations in-between the terms that mathematicians use. In this respect, Hegel was a great mathematical teacher because he was able to translate an abstract, and sometimes mystical, debate into more general notions that fitted into what we call now “Hegel’s system”. What I refuse to acknowledge is that Hegel’s take on calculus was in some sense better or more precisely formulated than the accounts of mathematicians. Hegel was not leading the debate in the mathematical field. His aim was to defend and justify calculus based on the “concept”– in the field that exceeds mathematical thinking or the thinking of Understanding (Verstand)^[4]. He was not interested in calculus because he wanted to persuade mathematicians that his view is better. On the contrary, he was interest in calculus because mathematicians formulated a new concept of infinity that was in accordance with his views on the true infinite, and what is more, they worked with the concept of infinity that was explicitly against the idea of bad infinite progress.

From our broader philosophical view dx and dy are only moments of a relation, existing only thanks to that relation. Therefore, they are qualities or determinations of that relation because when the relation tears apart dx and dy will vanish altogether. Yet, such a perspective is a perspective from outside mathematics, at least in the sense of Hegel’s critique from the preface to Phenomenology. There he explicitly states that mathematics cannot express the essence – that means the most general concepts and categories among other things also quality. Mathematics is a study of quantity, which means when the mathematician describes some mathematical object, it will be only in terms of mathematics (quantities). Such objects do have qualities, or features, but those are always expressed through the language of quantity.

The reason, why I am saying this lies in my disagreement with Houlgate’s last note on the calculus (Houlgate, 2022). Here is his reproach to Weierstrass’s formulation:

“Weierstrass thus conceives of a function’s limit – and of the derivative – in terms of the possibility of a “less than”. In contrast to Hegel, therefore, he continues to conceive of the derivative quantitatively, rather than qualitatively. [...] Hegel would not consider Weierstrass to have come any closer than his contemporaries to the philosophical concept of the derivative, which, for Hegel, is implicit in but distinct from that of the limit as such” (Houlgate, 2022, 396-7)

In my opinion, Weierstrass’s point was not to come closer to the philosophical (qualitative) concept but to a mathematical concept of the derivative. The second problematic part, for me, is why we reproach mathematician his quantitative approach to mathematical issues? I think this criticism could be raised against any mathematician who has to say something about the calculus. To repeat once again, Hegel does not put himself into the position that he has the precise mathematical formulation of the problem; his point was to:

“[R]eview the most important definitions of this infinite which have been given in mathematics. It will become evident that the thought of the fact underlying them accords with the concept developed here, but that their originators failed to establish them as concept and in applying them had again to employ expedients that go against their better thought”^[5] (SL 217).

First, the so-called originators are Newton, Leibniz, Euler and so on. Hegel reproaches them for their inability to establish those definitions as a concept, meaning that they lack proper justification and are in themselves contradictory. On the other hand, his role is to demonstrate that the thought or the idea underlying them accords with (übereinstimmend mit) his concept. In my view, this “agreement” or “being-in-accordance-with” does not mean that Hegel had an answer to a mathematical problem. Hegel’s thought is justifying calculus philosophically, in its own vocabulary and definitions formulated in the language that is connecting every concept and category with the whole of his Logic. This thought (of the true infinite) was, for Hegel, in accordance with what the mathematicians were thinking; however, the formulation in a specific mathematical language, which served as the justification, had to be provided by Weierstrass. Hegel have never aimed to provide the exact mathematical formula, his aim was to point out the similarities between his notion of the infinite and what was considered a different kind of infinite at that time.

1.2.4. Inverse ratio and ratio of powers

The exposition of the logical structure of the concepts of inverse ratio and ratio of powers is complex. I will not go into the most fundamental details. I highly recommend the more than 30 pages commentary (see Houlgate, 2022a) concerning this theme. Nonetheless, I will outline the main topics, problems and concrete examples because they are worth mentioning.

We stopped at the idea of the direct ratio. I said that, on the one hand, the ratio 1:3 is just a quantum, yet, on the other hand, it is also a governor for other ratios to preserve the established ratio of 1:3. Hegel calls such a governing ratio an exponent. So, 1:3 can be and is just a quantum, however, it could also be the exponent. When it stands in this position of an exponent its relation to itself can be represented by the following table:

Table 1

Exponent

1:3

Changeable quanta in relation to exponent

1:3

2:6

3:9

4:12

:

.

:

.

The ratio 1:3, so to speak, limits other ratios and preserves itself in them. We said that the concept of the direct ratio is an expression of the idea of infinite quantum. Where is then the problem, when there is still more to say about the true infinite vis-à-vis quantity? The issue with direct ratio is that it is a quantum. Thus, it is only a simple limited unit of quantity, however, there is a much more specific and concrete representation of quantity, namely a number. The moments that constitute a number are an amount and unity. Number is thus defined as a unity of a specific amount (of units). On the other hand, in the case of a quantum, there is no specific amount. In our scenario, where the quantum is 1:3 the notions of a unit and amount are separate (not united), divided by “:”. Therefore, the more explicit infinite quantum can be obtained only in the case where the exponent – that governs the variable quanta – is represented by a number. Because in a number, the notions of amount and unit are united, not held separate.

This means that we have logically proceeded from the idea of a direct ratio to the concept of the inverse ratio. “[T]he newly introduced determinateness gives the exponent the value of a product, the unity of unit and amount” (SL 274). The idea behind the inverse ratio stands for a relation between two values (quanta) where switching their terms or increasing one value while decreasing the other value keeps the product (exponent) constant. The table below shows one of the possible examples.

Table 2

Exponent (product)

36

Changeable quanta in relation to exponent

2:18

3:12

6:6

:

.

:

.

There are many logical differences when comparing the direct ratio with the inverse ratio. “Take [for instance] two quanta, A, the unit, and B, a certain amount of such units, where A is 3 and B is 12. The direct ratio between the two is thus 1 : 4. Now assume that these two quanta are in inverse ratio to one another. The exponent of that ratio will thus be the product of the two, or 36. If we now increase the value of A from 3 to 4, the value of B must decrease from 12 to 9 to preserve the value of the exponent. The direct ratio of 4 to 9, however, is 1 : 2.25, no longer 1 : 4. So not only do A and B change (as they can also do in a direct ratio), but such change alters their direct ratio, too”. [But the crucial difference is that] “in the inverse ratio the exponent coincides explicitly with the relation between the two one-sided quanta. This is because it is not only a fixed quantum in its own right, but also the product of the two quanta” (Houlgate, 2022a, 188-189). Yet, the true infinite could still be represented by a purer relation. What is the catch with the inverse ratio? It relates, in a similar way as a direct ratio, to variable quanta, namely, it prescribes the product of those quanta in advance, telling them: “I do not care what values you embody; however, the product of those values must be exactly 36”. It limits them in this way. Yet, we know that the limit is not a limit for only one of the sides of the relation. By limiting them it also limits itself. The variable quanta and the exponent are thus separated by a limit. The purest form of an infinite quantum would then be something that relates to itself through an other, is expressed as a number and does not endure such a limitation and difference.

Lastly, we shift our attention to the concept of the ratio of powers. But why the relation “x squared” is considered infinite? In fact, it meets all conditions mentioned at the end of the previous paragraph. “In the ratio of powers, however, a quantum changes through itself and by relating solely to itself. Since its “self” is in turn distinguished by the amount contained in its unity, the new quantum that it becomes must thus be determined solely by that amount. Accordingly, it must simply be that amount of that amount. If the original amount of the quantum is 3, the amount of the quantum into which it changes will be 3 multiplied by itself, or 3 raised to the second power. […] In the raising of a quantum to its second power, however, there is no amount that has to be preserved or attained. When 3 is multiplied by itself, the amount, 3, is not preserved, since the result is 9.” (Houlgate, 2022a, 202-203). This relation simply got rid of the quantitative limitation; it simply states that when the number is raised to the second power, it should be multiplied by the same amount of units it itself contains. Thus, every number that is raised to the second power will in this relation meet in its otherness only itself. There will be no difference. It, unlike the inverse ratio or the direct ratio, does not prescribe numerical values to its products or ratios.

Table 3

Exponent

x squared

Identical amounts

x . x

I intentionally put x into a column. The ratio of powers is for Hegel the relation, which left quantity as such and behaves purely qualitatively. The true infinite is here represented by a quality of the relation. “What happens in the ratio of powers is that the quantum continues outside itself in another quantum, not just because that is its quality as a quantum, but because it is now explicitly qualitative and self-relating as well as quantitative. The quantum thus proves to be “qualitative” in a more developed sense than we have seen so far: it no longer just has the quality that belongs to it as a quantum, but it is explicitly qualitative in being a quantum. In the ratio of powers, therefore, the quantum is no longer a simple quantum as such. Nonetheless, the quantum merely becomes fully and explicitly what it always is: that which continues beyond itself by virtue of its quality” (Houlgate, 2022a, 205)

1.3. True infinity as function

In the previous section we saw that the direct ratio meets the criteria required for the true quantitative infinite. The example of a quantum – 1:3 – that governs all other variable quanta (2:6, 3:9, 4:12, …), suggests that the governing ratio will be present in every case. It does not matter which one we pick; for instance, 20:60, “1:3” relates to those changeable finite quanta in an infinite way.

By following this logic, Pirmin Stekeler-Weithofer suggests interpreting the true infinite as a function. He says, following Hegel, that we cannot define an infinite sequence by finitely many examples followed just by “…” or “and so on”. “We can ‘define’ a determinate infinite sequence in arithmetic only by its law or rule. This law or rule is defined in its identity basically by three factors or ‘moments’: We need an expression of the rule f or law f or ‘function’ f(x). And we need an explanation of how to apply f or f(x). Only then we can say that f or f(x) is a ‘name’ of a rule or a function. Such explanations usually accompany paradigmatic teaching of examples. […] In the end, the real or true infinity of any rule f consists in this competence in following explicit rules and in controlling the correspondent rule following” (Stekeler, 2005, 243-4). Although this view is an interpretation, and Hegel never explicitly spoke about functions being the true infinite, I admit that this extension of Hegel’s idea is valid.

There are two reasons supporting this view. First, take as an example the quadratic function f: f(x)= x squared. To the values of the domain will be assigned the values of the range in accordance with the rule f. Those values of the domain and the range represent here quanta with which the function is related. The function prescribes to the values of the domain its range values – it (the rule) literally governs the relation. The finite quanta themselves stand in this relation as the other of the rule f. The function itself is different from those quanta because, in fact, it represents a quality of relation of those quanta; it is an expression of how they are ordered or how they are paired. The quanta are of a variable nature; in this scenario they may consist of: (1,1); (2,4); (3,9) etc., but what they have in common is the relation: f(x)=x squared . The latter is both in relation to every finite example, for instance to (4,16), and at the same time it is posited as a relation. This brings us to the second reason justifying the previous paragraph. In the language of set theory functions are defined as relations, concretely through the notions of the Cartesian product and the ordered pair (Levy, 2002, 24-6).

However, there are also at least two major problems opposing the idea of interpreting the notion of function as the true infinite. The first problem concerns the notion of the domain. The function f can enjoy its infinite self-relation only under the presupposition that the domain consists of a set that has infinitely many elements in it. However, the domain could contain only finitely many elements – it could be a set of positive integers in the interval from 1 to 100. If we apply function f only to those, we get only a finite number of outputs. Therefore, the self-relation of the function is narrowed into the mentioned finite space. Thus, the first problem represents a major difficulty; however, there is a way around it: we consider only as truly infinite those functions that are applied to a domain consisting of an infinite number of values. Here the latter notion of the infinite is presupposed. The assumed notion of the infinite is the bad infinity, integrated into the concept of the true infinite.

The second issue resides in the ambiguity whether we should understand the notion of function as the Hegelian notion of quantum. The example of a direct ratio with the value 1:3 meets the conditions of a quantum. It is at the same time a self-standing quantum in relation to other quanta and the governor posited as a relation of the infinite series for variable quanta. Yet in the case of a function f: f(x)= , I am not sure if it makes sense to say that it is a quantum. It is a rule, law, or operation with certain values, but it itself does not represent a value. When Hegel speaks about the quantitative infinite, he says explicitly that it is itself also a quantum – a limited unit of quantity. As I see it, the function is not a limited unit of quantity, as in the case of the ratio 1:3. If we simply strip away the notation symbol for the function, we get y=, this however prima facie does not signify a function. It signifies an equation of the two unknown variables, furthermore, we are now able to presuppose that behind y and x there is some limited representative of quantity, thus considering the whole we can think of it as a quantum as we did in the case with nxn–1. However, I think this problem could be resolved in the following manner: we simply admit that the notation f: f(x)= stands for positing the function as a relation (Hegel’s exponent) and that its quantum is y=, meaning a quantum in relation to other variable quanta of the infinite series. This distinction makes explicit the twofold nature of an infinite quantum. Considering the example with the direct ratio 1:3, such an explicit distinction does not take place, because we must be said whether we should take “1:3” as just a quantum or an exponent that governs the relation to other quanta. Thus, when I write “f: f(x)= ” I mean a relation as such and when I want to express the quantum in relation to other quanta ((1,1); (2,4); (3,9) etc.), I put down simply “y= x squared”. The first stands for a relation per se, the second stands for quantum in relation to other quanta.

My final remark, and what is in my mind truly worthy of appreciation is that Hegel has come up with the concept of the true quantitative infinity that: (i) is opposed to the idea of infinity going on and on, (ii) lacks any mystical or metaphysical entities – consists purely of defined notions, (iii) and that could be found in already well-known domains of mathematics – so to speak it lies before our very own eyes.

[If you would like to, I can provide the list of references in DMs. I have not put it here because of length of the article. ]

^[1] Original text: “On nomme quantité variable celle que l’on considère comme devant recevoir successivement plusieurs valeurs différentes les unes des autres.”

^[2]When I speak of being-in-itself, I have in mind general knowledge about a thing as such. For instance, generic propositions such as “O stands for water” or “A wolf is a predator of deer.” It is a mode of speech in which one expresses the universal as such. On the other hand, being-for-itself embodies the particular. It, so to speak, translates the universal into particular cases or examples. For the most part, it is the actualization, realization, or objectification of the universal: “Can you see that wolf over there? He has caught a deer and now is feeding on it.”

^[3] Such truism is shown in examples where we use italics, the latter is different and other than every word used in this sentence, so it stands out.

^[4] The Understanding here means to think analytically, with fixed, strictly defined terms and always in accordance with the rules. The Understanding stands in contrast to Reason (Vernunft) – it is a more abstract way of thinking or thinking in wider contexts, not fixed to absolute distinctions.

^[5] Emphasis on the word “accords with” is mine.

Žižek should be eternally praised for popularizing Hegel. I, too, knew about Hegel only thanks to him. The aim of this text is not to conclude that Žižek’s understanding of Hegel is a misunderstanding or a major misinterpretation. I regard the combination of Hegel and Žižek as a particular interpretation of Hegel; therefore, if someone feels like a follower of this type of Hegelianism, in my view, there is nothing wrong with it. On the other hand, one must state clearly that Žižek’s Hegel is not Hegel per se. There are evident points with which Hegel would most probably disagree. So, this text is a presentation of those differences.

Psychoanalysis contra Antipsychologism

As we all know, the “Slovenian Troika,” namely Žižek, Zupančič, and Dolar1, is influenced to a large extent by Lacanian psychoanalysis. However, it was Lacan himself who had already made the link between Hegel and psychoanalysis, thus, I see Žižek as a continuation of this tradition. Alain Badiou has this famous saying—which captures the best of both his philosophy and the philosophy of the Slovenian Troika—that “in order to be a philosopher, one must get through Lacan’s antiphilosophy.” Whatever that exactly means, it simply says that Lacan is the window-passage to philosophy.

The opening runs through psychoanalysis itself. In Hegel, we can find something very similar. First, in Phenomenology, consciousness goes through a journey of suffering, setbacks, and disappointments. Such an experience might be comparable with a session with the psychoanalyst. Only after this dangerous and hard odyssey is consciousness able to sublate itself to the higher dimension of categories—Hegel’s Science of Logic.

The difference lies in a small detail: Hegel says that this road of suffering is not a sine qua non condition for entering Logic. One can start reading Logic without any previous unpleasant experience, yet such a reader must be able to abstract in order to understand. The beginning of Hegel’s masterpiece rests on the ability to abstract from the sensual, the personal, and that which is merely imagined or felt. Only when one is unable to do this does one have to go through the hell of Phenomenology.

Once we get rid of feelings, perceptions, or metaphors, we are able to set out on the path of knowledge. Of course, we cannot get rid of them absolutely, they serve as steps towards knowledge, yet they cannot guarantee it or justify it. It is funny how Žižek repeatedly mentions one of the most famous passages from Hegel’s Philosophy of Right, namely the passage about Minerva and how she spreads her wings with the coming of dusk, yet does not notice what Hegel says on the very next page:

Everything, other than the reality which is established by the conception, is transient surface existence, external attribute, opinion, appearance void of essence, untruth, delusion, and so forth.2

Hegel, however, mentions psychology in Part III of the Encyclopedia. The main topics are the soul, consciousness, feelings, impulses, and so on. Those, as such, are only subjective phenomena; they are, to be sure, worthy of study, but they can never express, in Hegel’s sense, knowledge in its wholeness.

…induced phenomena of consciousness do not originally appear in the form of a thought, but as a feeling, a perception, or mental image—all of which aspects must be distinguished from the form of thought proper.3

Žižek sometimes claims that he also likes Kierkegaard, which makes total sense. Kierkegaard was the main opponent of Hegel. Kierkegaard reproaches Hegel for not taking into account subjective life, subjective experience, personal trauma, and other subjective phenomena. In defense of Hegel, one has to say that this reproach is more hysterical than legitimate. Yes—Hegel is not the type of philosopher who talks about melancholy, depression, and the personal bullshit we are all getting through. On the other hand, his aim was totally different: his aim was to build philosophy on the firm ground of science. Human beings, in the end, are zoon politikon; they are nothing without society, without the whole. Why, then, focus on subjective, existential, and personal storytelling?

One of the best accounts of Hegel’s antipsychologism is provided by Stephen Houlgate in his book Hegel on Being, Volume II.

Picture Thinking

This brings us to the second major difference between Žižek and Hegel. I would like to call it an appeal to imagination. Žižek is famous, among other things, for theorizing about movies and cinema. I admit that he is skilled at noticing and interpreting one minor moment in a film and showing its universal value. I also like how he can find almost the same thing in a variety of movies, pieces of art, literature, and philosophy. He truly has a mind for associations. One could say that he could have been a good detective.

The problem is that each one of his books is full of jokes, movie scenes, psychoanalysis, and personal experiences. I do not claim that there is no philosophy, or that there are no philosophical points worthy of mentioning. I mean, to be sure, one can always “distill” the important, universal, and philosophical. I would never go as far as Chomsky and say that there is no content.

On the other hand, I think this plurality of particulars—scenes, jokes, experiences—is more often arranged in such a manner that it mimics an argument, yet there is no actual argument.

It is sometimes the case in Žižek’s work that he mentions some philosophical concept and then brings a heap of particulars to support the notion. But those are only examples, which, if read in good faith, can at best be interpreted as an inductive argument. I do not reproach Žižek for not arguing at all, he does argue, but even when he does, one has a hard time finding the argument.

Hegel, too, uses a bunch of examples that should support his view, yet those are always only of contingent matter. Their function is to explicate the content of an argument that actually took place before the mentioning of the examples. In other words, his examples merely serve to illustrate the point, not to be evidence for the point itself.

Hegel is well aware that examples belong to the sphere of Vorstellung (visualization, introduction, imagination, or presentation), certainly not to the formal argumentative side of things. Such mental images are good for introducing someone to the point you would like to make, but should not be considered evidence or premises.

Ontological Commitments

I bet you must have heard about one of the most famous Žižekian examples of the world being incomplete. Let me briefly state it.

—God is like a programmer of a video game. He is the creator of the world; he has programmed houses and their interiors, roads, and characters. However, there are houses that are not simply part of the mission or of the main goal, and thus their interiors are not programmed. Or there is a deep forest, yet it serves only as an impenetrable background.

This example should bring to mind—at least in an image—contemporary “limits,” “advancement,” or rather “knowledge” of quantum physics. The issue is that even physicists cannot come to terms with which interpretation fits the measured data best. But Slavoj, with his “gut feeling,” comes to the conclusion that the world must be incomplete in itself. Of course, there are some physical theories stating this, but that’s the problem: they are only theories. Science itself has limits and cannot, by its own means, explain everything. Theories are usually falsified or revised; there is not a single theory that has not been altered or falsified in some way.

Hegel knew this very well. Therefore, there is some “incompleteness,” but it isn’t a problem with the world—I mean the outside world—it is a problem with our concepts. They are always incomplete in the sense that they do not cover all worldly phenomena. In fact, Hegel was very modest in pronouncing truths about the outside world. He knew that this was the world of the natural sciences, of measurements and approximations. To put it the other way around, there are no ideal objects—like a right-angled triangle or any perfectly spherical object. The outside world is the world of the imperfect, of non-ideal objects. Is it then incomplete? No. Why should we interpret and judge the world according to the category of completeness? What proves to be incomplete are usually our theories about the world.

Thus, the only pieces of evidence in favor of the world’s incompleteness are a few minor theories and Slavoj’s gut feeling.

*

I claim, first, that Žižek is not only a follower of psychoanalysis, but that, for him, psychoanalysis occupies a special place. Secondly, Žižek is a master of images; however, I would not go so far as to claim that he produces simulacra. And lastly, he argues strongly in favor of a certain minor view in physics, for which he has only philosophical justification. He isn’t a physicist or a scientist; I do not believe that he can interpret or explain the mathematics behind quantum physics. Thus, his view has almost no significance in the field of physics. There is no doubt that Hegel would certainly be against all three of these positions, and I think they are in opposition to Hegel’s oeuvre as such.

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1. I think, Mladen Dolar is the best Hegelian in Slovenian Troika.

Logic has lost its final fight. I mean it quite literally. Logic and logicians tried in the last century to dominate the ground in philosophy. Their promise was simple: “let’s get rid of metaphysical ‘Aufbau’ and instead focus on language itself.” Since we are humans, we put “everything” into language, thus, if we could understand how this medium (language) works exactly, we might better understand the theories that we are creating alongside. Yes—this would guarantee us only a representation of reality but it is better than any metaphysical thought-castle. So, language, meanings, and words lie before us, let’s create models that can represent them best.

For now, the winner is Conceptual Engineering—one of the most popular trends in today’s analytical philosophy. The partisans of this branch claim that it is not enough to understand language, or create a precise model, language as such is flexible, plastic, and can be altered how we want. We are able to change the meaning of the words, in fact, we do that regularly. Language is not only a descriptive device for understanding the world, we express in it both goals and aspirations, we command, we promise, and we create, only thanks to its manifold character. How do you plan to formally capture a language model, where the given meanings may change tomorrow?

But what is Conceptual Engineering, actually?

Conceptual Engineering (CE):

CE= (i) The assessment of representational devices, (ii) reflections on and proposal for how to improve representational devices, and (iii) efforts to implement the proposed improvements. (Cappelen and Plunkett 2020: 3)1

Reading this for the first time might be confusing. So, let me break this down for you: (i) means an evaluation of concepts – whether the concepts we use are efficient, outdated, good etc. (ii) suppose have come to the point, where we dislike certain concepts, for instance the concept of ‘value’; imagine that the meaning of ‘value’ is the following: what people like, adore and praise. Say, you do not like that definition because you are a Marxist, so you propose that the meaning of ‘value’ should be: an amount of labor put into the production. (iii) then stands for the application of this new definition in society, usually done through action—in this case establishing a communist party.

Of course, there are also other definitions, even CE is sometimes called “explication”, or simply as “ameliorative analysis”. Yet, opening this debate on definitions and so on would only bring confusion.

What is then the leverage of CE in contrast to classical logicism? They both come from the analytical field, so why would they be in some sort of fight? Cappelen rightly claims that the analytical tradition was too focus on describing and has never taken into account its prescriptive character:

I think we’re now in large part blind to how bizarre this descriptivist turn in philosophy of language is. That blindness is for example reflected in Scott Soames’s history of analytic philosophy (2003a, 2003b). As Soames sees it in that work, the normative (engineering) aspects played a marginal role in the origins of analytic philosophy and philosophy of language. The central aims of the analytic tradition were all descriptive (to describe various features of our linguistic practices and conceptual structures) and work towards these aims had its culmination in the work of Kripke and other externalists. In my view, this is a fundamental misunderstanding of philosophy in the twentieth century. The most crucial aspect of philosophy in that period was the normative and engineering proposals: these projects were what initiated and motivated what we now describe as ‘analytic’ philosophy. The descriptivist turn in the 1970s was an historical aberration (Cappelen, 2018, 26).

Therefore, I consider the advantage of CE to be the following: it explicitly reflects its prescriptive dimension. Of course, one needs to first describe AND understand the status quo, in order to propose a new, worthy, or useful alternative. Thus, the general picture differs radically. The logician2 (formal mathematician) tries to describe the world—say, he creates a logico-semantical model; it’s him and the world. Maybe he prescribes something, yet he might not be aware of it. On the other hand, there is the conceptual engineer, who assumes from the start two or three perspectives. It is him, his worldview, and over another person who also has his own worldview (his own language). An engineer tries to convince the other or propose a new definition of concepts, so they can understand each other and be on the same ground, or, he simply wants to change the meaning because he thinks that the world will become a better place. If you define slavery as fundamentally bad and you manage to convince the majority that it is the case, the result is a lesser amount of unnecessary suffering in the world.

Anarchism of Conceptual engineering

Philosophers are obsessed with the truth. They propose many definitions, here is at least one from the tradition:

“In my view, which can be justified only by the exposition of the system itself, everything turns on grasping and expressing the True, not only as Substance, but equally as Subject” (Hegel, 1977, 10).3

It does not matter what this definition means but one can clearly see that it is a proposal of: how we should understand truth.

In logic, there are usually only two truth values: true and not true, 1 and 04. The whole aim of logical inquiry is to have a clear and effective means by which one can clearly decide which proposition corresponds to which truth value. These means are logical laws and rules. Logic simply promises that if you have a certain true proposition like ‘Hitler was a leader of Nazi Germany’ and you process that proposition using logical rules, it will be guaranteed that the processed proposition is still true. In other words, if you do not follow the rules like tertium non datur and the law of non-contradiction, you can never make a career in the field of logic. You simply must accept the rules because they hold in every possible world.

Yet, if you are a conceptual engineer, there isn’t a pantheon of laws. Of course, if you do not follow logical rules, you will have a hard time convincing someone to adopt your definitions and meanings of words. But it isn’t impossible. Do not get me wrong, this lawlessness is not a bug, but a feature. A logician might analyze or create a beautiful and valid argument, but if the meanings are going to change along the way, or over a longer period of time, his argument may not hold. For example, we might change the definition of the word ‘leader’ or ‘Nazi’ and the argument could collapse. An argument can hold only under the condition that meanings are not going to change. Engineers set everything from scratch: (i) what the meanings will be, (ii) what conditions something must fulfill in order to be considered this or that, (iii) what rules will be considered valid, and (iv) what rules will govern changing the previous rules.

Of course, nothing changes in an instant. Yet, in the case of conceptual engineering, we are in charge. If an engineer takes some logical system to be rigid or outdated, they simply propose another one or change the rules themselves in order to make them more relevant or updated.

Logicians—when creating an extensional logic for example—simply accept the given meanings in the same way as they accept the rules of logical tradition, their work is then to formalize them and create a model that guarantees logical entailment. An engineer, on the other hand, sets both the meanings of words and the rules.

The role of otherness and negation

In semantic logic, when discussing sense or meaning, we first define the words so everyone can understand the terms used. Though there are many kinds of definitions, I will omit the classification. Here are some examples:

Water =df a chemical substance whose molecules consist of two hydrogen atoms and one oxygen atom.

Or

Fruits =df the edible parts of trees, plants, and shrubs that have a lifespan of more than one year.

To generalize a definition: it says something like: ‘this means/is/stand for that’ . Logic then takes those meanings and considers them substitutable. So whenever is see the term ‘fruit’, I can substitute it with: the edible part of trees, plants, and shrubs that have a lifespan of more than one year. The point of semantic logic is then to come up with models that will guarantee us this possibility of substitution. A logician does not care whether the definition is right—in the end, he’s not a arborist or a dendrologist. He cares only about formally following the rules.

On the other hand, the engineer might reproach this with the following: yes fruits are the edible parts of trees, plants, and shrubs that have a lifespan of more than one year but those are nuts, too. What’s then the difference between a nut and a fruit? Or, do we want to stick with the original definition and equate fruits with nuts? Say an engineer would like to draw a difference between nuts and fruits, so he proposes a new definition:

*Fruits =df the edible parts of trees, plants, and shrubs that have a lifespan of more than one year, yet not nuts.

A logician is interested in what is equal to what, but does not analyze the definition. If he is given the definitions—identities of predicates—his whole point is to execute a long deduction procedure to see if the argument hold and the conclusion follows from the premises. The engineer suggests a new identity altogether.

An example of a logician’s work

1. x=y

2. y=z

3. if x=y and y=z, then x=z

4. x=z

An example of a engineer’s work

1. An engineer is given certain definition.

2. He/she sees that the definition isn’t enough because it causes confusion in certain cases, for example.

3. He/she proposes a new definition that resolves the issue.

An engineer, unlike a logician, takes into account, what I call “otherness”. They comprehend an aspect of concepts that is not like, or simply different from, their initial stage. In our example with fruit, the engineer saw that the definition of fruit also contained something other than fruits—namely nuts. To put it in general terms, they see what the definition should be and, at the same time, what it shouldn’t be but, nevertheless, is. In short, in their understanding of concepts, they also takes negations—the negative side or what is simply missing in concepts—into account; therefore, they are not satisfied with the existing definitions and suggest new ones.

Please! Don’t let me say it…

Conceptual engineering is, in fact, conceptual dialectics…5 Let me explain.

An etymological detour: Logic comes from logos (λόγος), meaning ‘speech’ , ‘reason’, or simply ‘word’. The prefix ‘di’ means ‘two’ and the prefix ‘dia’ means ‘between’, ‘across’, ‘through’. The word ‘dialogue’ then means ‘between words’, or ‘across speeches’. You get the point: you need at least two people to have a “dialogue”.

CE is also between two words, and worlds so-to-speak. Between the ‘first’ and ‘corrected’ versions. In other words, CE operates on at least two dimensions. It presupposes, as a practice, two perspectives: first, the immediate meaning of a term, and the second, meaning that should replace the former. CE, under these conditions, is a method of procedure—or practice—which is inherently dialectical. Why dialectical? Because an engineer proposes a new vision of the concept that is different from the original. They simply find something in the original to which they are opposed or with which they do not agree (otherness/negation). In our example with fruit, the engineer simply cannot accept equivalence of nuts and fruits, therefore, they fell they must somehow ameliorate the original definition with the clause “fruits are not the same as nuts”.

Here is what is meant by the dialectic:

Dialectic is, in fact, a richer and more supple form of thought-advance than mathematical inference, for while the latter proceeds on lines of strict identity, educing only what is explicit or almost explicit in some thought-position’s content, dialectic always makes higher-order comments upon its various thought-positions, stating relations that carry us far beyond their obvious content. (Findlay In: Hegel, 1977, vi).6

The most (in)famous dialectician in the history of philosophy is, of course, Hegel. Here are his thoughts on his method:

…it may be useful to say something about the method of carrying out the inquiry. If this exposition is viewed as a way of relating Science to phenomenal knowledge, and as an investigation and examination of the reality of cognition, it would seem that it cannot take place without some presupposition which can serve as its underlying criterion. For an examination consists in applying an accepted standard, and in determining whether something is right or wrong on the basis of the resulting agreement or disagreement of the thing exam­ined; thus the standard as such (and Science likewise if it were the criterion) is accepted as the essence or as the in-itself. …

“Consciousness provides its own criterion from within itself, so that the investigation becomes a comparison of consciousness with itself;…” (Hegel, 1977, 52-53)

Say, for example, we at the beginning set the definition of the fruits.

Fruits =df the edible parts of trees, plants, and shrubs that have a lifespan of more than one year.

What follows after “=df” is our first criterion. We will evaluate everything that falls under our criterion : “the edible parts of trees, plants, and shrubs that have a lifespan of more than one year” as fruits. But, now, we’ll come across the problem with nuts. Nuts aren’t fruits per se.

If the comparison shows that these two moments do not correspond to one another, it would seem that consciousness must alter its know­ledge to make it conform to the object. (Hegel, 1977, 54)

Thus, we say:

*Fruits =df the edible parts of trees, plants, and shrubs that have a lifespan of more than one year, yet not nuts.

And, this new definition serves us as a new criterion for evaluation. And this dialectical process is the method Hegel uses trough out.

Not a lost battle, but the entire war

When I initially suggested that Logic lost its final fight, I implied that there were several lost fights—so which ones are they? In fact, there were three major battles. But first, we must understand the causes of the war. Russell was, at the beginning, a Hegelian, then he lost his faith (in Hegeliansim, of course) and unleashed his attack. I agree that Bradley was, in fact, an idealist-monist who did not understand Hegel at all; thus, the attack was legitimate. Then, the story is familiar: everyone simply rejected Hegeliansim.

The first fight—the one against metaphysics—was lost by the analytical tradition thanks to Strawson, who showed that universals (“concepts”) simply exist. The second fight—against Hegel—was lost due to appropriation of Hegel within analytical tradition itself (e.g., Brandom, Stekeler-Weithofer, etc.). The defeat of the third and final fight is described in this article. Analytical tradition implemented the dialectical method in the form of conceptual engineering. The fight against Hegel and metaphysics is lost, all that remains is to realize it. This is the reason why I strongly support any inquiry into conceptual engineering—even though, for me, it will always be conceptual dialectics.

My point is not to convert everyone to Hegel. Yet those who despise him should at least present an argument against this article to prove otherwise. Until then:

My texts in connection to the issue:

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Foreword

[If you’ve already read any of the previous dialogs, you can skip the foreword and go straight to the introduction]

The previous Dialogue:

The history of philosophy is Philosophy itself. Therefore, without knowledge of this history, one cannot know what Philosophy is. I encourage you to join me on this series of texts where I will go through almost all philosophers and philosophies. I will not offer the usual history of philosophy that you can encounter in textbooks or Youtube summaries. My method of procedure is the following: the aim of every text in this series is to take a specific philosophy of the tradition and put it next to the philosophical attitudes, conceptions and views that followed, overcame or criticized it. The point is to address both concepts and problems in a dialogical manner, thus showing where the concrete thought resides, in short: how and why we have shifted from that view to another. In my mind, this is the only valid method.— Speaking in a crude way about Thales and making fun of the fact that he thought that water is the fundamental principle of everything means only that we apply today’s standards to the past. Such judgments are faulty, distorting and bending ancient ideas. Another misleading view stands outside history itself, judging what was right or wrong, true or false… as if the person making the judgment knows the truth with a capital T or confuses philosophy with mathematics where truth conditions are clearly set. Nonetheless, my hope is to present every stage clearly, creatively and faithfully to tradition. My second hope is to surprise learned scholars of philosophy. And my very last hope is to bring old—but valuable—thoughts and figures back to life, so they can speak to us once again. Well then, I wish you a pleasant reading.

Introduction

The following conversation took place on a cargo ship. Anaximenes meets Xenophanes — they are both passengers traveling to Colophon, a city on the coast of today’s Turkey. The meeting was completely arbitrary, one of the crew members of the ship knew both Anaximenes and Xenophanes, but they had never met each other or known anytihng about each other. Thus the crew member is here a bridge between the two, he introduced Xenophanes to Anaximenes in order to listen to their conversation—he knew it would pay off. He was so interested that he wrote down their talk, hoping many would find the same interest as he did.

ἄπειρον, ἀήρ, 𓇋𓏠𓈖𓀭

|Apeiron, Air, Amun|

ANAXIMENES

What a shame we haven’t met before. The sailor told me that you lead the discussions during the cruise. I, too, spoke with him many times to cut the boredom. So, who are you? Or is it better to ask: what occupies your soul?

XENOPHANES

You are right. We argue with the sailor frequently, however, that is because I travel a lot. By the way, he offers the best service. That partly answers your question, I love to see different cultures, however primarily their deities.

ANAXIMENES

So you are a “God hunter”?

XENOPHANES

A hunter kills its pray, yet, I would rather say that I am a collector. I haven’t killed the idea of God in me, however, my view of him is, to be sure, different from what the Greeks think of their gods. … But, let us go back to the collecting aspect of my daimon, whats your God?

ANAXIMENES

To be honest, I don’t know whether I have one. I consider myself a follower of the Milesian school, we are trying to understand and explain the world, without any godlike power. My teacher is Thales, he thinks that the arché is water. However, my usual partner in debates, Anaximander, thinks that the arché is apeiron – something infinite, indefinite, unbounded or indeterminate, lying under everything. I take my view as a culmination of their ideas. For me, air is what stands for arché. I admit, hearing this for the first time might seem strange, yet air is something that isn’t somewhere hidden beyond the finite, bounded and so on, but it is something infinite and determinate at the same time. We can feel it, thus, it is something ordinary that can, in the overall picture explain the world, not taking into account the divine providence.

XENOPHANES

Well, I admit that your arché is in some sense original. However, there is nothing new in worshiping rivers or mountains and other natural phenomena.

ANAXIMENES

Yes – of course, but I do not “worship” air. It is not about worshiping a particular river or particular planet or sun, or in worshiping animals – as the Egyptians do. It is about air as such.

XENOPHANES

Okay, we may agree that you do not believe that air has some divine power, but tell me then what is the origin of everything? Because if we were to follow your thought, we would have the following picture: there is a universe with a plurality of elements, where one of them is your air, the latter doesn’t have any divine power—it isn’t a God. Its role is only that it stands behind everything. Yet, how did it all begin? A mythical view gives answers to those question in a very concrete way. Egyptians, for instance, think that at the beginning there was this primordial chaotic water called Nun, as your Thales says, but then come the gods into the picture to establish order – the current state of our universe. When you just say that the origin and the principle of the world is air, what is the alternative to those questions? It seems that your air simply exists, existed and will exist, but there is no explanation of the beginning in your view.

ANAXIMENES

Look, I wasn’t there to experience what was at the beginning. However, I can explain to you how air mutates into other elements. When it is cold air turns into a heavier state, thus it alters gradually into harder more dense stuff like water, soil, and eventually stones. When you add heat, for example, when you set something on fire, it simply changes into smoke that turns into air. All of that can be explained without gods and without any divine power.

XENOPHANES

Yet, it cannot explain everything because there is no explanation of the origin as such.

ANAXIMENES

It seems that you presuppose some beginning of everything as an instance that occurred in one specific moment in time. What if there is no beginning of time. What if time also stretches to infinity?

XENOPHANES

But then there is nothing left but to simply assume that the time is in this sense infinite and that your air was not created but was always here. In this case, you are not explaining anything, you are just asserting it.

ANAXIMENES

As if the primordial waters and the order making gods, were not also mere assertions…

XENOPHANES

Hold on, I didn’t say that what the Egyptians believe is true. All that I am saying is that we should consider the relevant reproaches that could be raised from other points of view.

ANAXIMENES

Tell me then, what’s your view? Because up until now, you have occupied this comfortable position of someone who only poses questions and criticism. If you think that your view is better than mine, get it off your chest. However, I can promise you, I will be cautious and critical in the same way as you.

XENOPHANES

I have to admit that I like this position of mine. Let us continue examining your views. Remember? I am the collector. What I think does not matter, but I would like to store your ideas and compare them with many others that I preserve in my mind…

ANAXIMENES

… but you have just exposed yourself. You are a preserver of ideas, may be that is your way of life, your world of memories and divine temples of ideas. Or, you just do not have any idea about the world, so you hide your ignorance behind this veil of being interested in different cultures.

XENOPHANES

No. No. I can assure you that, in fact, I store in my soul some world-picture. It is actually in some way close to yours, yet there are a few things that may cause nuances.

ANAXIMENES

So, go on. Fill me with your “wisdom”.

XENOPHANES

I can’t argue with you when I see that your heart longs for revenge. I didn’t mean to offend you in any way. I simply argued.

ANAXIMENES

No, you were from the beginning against my proposal. All you do is you hide your “precious mystery”, your knowledge of cultures. I have opened up in a good faith and all you did was to mock me. When you heard that you might have a real “challenger” to your ideas on this boat, you immediately started taking an interest in me, because you would like to stay honored by these pure sailors as a great thinker. Because you want to be remembered in their thoughts as the smartest one they ever met. I was simply an obstacle to your aims an interests. Actually, I have no interest in talking with you. You stupid moron.

XENOPHANES

Look, I can reveal my position, if you want. I didn’t mean to hurt you…

ANAXIMENES

I do not care anymore, I bet it is full of nonsense. However, whatever it may be, remember that without the air and wind there’s no sail, no travel on a boat, none of you and understanding other cultures, and no sailors who would keep you in high esteem. I hope, we will never meet again and I do not want you ever to start talking to me again. Understand?

XENOPHANES

[smiles and says:] ναὶ δή |yes, indeed|.

And so they went their separate ways. From that moment on, they never saw each other again. Anaximenes hurried when the ship landed, never turning back. Xenophanes, however, looked at him while he was leaving the port. He regretted a little that he could not have been more enjoyable, yet that’s life. His journey, however, continued with the sailors, they had intently listed to their conversation, so they were, too, interested in Xenophanes’s view. He told them the following.

XENOPHANES

Those Milesians get annoyed pretty quickly, don’t you think?

SAILORS

Believe us, they are oversensitive. They are not used to harsh conditions as we are, haha. He might be speaking about water, air or whatever, yet only we know what those natural elements are really like. The Milesian would certainly change his mind, if he were to survive at least one storm on a boat, while hoping he’d one day hide under the skirt of his mother-land, HAHA!

XENOPHANES

Guys, don’t be so harsh towards him, he was too sensitive, yet he was certainly not stupid.

SAILOR (who wrote down the dialog)

We do not care about him, but as for you, finish your speech so we, too, could be wiser. Tell us your position.

XENOPHANES

As I told to him, mine is not so much different, only in some minor details.

SAILOR

Don’t keep us in suspense, just—go ahead, like a ship that breaks the wave.

XENOPHANES

Nonetheless, I take off from what Anaximenes said. I think his reasoning about the air was right, everything thanks to the air is pressed and squeezed together, thus, creating basic things. All the stuff is made of this compressed air, one can say metaphorically that everything is made of several kinds of these “clouds”. In my humble opinion, we are all these particular substances, compressed from the stuff, creating this one entity. A rock, a tree, a horse and so on. What I cannot admit, and where our ways part, is the aspect for which I reproached him. I simply cannot admit that this stuff exists without an explanation or any relevant cause. Someone had to create this ship so it could sail, thus, there has to be a God who created these particular “clouds” so they could be.

SAILOR

Yes, great Xenophanes, but wasn’t his point to explain the world without the gods, so he could come up with new and different explanations?

XENOPHANES

In deed, but it simply does not work in my mind. And when it comes to novelty, their ideas are not anything that would revolutionize thinking. I met his friend Anaximander once, on this exact ship, he talked with me about his apeiron, how it is the arché of the cosmos. Now with Anaximenes—air— it clicked in my head everything together. Yes—they say that water, air, or the indefinite is the fundamental principle of everything. Especially, air and apeiron, made me think because I heard about very similar connection. If we would consider apeiron, as something in the background of things, hidden or not on the surface, yet which reigns over all things, then we can make an exact transition to Egyptian Gods.

SAILOR

Come on, be more exact.

XENOPHANES

As you please. Because there is not much more to say. Anaximenes and Anaximander, simply stole the features of the most powerful of Gods, Amun (𓇋𓏠𓈖𓀭). He is the Egyptian God, sometimes called “the hidden one”, that is exactly Anaximander’s apeiron. However, Amun could be best compared with our Zeus, the one who reigns over the clouds. Yet, Amun is precisely associated with air. He is the one who is in the shadow and who is the master of air—and that’s our Anaximenes. Thus, when they claim, that they are bringing new ideas into the world, they are lying. They robbed an Egyptian deity of its attributes and are now displaying them as spoils of war. They did the same thing as in Troy… They are nothing more and nothing less than looters.

SAILOR

Hah. But when you steal something that means it is at least worth something, nay?

XENOPHANES

You are right… They robbed the wrong thumb, it seems. God is only one, he manages everything, he is the arché. It is funny how Greeks make fun of Egyptian gods because they are represented as animals, thinking that a God with a human appearance is any better. My God does not resemble anything or no one. Maybe I don’t even know what else to say about him. He simply transcends our realm of appearances.

SAILOR

So how do you know anything about your God, when he is simply out of the whole picture?

XENOPHANES

Perhaps, I just believe it to be true…

SAILOR

So, it seems in the end, Anaximenes wasn’t so stupid: he had acknowledged in the beginning that, he too, cannot explain everything.

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We all agree that mistakes are an integral part of our lives. We make them, we try to pay attention to them, and they sometimes occur without our knowing. The phenomenon of being mistaken, or simply forgetting something, is in some way essential to being human (essentialism!!!). For now, this also holds for AI. In the following text, I would like to provide a simple overview of what we actually think about mistakes from a philosophical perspective.

Today’s academic philosophy (mostly analytic in orientation) is marked by the influence of mathematics. We philosophers try to pursue the ideal of constructing an argument that is “impenetrable,” that is, without any mistakes or weaknesses. We want, so to speak, to achieve greatness in clear thinking. Papers containing such arguments look accordingly: they are full of clearly defined notions, mostly borrowed from mathematics or physics. We speak about possible worlds, functions, operators, numbers, and classifications. All in all, everything is done in pursuit of clarity, rigor, and precision; a mistake is persona non grata.

Do not get me wrong—these goals are admirable, and I personally support such an endeavor. If it is possible, we should simply avoid mistakes. Of course, one could trace the origin of these ideals back to the beginnings of philosophy, where Plato debated the Sophists about truth. But, in my view, the “official” beginning of the endeavor to avoid mistakes belongs to the modern era, starting with Descartes, then Leibniz, Spinoza, and Hume. I borrowed this idea from Deleuze, who discusses it, although this piece of knowledge is not difficult to obtain; one simply has to read the introduction to Descartes’ Meditations.

We all know that these philosophers were preoccupied with the sources of knowledge. Where does knowledge come from? Which sources of knowledge are reliable? Or, in other words: Is there a source of knowledge that does not produce mistakes at all? Today, we know that all such “sources” are prone to error. We can perceive something incorrectly, we can see things differently from others, we can think in contradictions, and so on (nothing else occurred in your mind so you put and so on). Thus, we have made a silent agreement in academia that formalism, rigor, logic, and mathematics are the only means by which we can uphold the ideals of objectivity, universality, and necessity. Therefore, one should not be surprised when someone who thinks like a mathematician becomes a determinist (there is no free will), a naturalist (who praises science uncritically), or an atheist (because there is no evidence for God’s existence), and so on. When you are holding a hammer, everything looks like a nail.

In fact, I wrote an article concerning the limits of mathematical thinking, so if you are interested, here it is:

When one reads, for example, Théorie des fonctions analytiques (1797) by Lagrange, a great mathematician, one sees only the deductions—the application of mathematical rules. Mistakes are absent, or at least they are not meant to be present. The same is true of any scientific or philosophical paper. Truth, so to speak, has the highest value, whereas mistakes are usually associated with categories such as bad, unwanted, better avoided, dangerous, or without value.

The aim of this text is not to claim the exact opposite—that mistakes are actually great. No. That would be equally one-sided. Some mistakes are indeed better avoided. There is really no point in making the same mistake again and again while telling yourself that you will thereby come to a deeper understanding of yourself. This is dogmatism in its purest form. You do not have to kill thirty people in order to understand that doing so harms their families.

However, I think mistakes are important. They are necessary, and everyone makes them along the way. They are an integral part of our education, our self-understanding, and our vision of a better society. When I am mistaken, I come to see why. Of course, if you do not know why something is bad, then you do not consider it bad in the first place. Mistakes are best understood as parts of lines of reasoning. We reason in one way rather than another because we have learned (have we?) from our mistakes. Our understanding of a subject matter is mediated through mistakes, time, and effort. Therefore, we know why things should proceed in one way rather than another.

No doubt, almost everyone would agree (why so sure?) with this view, even mathematicians and analytic philosophers. Even they acknowledge the importance of negation—that something did not go according to plan because an error occurred. They know that mistakes and inconsistencies push a theory forward. However, this insight never truly makes its way into their systems and theories. Mistakes occupy a special place there, standing in the shadows as a silent presupposition.

Note that analytic philosophers not only push mistakes to the margins of their papers, but they are also eager to demonstrate how others are wrong. Pointing out the mistakes of non-analytic philosophers is one of their specialties. In fact, they build an entire “judging apparatus” based on the criteria, ideals, and values shared within their own circles. This, of course, leads to withdrawal into oneself, which we can already observe in practice: their work is read mainly by their colleagues.

To sum up, mistakes occupy two positions in contemporary philosophy:

1. They are an implicit and silent presupposition of every text: “Mistakes were made during the research process. They were important because they helped determine the direction of the inquiry, yet the final form of the text is, hopefully, free of errors (hardly). The paper contains truth and only Truth.”

2. A mistake is something that belongs to authors of the continental tradition. The confusion resulting from not following grammatical or logical rules opens a space for metaphysical monsters. We, by contrast, are enlightened and informed; we are without mistakes. (This position is one of ressentiment.)

Philosophy once aimed to explain the universe as a whole. Such an attempt, we are told, was mistaken. I agree that philosophy cannot explain everything. Yet it can explain, at least, the fundamental concepts by which we attempt to explain everything else. Some (majority) think this is an unimportant task; others would say that even this ambition is too great. Let future historians decide. For now, while the issue remains unsettled, we should try to explain what we think can be explained.

When I say that we should at least explain the elementary concepts, then the concept of error is one of the fundamental ones. We all err. Thus, mistakes deserve proper philosophical treatment. What role do they play in the processes of cognition, understanding, and knowing the truth? How do we overcome mistakes? Should they be explicitly discussed in our works so that we become more attentive to them? Since we are all mistaken from time to time, what problems are caused by the majority of those mistakes?

These problems and questions cannot be resolved by the two approaches mentioned above: by pointing at others and saying, —> “You are the one who is mistaken” (2), or by presenting ourselves only through polished versions of our work that lack all imperfections (1). The latter probably has a deeper connection with our behavior on social media, where we post only beautiful pictures, exciting trips, and displays of toxic positivity.

To understand the truth, one must understand mistakes. One must speak about them and acknowledge them fully and explicitly. That is human thinking. That is how we come to understand our thinking, our concepts, and ultimately the world around us. The only major text that deals with this issue directly is Hegel’s Phenomenology of Spirit. There, one can see how mistakes are productive and how perspectives shift because of them. Hegel (haha, no one reads him anymore :) nice try) was the first to understand that we must accept mistakes, that they belong to us and play a crucial role in thought itself. Thus, if one takes mistakes seriously enough, one has to read and work through the Phenomenology. Otherwise, we will continue to rot in the practice of blaming one another for being mistaken while each side presents the Truth as though it were written on a single sheet of paper.

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Thanks in advance for your corrections in comment section!

I would like to devote this short commentary to ongoing similar phenomena present both in our culture and in the ancient culture of Greece. The inspiration comes mainly from the opening text of Christopher Nolan’s The Odyssey, which states: “A time of apparent magic.” This short comment made me think: why would one say that the story of Odysseus was considered magical during the time of Greek hegemony? Does this imply that we live in a world where magic no longer has a proper place? Do we live in the world which dealt with magic?

Gods

What should we consider magical? There are actually many candidates when considering ancient Greece. Here is my short list: the Olympian gods, witches, mythical creatures (Cyclops, Scylla, the Minotaur, sirens...), spells, prophecies, astrology, and many more.

I am almost sure that there is no sane person who believes that Zeus, the Hydra, or Hades really exist—meaning that we can find or encounter them in the world. Saying this should be uncontroversial, however, one never knows for sure. In our culture, we have got rid of such mythical figures. Furthermore, they are always marked by the following aspect: the divinities of ancient Greece were the gods in which the ancient Greeks believed. In this way, they are foreign to us because both the ancient Greeks and their gods belong to the past. (Maybe, this is the final stage of the death of the God, Nietzscheans may prove me wrong.)

It is true, and it should stay that way. There is really no place for the ancient gods in our culture and civilization, their place is in the past itself.

What should be considered my controversial thesis is that we have not actually moved that far away. In simple terms, we now have one God who stands behind everything; we have merely got rid of the plurality and instead embraced the One. What is surprising is that we have not actually got rid of such plurality entirely. We have only adopted a half-measure. I am speaking from the perspective of Christianity. Yes, there is only one God, yet there are angels and saints—figures whom we venerate. For example, Saint Florian is the patron saint of firefighters. This strongly reminds me of an ancient god, let us say Poseidon, who simply rules over a certain aspect of the world (the waters).

Of course, there are atheists; not everyone is a Christian. However, most of the world’s population is considered to be religious. We must believe—it is an essential human attribute. Yet, to put it generally, many people believe in many different things, gods, and destinies.

Mythical creatures and special places

Many people operate with the following distinction: on the one hand, there is the sphere of the mythical/fictional/sci-fi—in short, the unreal—and on the other hand, there is the real, or reality itself. I agree that such a distinction is sometimes necessary. However, one must also say that such a dichotomy is not always—that is, in every case—clear.

Really, no one believes, when watching Game of Thrones or The Hobbit, that dragons are real. Why, then, should we think that Cyclopes existed or still exist? Again, we should not think in this way, but, in my view, there are trans-natural creatures present in our culture as well. The honourable mentions are the Yeti, angels, and the Devil—Lucifer.

The best example of our time, however, is the alien. It has reached the White House, and everyone speaks of aliens; many people are convinced that they truly exist. Do not get me wrong—I, too, believe that there may be life somewhere in other galaxies and that we are “not alone.” Yet there is still a chance that we are.

In ancient Greece, there were special islands where strange things happened, and my claim is that we believe in something very similar. We have simply replaced islands with galaxies.

However, we do not have to travel several light-years away. There are plenty of examples here on Earth: the pyramids, Antarctica, crop circles, and the far side of the Moon.

*

Thus, in my opinion, we have not changed that much with regard to the phenomena discussed above. We still ask others, “What’s your zodiac sign?” Many people still, implicitly or explicitly, believe in such things. Since the time of ancient Greece, the creatures and gods may have changed, but the ideas and notions behind them are still present, only embodied in different figures. The actors are new, but the play still goes on.

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Foreword

[If you’ve already read any of the previous dialogs, you can skip the foreword and go straight to the introduction]

The history of philosophy is Philosophy itself. Therefore, without knowledge of this history, one cannot know what Philosophy is. I encourage you to join me on this series of texts where I will go through almost all philosophers and philosophies. I will not offer the usual history of philosophy that you can encounter in textbooks or Youtube summaries. My method of procedure is the following: the aim of every text in this series is to take a specific philosophy of the tradition and put it next to the philosophical attitudes, conceptions and views that followed, overcame or criticized it. The point is to address both concepts and problems in a dialogical manner, thus showing where the concrete thought resides, in short: how and why we have shifted from that view to another. In my mind, this is the only valid method.— Speaking in a crude way about Thales and making fun of the fact that he thought that water is the fundamental principle of everything means only that we apply today’s standards to the past. Such judgments are faulty, distorting and bending ancient ideas. Another misleading view stands outside history itself, judging what was right or wrong, true or false… as if the person making the judgment knows the truth with a capital T or confuses philosophy with mathematics where truth conditions are clearly set. Nonetheless, my hope is to present every stage clearly, creatively and faithfully to tradition. My second hope is to surprise learned scholars of philosophy. And my very last hope is to bring old—but valuable—thoughts and figures back to life, so they can speak to us once again. Well then, I wish you a pleasant reading.

Introduction

Thales is on his way back home to his hometown of Miletus. Right before the entrance to his house there are two well-known figures Anaximander and Anaximenes (yes, they even look the same in person). They heard rumors from the fish market about the argument between Thales and Mythos and they are curious about it. Both Anaximander and Anaximenes had spent some time with Thales in the past arguing about arché, this time they are ready to challenge him again. The content of the conversation was told to you by Anaximenes himself.

Ποιος είναι ο βασιλιάς του ουρανού

|Who is the King of Heaven?|

ANAXIMENES

Our dear Thales, you seem exhausted, let me help you with your purchase before we finish you for good.

ANAXIMANDER

Ohh, please! Let us help you, we would like to hear what happened.

THALES

You are right, take everything and follow me into my house. I still have some power to fight with you, though I know very well that there will be no mercy from your side.

[They followed him into the garden, situated in the middle of the mansion and surrounded by regularly watered trees.]

THALES

His name is Mythos. I don’t know from where he comes from, but he was one of the strongest opponents I have ever faced. Apart from the usual talk—that the Gods navigate our lives and destiny, he said something I had never thought of. He said something along the lines that my hypothesis about Water being arché means nothing more than applying godlike properties to earthly things. He was right about that, but I couldn’t admit it openly. Maybe you guys can help me to think that through. … Yet there is one more thing: though he argued, he constantly warned of the God’s wrath. I cannot stand when someone is trying to scare you, it is no surprise that he convinced others through fear only.

ANAXIMENES

What an interesting, yet at the same time, ordinary person, this Mythos. It is strange how someone’s mind cannot break free from the embrace of the Gods.

THALES

So unfortunate, he immediately associated Water with Poseidon and started to ask questions about him.

ANAXIMENES

However, it seems there is a grain of truth in what he says. From his point of view you just attributed features of the Gods to something as “common” as Water. If you told him that Water is the primary principle, it would seem to him that you were simply praising Poseidon. Perhaps your view could be, in his eyes, justified by the words of Homer:

Heed us, Poseidon, you who hold the earth 

We know that Poseidon rules the waters, such a line form Homer would support the view that he also holds everything together. Simply that he is the fundamental principle binding together the whole.

THALES

There is no doubt that Mythos sees the issue in and by those terms. There is no arguing about that. However, it doesn’t rule out my hypothesis. Whether the Gods do or do not exist, or whether I attributed their properties to something earthly, the next day one needs to drink, and plans need moisture, and life in general would necessarily need Water.

ANAXIMANDER

Yes—but there are many other necessary conditions that must be met for life to continue. Water is only one of them.

THALES

I am not disputing this, yet for me Water is the most essential one.

ANAXIMANDER

No. Arché should be something that doesn’t belong to the sphere of basic phenomena. It should be considered as outside or beyond the latter.

THALES

And what should that be?

ANAXIMANDER

Thales, you do not understand me. It isn’t something in the sense that ‘here’ we have water and ‘there’ is a rock, it isn’t one among many. It is rather something not bounded by earthly things.

THALES

However, you suggest that this apeiron is something nonetheless, yet only outside limited things.

ANAXIMANDER

I do say so. It is an unlimited, unbounded, infinite, indefinite something—that is arché. I mean, when we decided to cut the Gods out of the picture, we should cut also the phenomena that they represent. The fundamental basic principle is this apeiron that stretches across the cosmos and isn’t limited by it because the apeiron is a sphere that is the fundamental cause of every finite and limited thing.

ANAXIMENES

To me this sounds like made up bullshit.

THALES

I am trying to make sense of what you have said, Anaximander. I see also the motivation that pushes you into this direction, but is such a sphere immaterial?

ANAXIMANDER

It is immaterial, yet I am not ready to immediately admit that it has a spiritual essence. Apeiron simply means something that enables to some material to come into existence. When is something composed of a certain material it is limited or so to speak with borders. Apeiron is everything outside of these borders. A great analogy could be the following: abstract from everything limited and earthly, imagine only one person standing on a vast plain. The background or that what is not defined by any limit, yet constitutes the limitedness of finite entities is arché — the apeiron.

[While he was speaking, he painted the following image into the sand.]

ANAXIMENES

Okay, let’s sum up everything we have said up until now. Thales has abstracted from the Gods. He claims that we’ll manage just fine with the Water. One doesn’t need the superpowers of the Gods to explain certain things. You, Anaximander, say that we should also abstract from the immediate things— it is, in your view, better to not cherry-pick one element among many and argue in favor of it. Thus, according to you, the arché is the apeiron, something irrepresentable—that which enables the presentation of phenomena. However, isn’t it just a sheer abstraction? I mean, Thales can bring up arguments why Water should be considered arché but in this case I see no evidence.

ANAXIMANDER

And that’s the point. You really cannot see the evidence because it isn’t to be seen. One can only penetrate the apeiron with thought. The argument I am presenting is this: if we accept that we should get rid of the Gods, we are left with major issues. What is the meaning of the world? Who or what governs it? Is there an elementary principle binding everything together? Now let’s acknowledge to Thales that the arché is Water. We are then led by necessity to the reproach that was raised by Mythos: aren’t we just inscribing the properties of the Gods to something finite? Water can be easily evaporated by fire turning into steam and at the same time water isn’t the only necessary condition of life. To avoid such counterarguments, I propose this: let’s get rid of this guessing game of which element or material should be fundamental? Instead, we should abstract from the materials and elements themselves and claim the unlimited, undetermined and undefined to be the fundamental principle.

THALES

I see. Yet the issue that Anaximenes opened remains unanswered. The same could be said that there is some abstract God called Apeironos who cannot be represented by an animal, natural phenomenon or any image because he is simply out of the picture “creating the picture itself”. In fact, Mythos told me something about such God. —After our public conversation, he introduced me to the Jewish God called Yahweh. What you described, Anaximander, resembles a description of the mentioned God. He too, is above everything finite, undefined, in his sphere outside. Yet the only difference is that he cruelly punishes humans for representing him as some-thing or preaching other Gods. I guess your apeiron doesn’t have such quality.

ANAXIMANDER

I don’t see why we started to compare the apeiron with God. Apeiron was a result of our thinking—first by abstracting away from the Gods, and then abstracting from material stuff. Why then throw the Gods back into the picture?

ANAXIMENES

It’s simple. Because people outside our small thinking circle would need some analogy or comparison to even understand what you are talking about. Their thinking is marked by pictures, myths, Gods and so on. You have to explain to them what you mean. When Thales spoke about Water being the arché, it was far easier to imagine such a scenario that they could understand. However, when you start mumbling about the apeiron and how one is unable to imagine it, it becomes a vague idea.

ANAXIMANDER

It’s “vagueness” is in the end its own feature. When we speak about something that is Universal— the arché—it has to be ‘vague’ because it holds and embraces everything. Every thing, thanks to the apeiron, isn’t vague because every thing is an immediate, concrete stuff before us. However, one has to think beyond/over the thing(s), to see their fundamental principle. And there, behind every thing, is what summarizes all of being and that is the apeiron. That holds true even for Water.

THALES

Yet those are only assertions. Don’t take me wrong, we see that this thinking process led us to such a conclusion but there is no argument. No reason is supporting this view. I still hold the position that Water is behind everything and I can bring plenty of evidence supporting my point.

ANAXIMENES

No so fast, Thales. There is also a lot of evidence against your view. You seem, too, unable to admit the problems with your approach. Most of the Water is undrinkable and in certain temperature conditions it vanishes.

ANAXIMANDER

I agree, Water, as such, cannot be arché. It is too changeable and sometimes dangerous.

ANAXIMENES

So let’s follow this logic. If we rule out Water as arché, and at the same time, we would like to avoid the alternative of the apeiron—the abstract, vague idea—then there is a third option. In my view, the arché is Air. It is a nice principle to follow. Look closely to details. Water and its waves are formed by the strong winds. Heated water also turns into steam—air. Air also brings water in the form of rain. There are good reasons and evidence in favor of this view. On the other hand, it—air— is not bounded, there is no limit to it. I think, this proposal combines all necessary features that we would like to attribute to arché; air corresponds with all of them.

ANAXIMANDER

I have to admit that your idea is overwhelming, but how can you defend this view against the reproach that you just chose air to be arché, when it is—as with the case of water—only one of many elements.

ANAXIMENES

Air is the arché—meaning it is fundamental, not one among many. It is an element that makes up the possibility for many. Air actually brings movement to clouds, to water, it, so to speak, embraces everything, even the whole Earth. And if you expose everything to high temperatures it turns into dust and mainly to smoke. Thus, as I said before, it nicely combines the ideas of you and Thales and avoids the nuances.

ANAXIMANDER

Of course, tell this to someone and they will start to laugh immediately. They will call you the fool who speaks about Zeus but doesn’t know it. Your notion of the arché is too ordinary. Even Thales is more original because he opposes the public with his water. — So, they think he acknowledges Poseidon to be the greatest. But you … you play only along their lines by speaking about an arché that reigns over the clouds and waters. You might as well say that Zeus is the mightiest of the Gods or that he is the ruler of Olympos.

ANAXIMENES

Anaximander, you know very well that this isn’t what I mean.

ANAXIMANDER

I don’t think you know what you mean. I say to you that the identical idea is thought now by everyone, so you haven’t come up with something new. Thus we are at the very beginning where we have started. “Air is the origin, arché, because it shapes and rules everything, responsible for major changes, that causes others to be what they are.” What is the difference than between Air and Zeus?

ANAXIMENES

That we decided to cut the Gods out of the picture. We promised ourselves that we would explain the universe using different concepts than the ones we were taught.

ANAXIMANDER

Yet, you two try to explain the cosmos by something common, thus there is not much difference.

ANAXIMENES

Thales, help me to convince him. I stood by you when you argued with him.

THALES

There is really no one who can convince both of you. I have resigned, you heard my stance and my opinions. I am finished and I desperately need some rest.

ANAXIMENES

At least you know that we stand behind our words, never breaking the promise.

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Yesterday, 01.07.2026, two young people illegally climbed the Empire State Building. Apart from the proposal, the two also unfurled a flag bearing the slogan:

“WHEN THE POWER OF LOVE BEATS THE LOVE OF POWER, THE WORLD KNOWS PEACE.”

I have to admit that the idea of two young people proposing at the top of a skyscraper is really romantic. My fear prevents me from doing the same. In some sense, it is very attractive.

The message of love they sent to the world will have a strong impact. I am even a fan of them. On the other hand, we should not remain under the spell of love for too long but rather confront the harsh reality.

What I truly meant by the mentioned impact was that the message will touch our hearts, and it should make us think—or rather rethink—the way we see politics.

Let us read the slogan once again:

“WHEN THE POWER OF LOVE BEATS THE LOVE OF POWER, THE WORLD KNOWS PEACE.”

THE POWER OF LOVE is real and has the ability to attract people. However, we can feel this power only toward one person. I am speaking primarily about romantic love for one’s partner. Of course, most of us also love our parents, animals, and so on, but that is not the same kind of love with which you love your partner—the kind of love that makes you propose to someone.

THE LOVE OF POWER is not actually love but rather the desire to be in a dominant position over someone else. Power might play a strong role in sex, yet it is not love. You can love a person; you cannot love the abstract ability of a person to dominate others. You may enjoy or desire such power, but it certainly is not love.

The motto, at first glance, might suggest that all we need is simply to shift our perspective—to move from the love of power to the power of love, as if it were that easy.

There are two main problems.

1. The power of love can be directed only toward one person. A person who says that he or she loves everyone does not really love anyone. It is the same with friendship. If you are a friend to everyone, then no one is truly your friend. Therefore, in the sphere of politics, we cannot simply love everyone or be friends with everyone. This so-called UNESCO-style universal love is a chimera. I would even say that it is better if one does not harbor strong emotions toward politicians. Love simply is not a political category.

2. The power of love and the love of power are two wholly separate things. The first is an emotion directed toward someone else, whereas the second is a preference for being in a position of dominance. However, the second possesses a universal character, exactly what the first lacks. You cannot love everyone, but you can dominate everyone.

Unfortunately, the climbers’ message is not that clear. Love is not a magical instrument that guarantees world peace. In some sense, it reminds me of the naïve words of beauty pageant winners after they are crowned Miss Universe.

For further reading on why love is not a political category, I strongly recommend In Praise of Love, a short book by Alain Badiou.

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There are many infinities in Hegel. Mainly, there is a strict division between bad infinity and the true one. Apart from that there is a division of infinities in relation to the categories of quality and quantity. Although the concept of the true infinite is only one, the notions of bad and true infinity will take different forms regarding quality or quantity. In contrast to the concept of the true infinite, the bad infinity is represented by several instantiations. In other words, there is a plurality of bad infinities. Here is a list of examples of what Hegel does not have in mind concerning the true infinite: “The true infinite is not God, not perfection, not the summum bonum, not the universe as a whole, not a measureless substance or an infinite magnitude, not some form or species or pure concept or pattern existing outside things; nor is it empty repetition or the spurious infinity of infinite lines or an infinite regress” (Davis, 2012, 183). Such examples are the instantiations of the bad infinity. In the following part I will discuss: (i) why the latter is labeled as bad, and (ii) provide a positive definition of the true infinite under the category of quality.

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True Infinite regarding quality

Bad Infinity via negativa to true infinite

In total there are four ways in which the bad infinity can be represented. “First, there is endless finitude. Second, there is unceasing, infinite being that is co-extensive with, but qualitatively distinct from, finitude (and in which finitude as such thus vanishes): what we might call ‘immediate’ infinity. Third, the infinite takes the form of the ‘non-finite’ […]. Fourth, there is the progress to infinity […] (Houlgate, 2022, 240)”. It holds true for all four that they are similar. Such similarity will be evident in detailed analysis.

· Endless finitude: “one finite thing ceases to be and thereby mutates into another finite thing, which ceases to be and so on” (Houlgate, 2022, 238). For example, my body decomposes and what remains persists through time in another finite thing. In this case the infinite is a progress of finitude (of ceasing and dying), where one finite thing is replaced by another.

· Co-extensive infinite being: in endless finitude we have focused primarily on instantiations of what has persisted. Now we redirect our attention to the thing that persist through time. So, we put finite things away and see only the “matter” that is immortal. One can imagine some pantheistic view or the God of Spinoza. “The finite has thus vanished into the infinite and what is, is only the infinite (SL 110).” The truth of those finite things is the infinite itself that is qualitatively different and constitutive of the finite; therefore, finite things do not have an independent existence of their own.

· Non-finite: this kind of infinity is marked strictly by negation. It is not like anything finite. Hegel usually refers to this kind of infinite as a beyond. It lies beyond the finite; thus, there is a limit to a finite thing that makes a distinction between the finite and the infinite. “And so [infinity], as existent and at the same time as the non-being of an other [of the finite], it has fallen back into the category of the something, […]” (SL 110). Therefore, for the finite and the infinite, it holds true that: “each is placed in a different location” (SL 111). The infinite is literally something that is beyond the finite. There are two separate worlds so to speak – for instance, one here on Earth and the other in heaven. The criticism Hegel raises is the following: if we were to speak about the infinite as something beyond, separate, and distinct from the finite, we must admit that there is a limit that does the separating. However, such a limit is not only a limit for a finite thing, but it also divides primarily the finite from the infinite; therefore, it is a limit for both the finite and the infinite. Thus, such an infinity is just another finite thing. Say, for instance, there is me and the infinite universe. My skin is a border (limit) that separates me from the vast universe; the latter can go on and on away from me, yet my body and its insides are not the universe. My skin, as a limit, is a reminder of the infinite where it suffers its finitude. The same critique Hegel applies to the co-extensive infinite being. While it is something distinct from the finite, it is marked by a different quality; thus, there is some difference, in other words limit.

· Progress to infinity: this last notion may and should resemble the very first one; however, this one is enriched with the idea of the beyond or the limit. We start with one finite thing and instead of its death we have its passing into the world of the beyond. It transcends its finitude. We can find the same idea in Christianity: when someone dies, their eternal soul lives in heaven and thus continues. However, from the previous conclusion we know that this kind of infinity – beyond the finite – is not true because such an infinite is in fact finite. Thus, we have returned to where we started – finitude. Yet when something finite dies, there is something that remains; the parts of a finite thing mutate into another finite thing. But, when there is something that persists, it is infinite and as such different (distinct) from the finite. It is non-finite. Since it is something different from the finite, there must be a limit. The limit for an infinite thing means finitude. And so on ad infinitum. “This alternating determination of self-negating and of negating the negating is what passes as the progress to infinity, which is accepted in so many shapes and applications as an unsurpassable ultimate at which thought, having reached this ‘and so on to infinity,’ has usually achieved its end” (SL 113).

To sum up, the bad infinity is in general characterized by an endless progress and a strictly maintained division of the infinite as the beyond of the finite. This piece of knowledge will serve us as a point of departure to grasp the concept of the true infinite – the latter cannot stand on a never-ending repetition combined with two separate entities. However, the progress to infinity already discloses the inner nature of the true infinite in an implicit manner.

True Infinite as a Process

By observing the evolution of the infinite progress from a broader perspective, what we can conclude about it? We see that the finite passes into the infinite and at the same time we can see also that the infinite passes back into the finite. Each mutates logically into the other – they transform themselves into one another. Therefore, they are in some way inseparable. The bad infinity as a progress implicitly demonstrates that when one is separated from the other, it changes itself into its opposite. Thus, they form some kind of dynamic unity.

In my view, the perspective of unity has the greatest importance here. In thinking about the finite and the infinite, one must keep in mind that they are just moments of a certain movement. Being a moment of something means that the thing is not separated from it; it has some relation to the whole of which it is a part. “This inseparability is their concept […] There is not an infinite which is infinite beforehand, and only afterwards does it find it necessary to become finite, to go forth into finitude; the infinite is rather for itself just as much finite as infinite” (SL 123, R1). In this sense they are equal; there is no primacy superiority or domination; one without the other does not make any sense. To think them both at once, one must think of: “the nature of the infinite is that it is the process in which it lowers itself to be only one of its determinations over against the finite and therefore itself only one of the finites, and elevates this distinction of itself and itself to be self-affirmation and, through this mediation, the true infinite” (SL 118).

For an easier demonstration Hegel provides simple representations for both the bad and the true infinity. The straight never-ending line that stretches itself to infinity is the bad infinity. On the other hand, the circle expresses the sphere where the finite (a circle that occupies finite space) contains infinity in itself – where there is no beginning and end.

So far, we have defined the concept of the true infinity by terms like ‘inseparability of finite and infinite’, ‘unity and its moments’, and ‘process-movement’. Now, it is a valid question to ask: why do we hold then the finite and infinite as two moments, when the concept is defined as unity or inseparability? Why not say that infinity must be regarded in terms of a process and drop the distinction of the two altogether? In this scenario, one must answer that the true infinity is not only a process, but also a self-relation (Davis, 2012, 183). It is a relating of one to itself. However, we can speak of a relation only when there are at least two relata, so what exactly is relating to what in the self-relation? To answer this question, I have to go one step deeper.

The simpler resolution could be that the two relata are the frequently mentioned finite and the infinite. Yes – but the justification for such an external connection cannot stand just on the assertion that we should look upon the true infinite as unity or as one process. To resolve the issue, we have to go back to the beginning of the discussion about the infinite. Hegel states that in general the infinite can be defined by the categories of being and becoming, however, the category of existence (Dasein) has no place in such a definition because existence belongs to finite things (SL 108). I will not explain the category of becoming; it is evident that in order to understand a process, one has to think of something becoming something else and thus evolving. So, the focus should be put on the difference between being and existence. Such a difference could be defined by the following: everything has being, and it does not matter whether it is contradictory, made up or abstract object etc.; on the other hand existence belongs exclusively to things that are in the world so to speak. In short, they have some representation in the time-space dimension – meaning being-there (Dasein). It makes sense to say that the Pythagorean theorem does not exist because we cannot discover it somewhere in nature; nonetheless one cannot deny that it is in some way. Coming back to the infinite, yes, in its general sense it does not have an existence. It is an object of thought.

In my opinion, Stekeler-Weithofer rightly brings into the discussion the following dichotomies: “[t]he negation or contrast between ‘finite’ and ‘infinite’ corresponds in a certain sense to the contrast between ‘being-for-itself’ and ‘being-in-itself’ or ‘the particular’ and ‘the universal’ ” (Stekeler, 2019, 483).[1] And now comes the crucial point: to truly understand the self-relation of the true infinite means to understand the finite and infinite as the particular and the universal. Therefore, we can conclude that the finite and the infinite form a unity; however, such a unity is not indeterminate, we know that we cannot separate those two relata, yet there is some minor distinction between the two. Such a distinction is established by the division of the particular and the universal, or in another words, the self-relation of the relata is the relation between the particular and the universal and such a relation is a process. “As Hegel recognizes, the correct understanding of the concepts of the infinite, the eternal, and the trans-situational lies in the consideration of processes, whereby both the finite – namely, the limited existence of an individual thing or the finite life of a single living being – and the infinite, as it is sublated in the self-reproducing form of finite processes, are processes” (Stekeler, 2019, 486).[2]

After this long theoretical discussion here is an example that summarizes and ties everything together. Let us pick a concrete human being. This individual would be considered by all of us as a finite being – we all know that they will die someday. This person is a particular representative of the human Genus. The latter is the universal. To think in terms of bad infinity in this scenario would be to think that the Genus and the particular human being are two distinct separate entities, or that the point of humans is to grow in numbers ad infinitum. On the other hand, the true infinite means seeing that two particular human beings (finite moments of a process) in reproduction (the process itself) can create a new representative of a genus (self-relation of the genus and an individual). The genus is not something alien to humans, some alien force; it preserves itself only in relation of two individuals, thus creating a new individual that is a holder of the same genus. This is precisely what is meant by self-relation: that the human as genus exists in relation to the individual. Therefore, human beings are not only finite, but also infinite in the process of reproduction. The true infinity, according to Hegel, therefore has also this kind of existence or “thereness” in the world (SL 118-119).

“This, Socrates,’ she said, ‘is the mechanism by which the mortal partakes of immortality, both in body and in every other respect. The immortal does so in a different way. So, do not be surprised that every creature naturally reveres its own offspring, since this eagerness and love attends upon everything for the sake of immortality” (Plato, 2025, 208 B).

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[1] Original text: „Die Negation oder der Kontrast »endlich – unendlich« korrespondiert in gewisser Weise dem Kontrast »Fürsichsein – Ansichsein« oder »Einzelnes – Allgemeines«.“

[2]Originil text: „Das rechte Verständnis der Rede von Unendlichem, Ewigem, Situationsübergreifendem besteht, wie Hegel einsieht, in der Betrachtung von Prozessen, wobei sowohl alles Endliche Prozess ist, nämlich begrenztes Sein eines Einzeldings oder endliches Leben eines einzelnen Lebewesens, als auch das Unendliche, wie es sich aufhebt in der sich reproduzierenden Form endlicher Prozesse.“[2]

Bibliography:

Davis, A. (2012). HEGEL’S IDEALISM: THE INFINITE AS SELF-RELATION. History of Philosophy Quarterly, 29 (2), 177–194. http://www.jstor.org/stable/23212827

Euclid. (2008). Euclid’s Elements of Geometry (R. Fitzpatrick, Trans.). Euclidis Elementa, edidit et Latine interpretatus est I.L. Heiberg, in aedibus B.G. Teubneri, 1883–1885. https://farside.ph.utexas.edu/Books/Euclid/Elements.pdf

Fraser, C. G. (2005). Joseph Louis Lagrange, Théorie des fonctions analytiques, first edition (1797). In I. Grattan-Guinness (Ed.), Landmark writings in Western mathematics, 1640–1940 (pp. 258–276). Elsevier. https://cfraser.artsci.utoronto.ca/lagrangetheorie.pdf

Harris, H. S. (1997). Hegel’s ladder I: The pilgrimage of reason. Hackett Publishing Company.

Hegel, G. W. F. (1970a). Enzyklopädie der philosophischen Wissenschaften im Grundrisse II. Suhrkamp Verlag.

Hegel, G. W. F. (1970b). Hegel’s philosophy of nature: Encyclopedia of the philosophical sciences in basic outline Part II (A. V. Miller, Trans.). Oxford University Press.

Hegel, G. W. F. (1970c). Enzyklopädie der philosophischen Wissenschaften im Grundrisse III. Suhrkamp Verlag.

Hegel, G. W. F. (1971a). Vorlesungen über die Geschichte der Philosophie I. Suhrkamp Verlag.

Hegel, G. W. F. (1971b). Hegel’s philosophy of mind: Encyclopedia of the philosophical sciences in basic outline Part III (W. Wallace, Trans.). Oxford University Press.

Hegel, G. W. F. (1977). Phenomenology of spirit (A. V. Miller, Trans.). Oxford University Press.

Hegel, G. W. F. (2010). The Science of Logic (G. Di Giovanni, Trans.). Cambridge University Press.

Hegel, G. W. F. (2018). Wissenschaft der Logik (G. Lasson & W. Jaeschke, Eds.). Felix Meiner Verlag.

Hegel, G. W. F. (2015). Encyclopedia of the philosophical sciences in basic outline (Part I: Science of logic). Cambridge University Press.

Hegel, G. W. F. (2023). Phänomenologie des Geistes (16th ed.). Suhrkamp Verlag.

Houlgate, S. (2022). Hegel on Being:Volume 1. Bloomsbury Academic.

Houlgate, S. (2022a). Hegel on Being:Volume 2. Bloomsbury Academic.

Levy, A. (2002). Basic set theory. Courier Dover Publications.

Pinkard, T. (1981). Hegel’s philosophy of mathematics. Philosophy and Phenomenological Research, 41(4), 452–464. https://doi.org/10.2307/2107251

Plato. (2025). Syposium (D. Horan, Trans). Foundation of Platonic Studies [online]: https://www.platonicfoundation.org/translation/symposium/

Stekeler, P. (2005). Mathematical thinking in Hegel’s Science of Logic. In Deutscher Idealismus und die gegenwärtige analytische Philosophie / German idealism and contemporary analytic philosophy (pp. 243–260). De Gruyter. https://doi.org/10.1515/9783110179545.243

Stekeler, P. (2014). Hegels Phänomenologie des Geistes: Ein dialogischer Kommentar. Felix Meiner Verlag.

Stekeler, P. (2019). Hegels Wissenschaft der Logik: Ein dialogischer Kommentar. Felix Meiner Verlag.

Westphal, K. R. (2009). Cambridge companion to Hegel and 19th-century philosophy. Cambridge University Press.

The room is packed with students, slowly puffing on their cigarettes, completely unaware that future generations will envy this privilege of smoking during lectures. Félix, sitting inconspicuously at the edge of the room, keeps trying to perform a smoke trick we would today call a French inhale. His goal is obvious: he wants to impress the girl sitting to his right. Although everyone can see that he is blown away with her, he pretends otherwise.

Jacques Lacan ends his psychoanalysis lecture with the words:

“There is no such thing as a sexual relationship.”

Instead of an ordinary cigarette, he is smoking a nearly broken Cuban cigar that Sartre brought him back from a visit to Fidel Castro. The obvious fact that everyone is eager to leave is interrupted by a remark from Félix.

“What do you mean when you say there is no sexual relationship?”

Lacan takes a breath and begins.

“You see, Mr. Guattari, sex is never merely a matter of two people. Something I call fantasy always intervenes in copulation. It is a sort of third element that allows the pair to experience pleasure; without it, sex is merely mechanical movement, which by itself is insufficient for climax—indeed, I might even say that climax is impossible without it. One could summarize it this way: whenever there are two people, there are really three.

Fantasy is not simply about fulfilling, for example, sadomasochistic desires with one’s sexual object. Rather, it concerns the imaginary position from which we observe ourselves during intercourse, the way we reflect upon ourselves from the outside. One participant may imagine how he will later boast to his friends about sleeping with such a beautiful woman, or he may imagine the gaze of a former lover, provoking pangs of jealousy…”

The student impatiently interrupts him.

“Jealous love is the very beginning of thought for Proust. I’m not saying it’s your Ursprungsidee as well, but perhaps Freud would object that this is merely your personal experience. German captures the relation perfectly: what is mine, mein, is merely an opinion, Meinung; therefore it need not necessarily concern truth.”

“As I have said in many lectures,” Lacan replies, “truth has the structure of fiction. Whenever we say something, it is no longer truly us—it becomes something foreign. Once spoken, words and sentences enter an unfortunate state in which fate subjects them to every possible atrocity of interpretation.”

But Félix persists.

“What is your conception of love?”

“Since we’ve already descended into philosophical and metaphysical nonsense, allow me to correct you. A conception is not something true; unlike the concept, it is only the concept as a whole that is truth. The realm of its manifestation is not words but actions.

I do not think love has anything to do with truth. Love always ends in some embarrassing declaration about how much someone loves us, where instead of aspiring to the heavens of truth we cling to the abstraction of words. Does it really matter how many partners or lovers we have, or whether we cheat, when nobody is willing to give us the universe?”

The lecturer pauses for a moment and, trying to bring the tiresome questioning to an end, continues:

“However, if you asked me about my ideal vision of intercourse, it would look something like this: a woman is lying on her stomach reading a book. I begin making love to her from behind, and after my five-minute masterful performance I ask her how she liked it. She replies that I should stop bothering her with pointless questions because she still has two paragraphs left to finish reading. Voilà!”

Smirks and a subtle tension spread through the room. Only the more intellectually gifted students—or rather, almost everyone except Félix—understood what Lacan was getting at. Some were so intrigued that they even stopped thinking about the joint they planned to smoke after school.

Félix knows he has already gone too far, and therefore he must see it through. After all, only he who can destroy a thing truly has power over it.

“In my opinion, you’ve simply been disappointed in love a few times, and now you’re inventing theories to conceal the fact that you yourself are incapable of loving. I think your affairs with the French elite are proof enough of that.”

At this point the discussion has lost all semblance of a dialogue between teacher and student.

Lacan slowly draws on his cigar, tasting the unpleasant bitterness of burnt tobacco. He spits out a few fragments that have stuck to his lips and tongue.

“What gives you the right to present your opinion as a fact?”

“Perhaps your own inconsistency.”

The lecturer decides that the best defensive strategy is attack.

“Love is giving something we do not have to someone who does not want it. Exactly as in your case with the girl sitting to your right. If you manage to win her over, perhaps you’ll convince me otherwise.”

Félix chokes on the smoke, bursts into coughing, and the rest of the room erupts in laughter.

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Everyone can relate to the feeling when you are trying to advocate a stance that murder is unethical, and suddenly, someone comes up with that one convincing example where the intentional killing seems justified. Yet, we are still inclined to agree that, for instance, sexual abuse, child pornography or child rape are, as such, bad, evil and wrong.

The aim of this text is to argue in favor of universalism in ethics. Most of the time when someone uses terms like universalism and ethics in one sentence, relativists start to jump from the nihilistic underground. I can hear their voices: “There is no such thing as universal ethics; there are different cultures—each with its special mix of norms and morals. To claim that there are universal moral standards cuts off all diversity and plurality of moral systems.”

Of course, there are different moral systems and standards; to argue against this is to commit intellectual suicide. No one denies that. However, to focus on each culture and by comparison demonstrate—and mostly bring to the light— the differences means to lose sight of the forest for the trees. The forest can consist of leafy trees or needle-bearing trees but it would still be a forest with trees. There is no culture or civilization without ethical norms, analogously, just as there is no forest without trees. Every society has a distinction between good and evil, between required actions and actions that lead to punishment.

The ethical norms may vary, precisely like the trees. Every group, every civilization, in the end, lives under different conditions, by different ideas and ideals, with different friends and enemies, and in a different historical period. Although such things are variable, there are universal, abstract, and therefore vague frameworks and areas upon which we and others will agree.

I claim that if we take the example of murder—say it means intentionally killing someone who is one of us—all contemporary cultures would agree that murder is bad, wrong, etc. And at the same time, claiming the exact opposite would constitute an amoral stance. In many examples we can show similar universally valid ethical positions (lying, betrayal…). Yet there are many more examples where we would consider certain actions relative to a specific moral standard. For example, we in the West would claim that certain deeds of Muslim men are immoral towards their women because we would consider that behavior as unfaithful or inappropriate. Thus, there is a much larger set of examples that stand against universalism and I recoginze them.

The problem of vagueness

To see my point more clearly, keeping in mind the last-mentioned example about the Muslim men, I claim that Muslim men would also argue too that infidelity as such is bad. The concept of infidelity strikes them as well as a wrongdoing. The difference, between the Western and Muslim worlds, lies in the standards or criteria that we apply to actions and behavior—these differ greatly.

From now on, my thesis is: Ethical universalism is about concepts, meaning abstract entities. Because, if it were about concrete norms, specific situations, or extreme cases, it wouldn’t be universalism anymore. Many expect universal ethics to provide norms, values and ethical clarity in every situation, under any circumstance. Such universalism is unrealistic because it would require knowledge of every possible situation; such knowledge currently unimaginable. So too is the expectation that a human being can come up with such a general and everlasting ethical theory; expectations of such a theory are absolute not universal. Therefore, criticizing universal ethics for being vague is like criticizing mathematics for being too abstract when its objects are abstract entities…

Let’s take a famous example of a universal ethical stance, Kant’s ethics, and a concrete situation: you are hiding Jews and a Nazi officer knocks on your door. Of course, lying in general is bad but in this situation you know that if you will tell the truth, the people in your cellar will eventually die. To follow the universal principle “lying is bad” leads to killing. —BUT—!!! We were not formulating that principle on a background where you are forced to choose: either a lie or death. Thus, when we say that lying is bad we do not imply that it holds in every situation or circumstance. If you were to follow principles so blindly, you would be considered a moron.

Another great example is the situation during the COVID-19. A hospital is a finite place with a finite amount of space and breathing apparatuses. Of course, when you are in an extreme situation—one that happens less than five times in your life :)— where you face a decision to either provide medical help for an 85-year-old lady or save a younger man who has recently started a family, you choose the younger man. You have to be a utilitarian in that situation because, given the circumstances, it is the best you can do. Or, to take a different example, when you are a prime minister in a tough multilateral meeting, you sometimes have to be a pragmatist. Otherwise, you probably wouldn’t secure the strategic raw materials that your country desperately needs.

What should universalism in ethics mean

When I say that the objects of ethics are universal entities, I mean that literally. For something to be an ethical principle, it has to be universal (one can easily doubt also the existence of such principles but let’s assume that they exist). From what I have said, it follows that: when something that claims to be an ethical principle is not universal, it cannot be an ethical principle. Yes—to relativize ethics means to fall into nihilism. Without universal ethical principles there is no ethics.

What do I mean the term “universal”? Universal in this case means: it applies to all. But what is the trick that can overcome every relativistic view? Moral relativists argue based on the plurality of principles and how they usually contradict themselves. In the domain of law, for example, it can be that two norms on the same level are contradicting each other; however, the contradiction itself doesn’t prevent the laws from being particular or non-universal. In such a scenario there are two possibilities for resolving the situation. i) first, the judge himself decides which one to follow, or ii) the legislator comes up with a new law which resolves the contradiction.

Relativists are trying to convince us of a fact that we all already know. Yes—two cultures have different principles, just like two families living next to each other. Universalism in ethics doesn’t imply a scenario where two different cultures have identical concrete principles. However, we are creatures that need to have principles in order to function; thus we can—and in the end must—create a space or build a consensus around which rules are going to apply to all. A real-life example: when two different nations meet on the level of diplomacy, them simply follow the protocol; if someone breaks it or behaves inappropriately the meeting is over.

De dicto and de re

In logic or semantics we differentiate between two modes of expression: de dicto and de re.

Belief de dicto is belief that a certain dictum (or proposition) is true, whereas belief de re is belief about a particular res (or thing) that has a certain property.

(1) Ralph believes there are spies. [de dicto]

and

(2) There is someone whom Ralph believes to be a spy. [de re]

Now, my aim is to apply this distinction to the ethical sphere. My idea is to say that our moral principles are always formulated in the de dicto mode: ‘lying is bad’ , ‘murdering is evil’ . They are never pronounced in the way of: ‘John took a knife and killed Annie, therefore, he is evil.’ This is because we all know that such a description is not enough to qualify someone as a murderer. Annie might have been the first to try to murder John and he just acted in self-defense.

In fact, this distinction resolves the problem with our Muslim man example. I think, again, that he would agree with us that ‘infidelity is bad’ de dicto. On the other hand, when someone from the West observes his actions toward a potential new wife, they tend to see such behavior as unfaithful towards the first official wife. Thus, in the mode of de re we express the property of Mohammed being unfaithful. Evidently, he doesn’t think of himself as breaking the ethical principle, thanks to a different meaning attached to the term “infidelity”. Although we and Mohammed agree that infidelity is bad, we see his actions differently. But, at the same time, the principle holds universally. There is no breaking of the principle and there is no relativity within it. The relativity is in our understanding and the meanings of our concepts such as fidelity, freedom, and equality because, in accordance with those meanings we judge others as unfaithful, a murderer, or a thief … However, Infidelity, Murder and Theft —as abstract concepts— are and always will be universally bad.

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Broackes, J. (1986). Belief De Re and De Dicto. The Philosophical Quarterly (1950-), 36(144), 374–383. https://doi.org/10.2307/2220191.

If there is a queen in sciences, it has to be mathematics. No one can really doubt its significance and importance in almost all scientific domains. Whether we go into the realm of physics (which is formalized to the point where one works almost only with mathematical formulas), or we pay a visit to the field of logic, we are destined to meet mathematical notions, therefore, mathematical thinking. Keeping this in mind, my objective is to demonstrate the limits—why mathematical thinking cannot show the whole picture. In short: why isn’t relying on mathematics enough if we want to explain the world completely?

In demonstrating my aim I will proceed by following an argument in Hegel’s Phenomenology of Spirit. However, there is no need to worry about metaphysical demons or ghosts. The exposition of the argument is set in clear terms and by well-known notions.

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Limitless truth

In this part I will reconstruct objections that Hegel had risen against mathematics in the preface to Phenomenology. The theme of these dozens of pages is wrapped in the talk about usual suspects: Truth, Knowledge, Substance, Subject, Absolute and so on. A few sentences before mentioning mathematics, Hegel defines dogmatism, it: “is nothing else but the opinion that the True consists in a proposition which is a fixed result, or which is immediately known” (PS 23, §40). Thus, when we speak about the Truth, one sentence or some immediate piece of knowledge is not enough. What are then the strict conditions for knowing the Truth? To put it in a short and abstract way, it must be reached by philosophical endeavor – by reflexive act, time, and effort. Yes – I agree, it says almost nothing, yet it contains an insight. Hegel wants to say that non-philosophical domains cannot tell the Truth alone, to reach the latter philosophy is needed.

Having that in mind let us work with an assumption that the Truth cannot be expressed in one result sentence. Hegel then immediately brings onto the stage historical and mathematical truths as examples. In the case of historical truths, the accusation is that their character is contingent. Take as an example the following fact: ‘the second world war ended in 1945’. Not only we can easily imagine the end of war a year before/after 1945 or in any other year, but also the fact speaks about one particular event abstracted from all other events, reasons, conditions, causes, etc. Everyone can learn such “truths” by hearth. That holds true also for mathematical truths but in this case, we are more likely to disregard someone as a mathematician who “knows” math in such a way. To start properly, here is an example of mathematical theorem Hegel uses trough out:

We all know that the latter theorem is called Pythagorean theorem, and that it says something about right-angled triangle. We have just said that spelling out letters and numbers in the above-mentioned order is not enough for accomplishing the conditions for knowledge. One could simply say that without knowing the proof of the theorem, one cannot claim the status of knowledge.

“Yet, even in mathe­matical cognition, the essentiality of the proof does not have the significance and nature of being a moment of the result itself; when the latter is reached, the demonstration is over and has disappeared. It is, of course, as a result that the theorem is some­thing seen to be true; but this added circumstance has no bearing on its content, but only on its relation to the knowing Subject.” (PS 24, §42)

To provide a mathematical proof for certain theorem – in Hegel’s eyes – means to put down only the “genesis” of the thing. What is essential, is not reflexively comprehended – stays hidden in the knowing subject – without any presence in the result or proof itself. Philosophy, on the other hand, is more transparent, it provides both: the essence of the thing (concepts) and its existence (result and its genesis). In math, Hegel argues, are essence and existence external to each other. “The means employed, construction and proof, no doubt contain true propositions, but it must none the less be said that the content is false.” (PS 25, §43) Why is the content false, when the proof contains a true proposition? As a demonstration we will use the Pythagorean theorem. In the proof, Hegel claims, is our rectangular triangle torn apart, “dismembered”, into another figures (squares), and only after the procedure, is the original triangle reconstructed back again. To put it simply, in the process of proving, we lose the sight of the triangle and see only fragments which belong to different geometrical figures. Thus, the content as such is false because it is primarily about squares, not the triangle. (PS 25, §43)

But still, isn’t it too abstract? Can we make it a bit more concrete? Yes, of course, Primin Stekeler-Weithofer provides more to the detail analysis. He claims that in the proof of Pythagorean theorem, one must stop thinking in terms of lengths (relations between shorter sides and hypotenuse) and start to see the thing itself as a matter of ratios between lengths and areas.

“Hegel’s ‘mystical’ comment thus suggests that the problem of length relations in the triangle appears difficult only if we think merely in terms of lengths rather than areas—more precisely, in terms of adding and subtracting areas, and the relation between area size and multiplication of lengths. In short, Hegel rightly criticizes a deficiency in mathematics teaching that mystifies proofs—for example, by failing to clarify how we operate with areas and with length multiplication “[1] (Stekeler-Weithofer, 2014, 276-277).

Because of this failure to clarify the “essence” – elementary concepts – math is regarded as defective. Or, put other way around: “[t]he externality of the process is a mode of falsity in the properly speculative sense, because the mathematical entity is essentially an object of consciousness” (Harris, 1997, 115-116).

An example of mathematical procedure and proof

This part shows the above mentioned limits of mathematics in down-to-earth manner. Okay, take an example of simple equation.

Our aim is to find out the value of ‘x’ . Then the problem is: what is the value of x ? The final answer to our problem, or the final result, is x being equal to 8,5. Let’s prove that statement.

Proof:

1.)

2.)

add 35 to both sides

3.)

divide both sides by 10

We did proceed by valid rules and obtained the correct result. The whole time we were led by the aim of finding out the value of x. However, I can pose the following question: why did we proceed from step 1.) to step 2). in this particular way (by adding 35) rather than dividing by 10 first? In more concrete fashion: what is the criterion we applied for first adding and then dividing? Hegel thinks that those criterions are not exposed and stay hidden during the proving—or, rather mathematics itself is not able to expose them. Of course, one can first divide by 10 and then add 3.5 to each side and it will be also valid. In fact, there are many ways how to proceed but we all agree that some are easier, or more clear, or simpler, or one of the best. Yet those are qualities of that ways of procedures. Yes—you guest it right—and those qualities are precisely the abstract criterions why we decide to calculate rather in this or that fashion.

However, Mathematics is a study of quantity , not quality. Therefore, mathematics cannot discover or reveal the nature of those other categories we apply to obtain the knowledge about the world. If a Mathematician says that he had proceeded in this particular way because it is the simplest, he is not speaking from the domain of mathematics anymore. Simply, because he is speaking about qualities of certain way of proving.

Philosophy, on the other hand, speaks about qualities or features of things. Therefore, reveals both i) concepts it uses, and also ii) the genesis of its results.

Aftermath

Let us return to what Hegel calls result – so-called truth expressed in one sentence. His critique has one more special side to it. By the way, we can encounter such critique not only in Phenomenology, but also in Logic, there Hegel refers to such math results as dead sentences. Concretely: “In a non-actual element like this there is only a truth of the same sort, i.e., rigid, dead propositions” (PS 26, §45). They are dead because their nature is purely formal, they have no direct link to physical world of our everyday experience – of course that does not mean that they are unimportant. For Hegel, every formalism means death, frozen image of abstract kingdoms. Such realms: “refer to the world of experience only via appropriate projections. Hegel addresses such projections under the title “measure.” This holds for talking about geometrical forms as well as about numbers” (Stekeler-Weithofer, 2005, 246).

Mathematical objects, theorems and results are abstract-formal notions, as such they find their use only in Physics, Chemistry, Biology etc.… The problems we touched in this short text are methodological. In my mind, Science alone cannot explain the world, everything cannot be reduced to applied mathematics or translated into the mathematical language. There are abstract criteria we apply in our everyday life—as we showed it is the case also with mathematics. Hegel calls those criteria categories, one can simply call them notions or values. Nonetheless, to understand the world one has to understand also those abstract entities because we judge the actions and things by criteria that have a different nature than quantity.

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[1] Original text: „Hegels ›mystischer‹ Kommentar sagt demnach, dass die Frage nach den Längenverhältnissen in D nur dann als schwierig erscheint, wenn wir bloß an die Längen und nicht an die Flächen bzw. an Flächenadditionen und Flächensubtraktionen denken, ferner an den Zusammenhang von Flächengröße und Längen-Multiplikation und wenn wir deren Beziehung zu Längen-Proportionen aus dem Auge verlieren. Kurz, Hegel beklagt sich zurecht über einen Mangel im Mathematikunterricht, der die Beweise mystifiziert, indem er z. B. nicht klar macht, wie wir mit Flächengrößen umgehen und mit Längenmultiplikationen.“

Bibliography:

Harris, H. S. (1997). Hegel’s ladder I: The pilgrimage of reason. Hackett Publishing Company.

Hegel, G. W. F. (1970a). Enzyklopädie der philosophischen Wissenschaften im Grundrisse II. Suhrkamp Verlag.

Hegel, G. W. F. (1970b). Hegel’s philosophy of nature: Encyclopedia of the philosophical sciences in basic outline Part II (A. V. Miller, Trans.). Oxford University Press.

Hegel, G. W. F. (1970c). Enzyklopädie der philosophischen Wissenschaften im Grundrisse III. Suhrkamp Verlag.

Hegel, G. W. F. (1971a). Vorlesungen über die Geschichte der Philosophie I. Suhrkamp Verlag.

Hegel, G. W. F. (1971b). Hegel’s philosophy of mind: Encyclopedia of the philosophical sciences in basic outline Part III (W. Wallace, Trans.). Oxford University Press.

Hegel, G. W. F. (1977). Phenomenology of spirit (A. V. Miller, Trans.). Oxford University Press.

Hegel, G. W. F. (2010). The Science of Logic (G. Di Giovanni, Trans.). Cambridge University Press.

Hegel, G. W. F. (2015). Encyclopedia of the philosophical sciences in basic outline (Part I: Science of logic). Cambridge University Press.

Hegel, G. W. F. (2023). Phänomenologie des Geistes (16th ed.). Suhrkamp Verlag.

Pinkard, T. (1981). Hegel’s philosophy of mathematics. Philosophy and Phenomenological Research, 41(4), 452–464. https://doi.org/10.2307/2107251

Stekeler, P. (2005). Mathematical thinking in Hegel’s Science of Logic. In Deutscher Idealismus und die gegenwärtige analytische Philosophie / German idealism and contemporary analytic philosophy (pp. 243–260). De Gruyter. https://doi.org/10.1515/9783110179545.243

Stekeler, P. (2014). Hegels Phänomenologie des Geistes: Ein dialogischer Kommentar. Felix Meiner Verlag.

Stekeler, P. (2019). Hegels Wissenschaft der Logik: Ein dialogischer Kommentar. Felix Meiner Verlag.

Westphal, K. R. (2009). Cambridge companion to Hegel and 19th-century philosophy. Cambridge University Press.

The history of philosophy is Philosophy itself. Therefore, without knowledge of this history, one cannot know what Philosophy is. I encourage you to join me on this series of texts where I will go through almost all philosophers and philosophies. I will not offer the usual history of philosophy that you can encounter in textbooks or Youtube summaries. My method of procedure is the following: the aim of every text in this series is to take a specific philosophy of the tradition and put it next to the philosophical attitudes, conceptions and views that followed, overcame or criticized it. The point is to address both concepts and problems in a dialogical manner, thus showing where the concrete thought resides, in short: how and why we have shifted from that view to another. In my mind, this is the only valid method.— Speaking in a crude way about Thales and making fun of the fact that he thought that water is the fundamental principle of everything means only that we apply today’s standards to the past. Such judgments are faulty, distorting and bending ancient ideas. Another misleading view stands outside history itself, judging what was right or wrong, true or false… as if the person making the judgment knows the truth with a capital T or confuses philosophy with mathematics where truth conditions are clearly set. Nonetheless, my hope is to present every stage clearly, creatively and faithfully to tradition. My second hope is to surprise learned scholars of philosophy. And my very last hope is to bring old—but valuable—thoughts and figures back to life, so they can speak to us once again. Well then, I wish you a pleasant reading.

Introduction

We are in ancient Greece where thoughts, physical phenomena and destiny are shaped by both the Gods and humans. The Gods themselves—much like humans—have their ruler. Polytheism forms the atmosphere on every island and mainland. Your education is shaped by legends and myths, thus mostly by stories. You have probably heard about great kings and heroes who fought hard battles; on the other hand, life does not consist only of mythical representations. There is some knowledge of different cultures and languages and you have came across abstract objects like numbers.

You are at the local fish market, you see people gathering around two men and you eavesdrop on their conversation.

[Since Thales was the first philosopher, his co-speaker will be constructed figure called Mythos, one can simply imagine Homer or Hesiod instead, I decided otherwise.]

Where it all started…

MYTHOS

Thales, why would you say that Water is the fundamental principle of everything? Do you mean that the great Poseidon is the strongest God, or what?

THALES

I did say that Water is arché. That doesn’t mean Water is only the fundamental principle, arché means also an origin or first cause — cause in the sense of an explanation, or a culprit; the one who is guilty of something, the one who caused something. I will give you an example: If you take any direction, you will eventually come into contact with a lake, river or sea. If it is too cold, what changes your surroundings? —Ice and snow. If it is too hot, what is the cause of drought? — Lack of moisture. What can be both the blessing and the danger? — Rain. What is running your organism? —Liquids. Thus, I concluded that whatever example you name, whatever process you analyze, wherever you go, you eventually encounter Water as the cause or the necessary condition. Therefore, Water is arché.

MYTHOS

So, you cut the Gods out of the picture?

THALES

Principally—yes. I reduced the plurality of phenomena to one simple element. There are many things in the world and I consider Water to be the most important of them all. It is a more efficient way to perceive the world. If you let yourself believe that your life is determined by the will of many gods you cannot understand—and therefore—explain much.

MYTHOS

I agree, it may be efficient in some cases but, on the other hand, isn’t it a bit too reductive to see the world only through one lens? You may “understand” the phenomenon of Water but it is in relation to other elements. Yes, one has to drink, however, one has to eat also. And food needs both water and soil.

THALES

I am not saying that other things do not exist or that they are not important. My point was that it is much better to find and understand one universal element that is present in every case, rather than admit that there is a plurality or complexity of things that we do not know how they work together.

MYTHOS

The Cosmos is a complex creation. I admit that. Although we might not have the whole picture, we know certain things. For instance, we know that Demeter goes once a year to the Underworld to see her daughter Persephone, during her stay cold and winter come.

THALES

Such an assumption may be true, yet my view offers some valid predictions too. Here is one example that says it all. If you work with the hypothesis that Water is arché and at the same time you observe that there is less and less rain falling every year, you can by some calculation come to the conclusion as to which year there will be no water on the field and thus no harvest.—Actually I did the calculation and bought up all the grain in our town a year before the drought came. At first everyone was making fun of me: “Why is he collecting such tons of wheat? Guess his wife has a big appetite.” The next year they were begging on their knees just for a small piece of bread. I replied: “Why? Guess your wife has a big appetite. Ha ha ha.”

MYTHOS

My goodness. That’s a kind of cruel thing to do. The Gods will certainly punish you.

THALES

I am not afraid of their punishment. Only a lack of Water can punish me. Gods know only how to spread fear and guys like you help them. In the end, only the thirsty can experience true fear for their life. Everyone can be thirsty, even fearless Achilles, thus, the heel wasn’t his greatest weakness.

MYTHOS

I see. And I truly feel for you. Yet, here is my piece of advice. It sometimes doesn’t really matter whether the Gods exist or not. And we people aren’t that stupid to think that if someone were to climb Mount Olympus, he would see Zeus sitting on his throne screwing up Thetis. Gods aren’t just waiting somewhere to be found and people know that reality is a bit more complex. But. You should be concerned at least about the people who truly believe that the Gods do exist. If I were you, I’d be afraid of those. Speaking loudly about the Gods—like you do— brings troubles (and it really will). You live in a community where the Gods are present through rituals, offerings and sacrifices. You may be rich or wise but to get the whole polis riled up against you is not the smartest move. —To disrespect what they consider sacred is a mistake.

THALES

I expected everything. That you will moralize, that you will try to scare me—but those are not my practices. After all I am not saying that the Gods do not exist, for me everything is full of life— and even the Gods may play some role in this world. All that I am saying is that, I think, Water is the Principal and Universal Substance of all being. Even the great Zeus, when he’s practicing throwing lightning bolts, brings rain with it. I really don’t know how I should explain myself better… On the other hand, I have to agree with you that after that calculation experiment some people were pretty angry at me. They killed one of my horses and offered it to the Gods, hoping that they will send some rain. As the godlike Homer said:

"Now seek some means his fatal wrath to end,

With prayers to move him, or with gifts to bend."

MYTHOS

And you consider this to be the full understanding of the cosmos? Did your knowledge also predict the behavior of those people? I think you already regret those deeds that resulted in the death of your horse. Seems your theory isn’t that powerful. Thus I will answer to you also with Homer’s lines:

"Let me an ancient fact unfold

A great example drawn from times of old

Whom heaven adorns, superior to thy kind,

With strength of body, and with worth of mind!"

THALES

You are smarter than you seem. Full of ancient wisdom. But tell me:— you believe that everything in Heaven and on Earth depends on the aims and will of the Gods. If I were to test you, almost certainly you would answer me that you don’t know the will of the Gods because such a thing isn’t to be known. There is no knowledge of the Gods interests. Therefore, after all, you know almost nothing. My thesis doesn’t make a claim to be the ultimate knowledge. I think, thanks to the examples that I mentioned, that my conclusion is more reasonable and more intuitive than your proposition that there are many gods organizing our lives. I am not claiming to know all the effects, consequences and results of my teaching—yet such arrogance could be met in your circles, where one of you claims to know everything because of his divine origin. Now comes the time when I will be the one who gives advice:

Be more modest, abstract from the Gods and see the only thing that binds us all,

We do not have to guess or speculate, just admit what is before our own eyes that Water is the most precious of them all.

MYTHOS

You won’t convince me with Oracles, your theory is one-sided, don’t you see that. It may be in accordance with evidence but how would you explain destiny, where we should look for meaning, what’s the origin and the beginning of the cosmos? How would you persuade others who do not listen to reason? We pray to the Gods and make sacrifices because it gives us hope. Life is sometimes good but we often experience harsh conditions. Yes—when we are attacked and the fire expands, we are thankful for the extraordinary power of Water to calm the flames. In fact, we are thankful everyday when it slays thirst but there are for us much more important things than water—the exceptional feelings of Love, Pride and Glory. Yeah, Water is almost everywhere and so it is often worthless. Although the Gods can throw us into misfortune, one can be lucky thanks to sacrifices. But, as you said previously, Water could be also a danger. Thus, it doesn’t make us very hopeful.

THALES

I couldn’t disagree more…

MYTHOS

[Suddenly interrupts him]

… I don’t understand the point of why is your arché unique. Being the origin, fundamental cause or guiding principle, all such definitions are formulated by Religion, those are attributes of the Gods. In that case, you are swapping the features of supernatural beings with something much simpler and more ordinary. You lovers of wisdom are rightly considered to be in opposition to Myth and Religion. However, one has to acknowledge that you took over —or rather stole— from Religion some fundamental concepts like: chaos, the One, principle, first cause etc. and simply attributed them to Water. Thus, you suggest, when we are before the dilemma: what is the arché? Gods? Or something else that also fits godlike attributes, yet is much easier to imagine, encounter and is more intuitive. You think we would rather choose the second alternative? Your principle: “Let’s cut the mythos bullshit and instead let’s work with a much simpler hypothesis.” simply doesn’t work. You use the same language as we do, yet you speak about earthly phenomena…

THALES

You are right, it is no surprise that I don’t have any other language, notions, concepts or vocabulary. Though, I can explain my thesis using them.

MYTHOS

I met people like you. Speaking about the One, Universal, Fundamental … and Principle to all. They believed in one God. —What’s funny is, they were slaves to the Egyptians. No surprise …Many gods can overpower one alone. Yet, we can all agree that it’s not a fair fight…

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Philosophy of Science could be a dangerous business. Science is dangerous. Its results can kill many, then, what stance should we take on this issue? How to interpret findings? Or should I rather say constructs of science?

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Introduction

The text is intended as a revision of the famous article “Realism and the Historicity of Knowledge” by Paul Feyerabend. The aim of the first part is to reveal the shortcomings of the introductory part of the mentioned article. The content of the second part will be a comparison of the so-called constructs (atoms/gods) and their relationship to the constructors. I will mainly build upon the comparison of scientists to sculptors. I will show that Feyerabend is not a pure constructivist and acknowledges a certain form of objectivity.

Feyerabend and Analytical truths

Feyerabend states two assumptions at the beginning of his famous article. For the sake of correctness, I will present them in their entirety.

“The first assumption is that the theories, facts, and procedures that constitute the (scientific) knowledge of a particular era are the result of a specific and highly idiosyncratic historical development.

The second assumption is that what was discovered in this special and culturally conditioned way (and is therefore formulated and explained in special and culturally conditioned terms) exists independently of the circumstances of its discovery. We can separate the path from the result without losing the result. This assumption I will call the ‘separability assumption’” (Feyerabend, 1989, 393-394).

I will consider the second assumption to be Feyerabend’s definition of realism. His goal, in my opinion, is to demonstrate that the mentioned assumptions cannot be true at the same time. I will not go into the details and arguments that Feyerabend presents, because I agree with them. Although I think the argumentation of the article is correct, I will attempt to demonstrate a case in which we can think both assumptions simultaneously.

An example that satisfies both of the following conditions, specifically that it is:

• a theory, fact, and procedure which, as a result of a specific historical development, establishes knowledge, and simultaneously,

• exists independently of the conditions of its discovery,

is precisely a mathematical or logical theory. Of course, not every mathematical or logical theory has a character that would satisfy both assumptions. However, if we are speaking about Euclidean geometry or the law of tertium non datur, then these are entities that are, in their own way, trans-historical. The Pythagorean theorem will be true and has been true across thousands of years, the conditions of its origin do not really matter. “Just as the Pythagorean theorem held true before its discovery, logical laws also hold independently of whether anyone thinks them or not, and independently also of whether anyone uses them as model paths from one set of truths to another truth or not” (Gahér, 2013, 28). Furthermore, the Pythagorean theorem was “discovered” by several cultures independently of each other; it had a different name in China, a different one in Egypt, and another in Babylon (Benson, 2021). Yet despite this, it was precisely the same single piece of knowledge regarding the relationships of the sides of a right-angled triangle with the areas of the squares constructed over these sides.

Yes, one can counter-argue as follows. Formal, theoretical, and abstract objects may have a trans-historical character, they do not change, they exist independently, and different cultures understand them the same way. However, Feyerabend’s goal was not to investigate mathematics or logic. His examples are from physics, chemistry, and biology, so why drag purely theoretical sciences into it?

My answer then is as follows: yes, with a charitable reading, one can accept the assumption stating that Feyerabend’s critique of realism concerns only the natural sciences, because Feyerabend shows the relativity of the entities of these sciences. However, the acceptance of this assumption leads to the following conclusions:

i) Either the theories, entities, and laws of mathematics and logic are non-scientific knowledge, because Feyerabend’s first assumption speaks precisely about scientific knowledge.

ii) Or we accept that the latter mentioned are scientific knowledge, but Feyerabend’s assumptions do not account for them.

I think that conclusion (i) cannot be agreed with, and no one will agree with it either. Thus, only the second option remains. If, however, Feyerabend omits mathematics and logic or forgot about their scientific nature, then it must be admitted that his assumptions are set too generally.

Now I would like to return back to the beginning and finish the main argument. Conclusion: if we take Feyerabend’s assumptions literally, then we have not gotten rid of realism, because we have examples of trans-historical entities and truths. On the other hand, if we are charitable and read the assumptions as concerning exclusively the natural sciences (Science), then we must admit that they need to be reformulated, because their wording is vague.

Atoms, Gods, and Sculptors

In the final part of his article, which bears the title “Humans as Sculptors of Reality”, Feyerabend compares people to creators. “According to this account, scientists are sculptors of reality – but sculptors in a special sense” (Feyerabend, 1989, 404). In the sense that scientists not only causally act upon the world, but also create semantic conditions that connect old familiar effects with new projections. My goal in this part is therefore to demonstrate that there are projections and there are projections. I will not argue against Feyerabend; I will argue with Feyerabend against what let us operationally call pure constructivism – the meaning of this phrase represents a position where all constructs have an equivalent position: the fact that they are just a construct.

Gods, Atoms, and Their Similarities

At first glance, it might seem that Feyerabend places ancient gods and elementary particles on the same level in a certain sense (Anything goes!). In a certain sense, it actually is so. My point, however, is to show that these two heterogeneous entities cannot always be placed just side-by-side. What is the case, then, when they can be placed on the same level? It is that very negative stance toward trans-historicity. Feyerabend wants to say that if we accept the hypothesis of the independent existence of atoms, then naturally we should, based on the same standard, accept the independent existence of Greek gods (Feyerabend, 1989, 395).

A frequently repeated argument – against the god / for atoms – is built on empiricism – we have empirical measurements of atoms, but we cannot observe Zeus. Feyerabend, in my view, correctly says that empiricism and experiment cannot be the deciding criterion for whether some god exists or not, because a god is not an entity that will be waiting somewhere freely in nature for someone to come and observe it (Feyerabend, 1989, 398). But that, on the other hand, does not mean that the Greek gods were beings that had no manifestations we could observe.

“Gods could interact with people – this was allowed by their anthropomorphic conception, richly documented in the Homeric poems. In contrast, the revelation of a god (epifaneia) was part of a ritual accessible only to the initiated, meaning the mysteries; but it could also occur through intense thinking” (Hošek, 2004, 32). Moreover, any ordinary natural phenomena (lightning, a bountiful harvest, cooling temperatures) were considered manifestations of the gods, even offering repeated evidence.

A good example is the goddess of harvest, Demeter, who once a year departs to Hades to see her daughter Persephone. This departure of Demeter from the stage, and her distance from the human world, meant that the winter period (a period without harvest) was beginning. This myth, however, thanks to this repetition, also offered correct predictions – we know that: if Demeter goes to her daughter, then winter will occur (as long as winter always occurred, the entire implication will always be true).This might be too strong of a statement, but similarly to a scientific theory, the Greek gods also offer observable data, repetition, and predictions. Therefore, precisely these criteria cannot decide on the scientific status of atoms and the unscientific status of Greek religion. Let us try, then, to compare atoms and gods from another perspective.

Gods, Atoms, and Their Differences

Let us begin with what gods and atoms have in common, which is that they relate to some natural phenomenon. For the rest of the text, I will work with the example of lightning (for obvious reasons, it best connects atoms and Zeus). Let us now ask the same question – What is lightning? – to a scientist and to a believer in a Greek deity.

For the believer, as we already mentioned above, lightning is a manifestation of a deity – it is a force whose manifestation is that natural phenomenon we call lightning. For the scientist, lightning is a natural phenomenon, specifically a strong electrostatic discharge, or put in layman’s terms: a discharge of electrically charged particles with other particles. In any case, this is not about an exact scientific description right now. I want to say, however, that despite the fact that both see the same thing, they imagine something else behind this phenomenon.

What is that something else? Of course, a scientist who says that lightning is the consequence/manifestation of an electrical force explains almost nothing, saying nearly the exact same thing as the believer. The believer would merely swap one word – he would cross out the word “electrical” and write “Zeus’s” in its place. The essential difference lies in the fact that the believer imagines an agent – a subject (Zeus) – behind the phenomenon of lightning, whereas the scientist imagines a sort of regular process. Therefore, I think that the primary difference between the scientist and the believer is that the believer understands natural manifestations as the will of someone, whereas the scientist understands them as observable consequences of processes that are inherently regular, discoverable, comprehensible, objective, and not guided by will.

Let us return, however, to the debate about constructivism and realism. The analogy with the sculptor that Feyerabend uses is unfortunate. Thanks to it, one can very easily slip into what I have designated by the term pure constructivism. There is a yawning gap between the constructor of Zeus and the constructor of atoms. I acknowledge that the material (the phenomenon of lightning): “is more pliable than is generally realized“ (Feyerabend, 1989, 405).

But:

“I think that even though one can potentially consider the creation of ever new alternative theories, in the light of which we will be able to interpret and explain the set of given facts, the practical situation in science is much more complex, the formulation of theories encounters various ‘fuses’ and ‘barriers’, and scientific practicality does not support the aimless creation of new theories. Even though theories are the result of human creativity and imagination, they are not invented in a completely arbitrary way. And even if they were, they must demonstrate their abilities to solve problems and must subject themselves to complex testing procedures” (Viceník, 380).

Yes, the sculptor of Zeus can carve anything into stone that his will desires. In contrast, the constructor of atoms is an architect building in a cramped alleyway; the building must adhere to height limits, and every space in the building must have a window, and even during the construction itself, he must create space for the normal flow of traffic around the intended new building (research in accordance with the rules of the scientific community). This, of course, does not mean that he will not disrupt traffic and bypass some rules – much like a scientist who deliberately violates the principles of a certain paradigm.

Feyerabend and Objectivity

I will begin this part unusually. Let us accept the following distinction of the concept of objectivity from Hegel – I present it only because I consider it useful for this text.

“Hegel claims that the concept ‘objective’ can have three different meanings. It can mean, first, that which is located outside of us in space; second, that which is general and necessary; and third, that by which something is in itself, that which is there [was da ist], as opposed to what we merely think” (Houlgate, 2022, 28).

The first meaning of objectivity is thus that something lies outside of us. The second meaning let us call by a term more acceptable to us, analytic truths. The last meaning we will identify with what we already know well, considering those entities to be in themselves which are trans-historical.

What is Feyerabend’s relationship to this classification? We well know that Feyerabend rejects trans-historical entities. Regarding analytic truths, he does not take a stance in the text, and the issue of the consequences of this absence was addressed by us in the first chapter. Let us turn, therefore, to the first meaning of the word objectivity, meaning objectivity in the sense of entities outside of subjects – “out there”.

I think that Feyerabend has a positive stance toward this kind of objectivity:

“Scientists, [...], built upon their predecessors to create first metaphysical atoms, then crude physical atoms, and finally complex systems of elementary particles out of a material that did not contain these elements but could be shaped into them” (Feyerabend, 1989, 404).

In this quote, it is best seen that from the beginning he assumes some sort of material outside of us, which, like playdough, we can mold into various shapes. But even if we molded the playdough into the shape of a toy car, that does not mean the playdough itself contains it.

Precisely at this point, I think Feyerabend differs from pure constructivists, because they would consider even the given material (the playdough) to be our construct. Therefore, I think that Feyerabend’s relativism is not a pure relativism. Constructs are bounded by “something out there”. Whatever we call that material (nature, matter, substance), it follows from Feyerabend’s constructivism that even if a theory is formed, it is constructed on something that is objective (outside of us) and which allows only certain interpretations, not arbitrariness.

Conclusion

Atoms exist in a completely different way than gods. To say that atoms are just one of many constructs of science is intuitively unacceptable – and this intuition is justified. For that, a simple comparison of phlogiston and the atom is enough; they also exist in a completely different way. Atoms are, despite this, the creation not of a sculptor, but of an architect. The material that forms them, however, is not the result of our processing and our activities. Atoms are real to the extent that we are able to work with them, whether in the form of a nuclear power plant or a nuclear bomb. The fact that we created atoms means only so much: that we divided and arranged parts of the world in such a way that the results of this layout are the entities we call atoms. For me personally, atoms are more real because the threat of a nuclear bomb/power plant explosion is more destructive than a hex or the ill-will of the gods.

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Bibliography:

BENSON, T.: Pythagorean Theorem, NASA Official, 2021, [online] available here: https://www.grc.nasa.gov/www/k-12/rocket/pythag.html

FEYERABEND, P.: Realism and the Historicity of Knowledge, The Journal of Philosophy, Aug., 1989, Vol. 86, No. 8 (Aug., 1989), pp. 393-406.

GAHÉR, F.: Logika pre každého (Logic for Everyone), Iris, 4th expanded edition, 2013.

GÁL, E. – RÝBÁR, J. – SEDOVÁ, T. – VICENÍK, J: Doktrína realizmu: nutnosť alebo prívesok? (The Doctrine of Realism: Necessity or Appendix?), Organon, 1998, No. 4. electronic

HOŠEK, R.: Náboženství Antického Řecka (Religion of Ancient Greece), Praha: Vyšehrad, Edice Historica, 2004.

HOULGATE, S.: Hegel on Being: Quality and the birth of quantity in Hegel’s Science of Logic, London: Bloomsbury Publishing Plc., 2022.

If you have 20 minutes, this one is probably worth the time.

Introduction

It is impossible to doubt that the ontological argument (OA) plays a significant role in Hegel’s philosophy; what brings astonishment, however, is that there is no extensive secondary literature on this subject. This is the position offered by the Stanford Encyclopedia:

For this reason, the aim of this work will be to provide an answer as to whether Hegel offers his own ontological argument at all. It is interesting how the Stanford Encyclopedia includes “Hegel’s OA” within the taxonomy of ontological arguments, but only in quotation marks, and subsequently mentions the passage cited above. To ensure that this OA avoids the fate of Columbo’s wife, it is necessary to ask the question: does such a thing as Hegel’s OA even exist?

Unlike the literature devoted to this subject, I have decided to take the path of the gradual development of concepts within Hegel’s Logic. This moment exposes this work to the critique that it is merely a description of Hegel’s work. This is partly true; however, only the development itself can point to the importance it holds in Hegel’s philosophy, and only this development shows the need to think things through. “Hegel believes that the primary business of philosophy is the translation of representations (Vorstellungen) into thoughts, or the reflection on the deeper meaning of our experience by means of thinking things through” (Brinkmann, Dahlstrom). This means that the content of what we will be dealing with, even if it began with experience, takes place in the “element of thinking,” which might have been laughable to Hume; however: “We must not let the content of our mental pictures [representations] drive our thinking about incorporeal realities (...)” (Visser, Williams). Because: “Only in thinking and as thinking is this content, God himself, in its truth” (Hegel)

1. The Path to God

a) Being

The challenge established by Hegel’s philosophy implies the absence of the illogical (sensory, willed, represented...), thus even the will of the author, who might want to artificially create premises from Hegel’s work and thus create an original Hegelian OA. The Logic begins with Being (Sein), and it is precisely here that one can discover Hegel’s first mentions of the OA. Let us begin, however, first with what Being is for Hegel. Being is the poorest logical determination; it is something indeterminate and immediate, and therefore also the most abstract. “’Being’ is the poorest, most imperfect, notional determination (everything in some way ‘is’, even my craziest phantasmagorias); only through further notional determinations do we get to existence, to reality, to actuality, which are all much more than mere being”(Žižek).

In the notes on Being, Hegel arrives at Kant’s refutation of the OA, which we will mention here only very marginally, as this problem is sufficiently discussed. It is best to start with a joke: “that Kant discovered that ‘being’ is something other than ‘concept’”(Harrelson). Hegel, of course, agrees with Kant that concept and being are two different things as long as we are talking about a hundred thalers, because in this case existence is not a real predicate. “According to the definition of finite things, concept and being differ from each other in them; concept and reality, soul and body are separable from each other, and therefore they are perishable and mortal (...).”Hegel is trying to point out that Kant is comparing the incomparable. “According to Hegel, Kant’s barbaric triviality lies in the fact that we all know that concept and being cannot unite in finite beings. The ontological proof, however, refers to an infinite being”(De Lourdes Borges). “[In Kant] God suffers comparison with a small sum of money” (Harrelson). In any case, it would be a mistake if it now sounded as though Hegel is merely a proponent of Anselm’s OA; we will get to this point later. The best summary of this dispute between Kant and Hegel is offered by Gilles Marmasse:

“A Kantian might say: I would rather have a hundred thalers in my pocket than a hundred thalers in the mind alone. A Hegelian might answer: I myself would prefer a well-thought-out economic theory or a government that ensured economically effective policy over a hundred thalers in my pocket. It seems that Kant, in his critique of the ontological proof, makes the given sensory object the only type of existence that can present itself in experience.”

Being or existence is not only possessed by things that are, loosely speaking, in the external world; being is also possessed by entities that are within our mind. Whether they have some external representation is another question, but here it is necessary to remember that God is not an object for sensory cognition; He is reachable only by thought, or rather by reason. Because God is not something finite: “God is not something I can have (or not have) in my pocket...” (Žižek).

b) Finitude and Infinity

Our exposition ended at “determined being,” which is finite (Kant’s hundred thalers); we said that God, compared to a hundred thalers, is infinite. The Understanding (Verstand) now understands God (the infinite) as something standing above the finite. Hegel sets a clear task: “the main thing is to distinguish the true concept of infinity from bad infinity, to distinguish the rational infinite from the understanding’s infinite.” When we now look closer at the relationship between the finite and the infinite, we see that the infinite is only a negation standing against the finite. The finite has thus raised itself above itself to the infinite through negation. Through this negation, it crosses the boundary by which it reaches the infinite, but it equally sets a boundary for the infinite, which it thus also makes finite. An infinite with a boundary is, of course, not infinite. The infinite is thus only “the other” of the finite (finite | infinite). “If we place the infinite and the finite in a qualitative relationship as being “other” to each other, it must be called bad infinity, the infinity of the understanding (...)” (Hegel). This abstract infinite standing in opposition to the finite, which is connected to it through negation as “non-finite,” is bad infinity, and therefore just as finite as the original from which we started and which has another infinite beyond the boundary again, ad infinitum. Hegel calls the mutual transition of the finite into the infinite and vice versa the infinite progress, which will play a role later in this work. Infinite re/progress is also a form of bad infinity: “having arrived at that point: ‘and so on to infinity,’ the thought usually ends”(Hegel).

What then is true infinity? Because if God is not this infinity standing above the finite world, what is He then? As we mentioned above, such an abstract infinity standing above the world is simultaneously a finitude that considers infinity to be unreachable because it is constantly trying to reach it but knows it will never reach it (infinite progress).

“(...) being fixed as only negative, it is not even supposed to be existent—it is supposed to be unreachable. This unreachability is not, however, its privilege, but its defect (...). The false is unreachable; and we must recognize that such an infinity is false” (Hegel)

As is customary in the dialectical process, a further negation must occur, which overcomes both the finite and the infinite (which is actually also just a finitude). Thus arises true infinity, which is not like the first infinity (which was just a negation of the finite), but as an affirmative infinity, which is the result of the mutual interaction of the moments of the finite and the infinite. Affirmative infinity is no longer just an abstract “other” of the finite, but something determined thanks to its moments, where finitude is already incorporated into infinity.

“This determination of true infinity cannot be expressed by the formula of the unity of the finite and the infinite which we have already criticized; unity is an abstract immobile equality with itself and its moments are likewise immobile existences. The infinite and both its moments are, however, essentially only becoming, but one that is further determined in its moments” (Hegel).

Infinity thus determined has various consequences. God no longer dwells in his transcendent level but is rather immanent to the world; or rather, what we consider the finite world is immanent in God and thus not foreign to him. God is thus an infinite becoming in the world.

c) Ground and Existence

Ground

An argument is a system of propositions that stand in a relation of grounding to one another. The premises are the grounds of the conclusion, which is that which is being justified. Simply put, on one side we have the ground, and on the other side that which is grounded. Hegel places the category of ground in the second book of the Logic, which is the logic of essence. Essence is always the essence of something, so this sphere concerns relation; therefore, this part of the Logic is relational. Categories here appear in pairs, where one has no meaning without the other. The same applies not only to ground and grounded, but also to condition and conditioned, cause and effect, proof and what is proved, etc. “Nothing is in the ground that is not in the grounded, just as nothing is in the grounded that is not in the ground. When we ask for a ground, we wish to see the content determination twice: once in the form of what is posited, and again in the form of being reflected into itself, of essentiality” (Hegel). The argument thus forms one single content, which we see in two ways, in the form of mediation.

Ground as such suffers from various defects. The first, following from the previous exposition, is bad infinity in the form of an infinite pro-/regress, where we endlessly attempt to ground the premises of premises. “It is similar to ordinary proof, where the grounds adduced themselves require further grounds, and so on to infinity” (Marmasse). The second problem that we can find in Hegel’s work is that grounds can be found for virtually anything: “Therefore the search for and adducing of grounds — on which reflection is based — is an infinite running about that contains no final determination; for every thing one or several good grounds may be adduced just as well as for its opposite, and there may be many grounds without anything following from them” (Hegel). The third problem is the dialectic of ground and grounded, their mutual dependence upon one another. At first it appears that only the grounded (conclusion) depends on the ground (premise), but when we look at it from the other side, the ground becomes a ground only in the grounded, that is, it acquires its being only in another. It necessarily requires mediation for its existence, and this mediation is provided by the grounded, which in this way becomes its ground. “The inner thing [the content of ground and grounded] (...) is groundless and emerges from the ground only insofar as the ground has perished and is no more; it emerges from the groundless, i.e., from its own essential negativity or from pure form” (Hegel).

Existence

“The proofs of the existence of God adduce the ground of this existence. This ground does not wish to be the objective ground of the existence of God, for God exists in and for himself. Thus it is only a ground of cognition.” That means only a ground in itself, which is a ground existing in another, for example in the subjective individual. Yet essence, in order to be essence, must contain the ground of its existence within itself and not in another; therefore the ground must perish and become immediate. “Thus the absolute essence actually comes forth from the groundless; the ground sublates itself, and so there also disappears the appearance of a relation attributed to God, namely that he is grounded in something else” (Hegel).

Since the ground has vanished and we are left only with immediacy, this does not mean that we are to accept God merely by faith, which is indeed only immediate knowing. That would mean giving up the mediating movement, whose result is not emptiness, namely that the ground has disappeared. This disappearance must be understood positively, namely that it mediates for us the content that was only mediated in ground and grounded.

“The mediation by ground (Grund) sublates itself, but does not leave the ground behind, so that what emerges from it would merely be posited and would have its essence elsewhere, namely in the ground. Rather, this ground as abyss (Abgrund) is vanished mediation; and conversely, only vanished mediation is at the same time the ground, and only through this negation is it equal to itself and immediate”(Hegel).

The relevant question is: why does Hegel create such a complicated theoretical passage at all? The answer, however, is very simple. Essence cannot have the ground of its existence outside itself; absolute existence cannot be determined as a predicate or determination standing merely beside it, that is, in another. Essence must be identical with existence. “Essence is existence; it does not differ from its existence. Essence has passed over into existence because as ground it no longer differs from itself as grounded; that ground has been sublated” (Hegel). Essence has thus mediated itself with itself and defined itself as existence.

If substance did not possess this determination of immediacy, it would become merely determinate being, which we could once again compare to Kant’s hundred thalers, which have the ground of their being outside themselves. Such being “acquires the determination of otherness and relates itself to another. Thus something existing is mediated by another, and existence is generally the side of its mediation” (Hegel). Harrelson nicely summarized the dependence of these hundred thalers: “If I imagine one hundred thalers, I abstract them from every relation. But even as I imagine them, they are related to me, my property, etc. Since the content as representation consists in nothing other than separating this from its context, it is a false and illusory concept. In reality it does not possess the independence I ascribe to it; the independence is instead ‘a borrowed form attributed to it by the subjective understanding.’”

For precisely these reasons, I do not consider it appropriate to attempt, more than 200 years after Hegel’s death, to artificially search within his work for an argument that at least does not explicitly appear there. This is what Redding and Bubbio attempted in their article: “We reconstruct Hegel’s implicit version of the ontological argument in light of his anti-representational idealist metaphysics.” Their work does not involve the development of concepts, which is the most essential feature of Hegel’s philosophy. Hegel in no way offers a definition that would remain fixed throughout the work, because everything within this philosophy is in motion, constantly driven by the activity of negativity. To produce a result consisting of premises and a conclusion labeled “Hegel’s ontological argument” is to stand opposed to its basic principles.

“For the matter is not exhausted by its aim, but by its execution, nor is the result the actual whole, but rather the whole together with its becoming.”

“The whole, however, is only the essence completing itself through its own development. Of the Absolute it must be said that it is essentially a result, that only at the end is it what it truly is; and precisely in this consists its nature: that it is the actual, the subject, or the becoming of itself.”

“Dogmatism as a mode of thinking in cognition and in the study of philosophy is nothing other than the opinion that truth is contained in a proposition that is a fixed result (...).” (Hegel)

By writing Hegel’s ontological argument, we would arrive at the stage where the entire dialectical process becomes fixed; we would stop the machine at the point where it possesses the determinations of ground and grounded, that is, at the stage of mediation where essence has existence and ground outside itself and not within itself. Since we are dealing with Hegel and the absolute being, we cannot stop at the second book of the Logic but must proceed toward the Absolute.

d) Objectivity and the Critique of the Ontological Argument

Different forms such as being, essence, or concept require their own forms of proof. According to Hegel, the ontological argument (OA) is mediated through judgment, that is, it takes the form of a syllogism. “The ontological proof proceeds from the concept; it proceeds from the sum total of all realities and then subsumes existence under reality as well.” One cannot conclude that the OA is an incorrect judgment; Hegel regards it as the first attempt to unite thought with existence, which he considers praiseworthy. The problems lie elsewhere.

From the previous exposition we arrived at the point where essence mediates itself with itself, meaning that it has no external other that mediates it. This content, which was essence, is now the concept as such. The concept, in the form of judgment, in the case of the OA arrives at its existence. Yet it suffers from the defect that it is only a judgment, and thus the concept determines itself merely as concept in itself and not for itself. “That pure concept passes through the finite forms of judgment and syllogism because it is not yet posited as in and for itself one with objectivity (...).” As mere judgment, it is an abstract “metaphysical emptiness of the sum total of all reality.” In order for the concept of God to rid itself of this abstract emptiness, it requires determination. The concept acquires determination only through its realization. Such a concept of judgment is not realized at all, and therefore we should not be surprised that it suffers from the problem that being can be denied to it, opposed to it, and declared a subjectively constructed fiction.

The subject (the concept of God) acquires determination through the predicates implied within it, but because of its lack of realization, the concept of God is incomplete: “the subject acquires determinacy and content only through its predicate, whereas prior to this, however much it may be for feeling, intuition, and representation, for conceptual cognition it is only a name (...).” This does not mean, however, that if we now determine God as infinite, essence of the world, creator, Jesus Christ, we have thereby attained a concept that is both in itself and for itself. In this case, the aforementioned are only subjective determinations of the concept; in order for the concept to determine itself, it must do so itself, and therefore God is “known only in his activity.” Without realization, and therefore objectification, the concept remains unknown.

It would, however, be mistaken to think that by this objectification we mean something like recognizing the concept of God in miracles, or in something intended for empirical experience. God is spirit, and as spirit he is accessible only to rational cognition; therefore it is nonsensical to think of being only within the framework of the external world. “Certainly, the difficulty of finding being in the concept in general, and likewise in the concept of God, is insurmountable if being is supposed to be such as occurs in the context of external experience or in the form of sensible perception, like one hundred thalers in my possession (...).” Hegel gives examples of the existence of objective non-sensible things (which exist only in the subject as consciousness), such as various rational, theoretical, or moral principles.

However, the most convincing example, found in a somewhat different context in the article by Bubbio and Redding, is marriage, where “the agreement of thought (concept) and being cannot be considered in the same way as in cognition (...).” Marriage is marriage only insofar as the thought (or concept) is simultaneously its existence. It would probably be very difficult to live in a marital relationship if one of the partners did not operate with the concept of marriage. In such a case, where the thought is absent, being is absent as well, and the marriage simply does not exist.

e) The Idea and the Absolute Concept of God

Marriage, however, is something finite, as evidenced by the possibility of divorce. Therefore we cannot compare such a concept with the concept of God. Marriage involves a concept burdened by subjectivity, which has objective validity but remains entirely dependent on the subject. The concept of God does not suffer from this defect because “this inseparability of concept and being applies absolutely only to God (...).”

In the previous section we examined Hegel’s critique of the OA, where “this unity of concept and being is presupposed, and the mistake lies precisely in the fact that it is only presupposed.” In order that this unity of being and concept not remain merely presupposed, it is essential that it realize itself, that is, that it also attain being for itself. God acquires his being-for-itself through his objectivity, that is, through objectification. The concept thereby becomes an object for the concept itself.

Within the Christian religious context, we may understand the person of Jesus Christ as the particularization of the divine concept, in which God becomes an object for himself precisely in Christ’s person. The embodiment of the divine concept (in this case as spirit) is also the community of believers, within which God appears (not in the sensory meaning of the term) and manifests himself as true. “We may say, for example, that in the Christian religion the Dasein of Christ is a concrete body (the moment of concrete finitude), and that the Dasein of the Holy Spirit is the human community (the moment of concrete totality)” (Marmasse). Very simple and rather unremarkable examples may be individual acts of forgiveness, reconciliation, or love, in which the concept of God passes into being and thereby demonstrates its unity with it.

In the religious sphere this content (the concept of God) is grasped through imagination, faith, and feeling. In the Logic, this same content appears as reason, which manifests itself as the absolute Idea, the unity of theoretical and practical reason, soul and body, concept and objectivity, subjective and objective. At the same time it must be added that “unity” is a very poor term, as we already mentioned above, because the Idea is something that is a process. Spirit is in constant motion: “this infinite concept is the negative relation to itself; this manifold is judgment, differentiation; the differentiated, which at first appears as something external, spiritless, non-divine, is identical with the concept. The unfolding of this idea is absolute truth. In the Christian religion it is known that God has revealed himself, and God is precisely this: to reveal himself means to distinguish himself; what is revealed is precisely that God is revealed.”

In the Logic, the absolute Idea showed itself as the method that guides all cognition. “Cognition, however, is conceptual thinking, and its beginning is therefore only within the element of thought.”

We certainly cannot think about Hegel’s God as though it were some spirit from another world existing outside finitude; Hegel’s God is immanent to the world in its community. Hegel is a major critic of otherworldly entities and metaphysical inaccessible abstractions. On the contrary, God is a continual becoming. Hegel also says that God in his immediacy is nature, thereby indicating his affinity with Spinoza. Yet as we already know, God cannot remain immediate but must mediate himself with himself so as not to remain merely abstract. This mediation is achieved through the negative moment, through something standing opposed to him, namely the subject that reflects this nature. Thus the opposition subject (spirit) – nature, subject – object, concept – being is reestablished. It is impossible to say that only one side of this opposition is the truth; that would result in one-sidedness. Hegel gives the example of soul and body: one without the other simply means the destruction of both. Through the negation of negation, where opposites become aware of their interdependence, we arrive at a more concrete understanding of them and at the insight that “everything depends on grasping and expressing the true not only as substance but equally as subject.”

Conclusion

The only possible way to think about Hegel’s own ontological argument is to accept Hegel’s entire work as one great and extensive ontological proof, in the sense that we place an equals sign between the absolute Idea and God — a view that has several defenders. If we demand premises for Hegel’s OA, we are condemned to a futile search, which I consider to have been demonstrated by this work.

Hegel works with Anselm’s OA in very important passages of his work; this argument serves him as a tool for explaining certain concepts within his philosophy. Hegel criticizes it only because it proves a God who is a metaphysical emptiness. Therefore Hegel “corrects” the concept of God within Anselm’s OA so that it is no longer an abstraction. Yet this does not produce Hegel’s own argument, because Hegel offers no new or independent reasons for how this existence might be proven.

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Literature:

1. Oppy, Graham, “Ontological Arguments”, The Stanford Encyclopedia of Philosophy (Fall 2023 Edition), Edward N. Zalta & Uri Nodelman (eds.), URL = https://plato.stanford.edu/archives/fall2023/entries/ontological-arguments/ .

2. VISSER, S., WILLIAMS, T.: Great medieval thinkers: Anselm, Oxford University Press, Inc., Madison Avenue, New York, 2009.

4. HARRELSON, K. J.: Ontological Argument from Descartes to Hegel, Humanities Press, Kindle Edition, 2010.

5. DE LOURDES BORGES, M.: Hegel and Kant on the Ontological argument, Federal University of Santa Catarina In: The Paideia Archive, Volume 11, 1998.

https://www.meta-religion.com/Philosophy/Biography/Immanuel_Kant/hegel_and_kant_on_the_ontologica.htm

6. Hegel, G.W.F.: Logika ako veda I. diel, Bratislava: Nakladateľstvo Pravda, 1986.

7. Hegel, G.W.F.: Logika ako veda II. diel, Bratislava: Nakladateľstvo Pravda, 1986.

8. Hegel, G.W.F.: Fenomenologie ducha. Praha: Filosofia, nakladatelství Filosofického ústavu AV ČR,v. v. i., 2019.

9. Žižek, S.: The sublime object of ideology. London: Verso, 2008.

10. MARMASSE, GILLES. “HEGEL AND THE ONTOLOGICAL PROOF OF THE EXISTENCE OF GOD.” Hegel-Studien 46 (2012): 79–100. https://www.jstor.org/stable/26593116 .

11. REDDING, PAUL, and PAOLO DIEGO BUBBIO. “Hegel and the Ontological Argument for the Existence of God.” Religious Studies 50, no. 4 (2014): 465–86. http://www.jstor.org/stable/43670545,

12. Hegel, G.W.F.: Encyclopedia of the Philosophical Sciences in Basic Outline (Part I: Science of Logic), Cambridge: Cambridge University Press, 2015.

13. Hegel, G.W.F.: Lectures on the Philosophy of Religion, Stuttgart: Newcomb LivrariaPress, 2023.

We know that Neil is popularizing Science. He is not a scientist per se. I think that his position—speaking about science and make the PR for the latter—is valid. Science do need such persons in order to be able to communicate its results and introduce positive aspects of science to the public. I, personally, do not think that Neil is some kind of defender of scientism (dogma that only science can explain and will explain the world). Yet such question itself (at least in implicit manner) suggests that Scientists really do not need anyone. Maybe it might me shocking for some of you but I agree with that statement.

Thus, let’s start again by posing the question: Do Scientists Need Philosophers? The video ends by the following answers: YES. The reasons for such optimism are: a) scientist are too specialized, b) their view is too narrow, c) philosophers do speak about the most general principles every human being uses in order to be able to participate in clear, distinct and rational actions and statements. And, I think, those are valid points. Yet my reproach is that scientists can and will do science whether those points are relevant or not.

Does really anyone need philosophers? Probably not. We philosophers are not so important in society. But everything depends what we mean by the word “important”. Generally speaking doctors, policeman or firefighters are more important than philosophers. In the imaginary scenario where my leg is broken I am in need of the doctor. Okay, let’s ask more serious question than the bombastic title: ‘Is there any scenario where is the philosopher more important than anyone else?’ Yes—there are!

An evident example could be a debate where some follower of Andrew Tate explains to the public why is it useful for a woman to be loyal virgin cooking for her Macho husband who just returned from the gym. Or, where the priest utters nonsense like: ‘You should follow Jesus, otherwise you will burn in hell’.

Many of you will say that such sentence are unimportant matter because those utterances do not represent an immediate harm. I agree. Nonetheless, they harm society in the long run. So, now comes my thesis of this text: philosophers are good in problematizing, questioning and criticizing approaches that could harm the whole (the society), yet the evil of those approaches is usually hidden, not evident but sometimes crystal clear.

Of course, the majority would say that the policeman or the doctor is much more important. When you feel the pain right now — you really need a doctor. He will immediately ease the brutal presence of the pain. Yet there are matters and issues that are distant, future, delayed. Furthermore, need as such is something which has to be fulfilled here and now. It marks something immediate. I need to drink water or I need to dress myself. To say: ‘I need philosophy’, the word ‘philosophy’ does not correspond in the same way to the verb “to need” as in the case of thirst.

Bigger picture

To repeat the point: Scientists do not need Philosophers. When a scientist wants to do science it is much useful when he forgets all distractions and focuses himself on the subject matter. Such reductionism is a positive thing. Even artist does not need philosopher in order to create.

Now the relevant question to ask is: What is the point of philosophy? Yes—such “big question” would need bigger space. Although my answer would be brief, I suppose it will not miss the target. I am not saying anything new, just repeating the old cliché: Philosophy is about the Concept. Philosophy brings to light something we would not see without her. Without the concept of Alienation or the concept of Ressentiment we would simply do not see, ergo do not know.

The point of Philosophy can be summed up in the following: it is a space where for example both—evolutionary biologist and christian bishop—could meet and state their positions with clear terms by standard rules. Philosophy is the domain where Mathematics can meet God or Biology. Every position there could be well defined and “measured”, compared by standards of argumentation.

Thus, Philosophy can see the framework of the logical space (all the phenomena covered by some thought). Its “superpower”—for what it is good for—is precisely that it can see the borders of Religion, Science, Art and so on, since its subject matter is Concept as such. Contra example will demonstrate clearly what I mean. Take Religion, it tries to explain everything, yet it fails to do so (Bible is wrong in so many facts about our world). Or, take any scientific theory, it got some always more or less points wrong. Pythagoreans took numbers and say that everything consists of numbers. Okay, I hope you can see the point now, whether its mathematics, physics, biology, chemistry, psychology, neuro-science, they all has to comprehend and understand that there are limits to their field. You cannot explain love only in terms of chemistry or sex only as reproduction. There is so much more to them. Certain phenomena go way beyond the fields I mentioned above. To reduce the world to physics an explain everything in terms of moving bodies, waves, particles and quantum fields is misleading.

Philosophy is a map, it should be used for orientation between our scientific knowledge, religion, culture and so on. We humans (not scientists) need a map. Without (such map) concepts, in my view, humanity is lost. Those killers of philosophy should, therefore, rot in their stupidity.

Here is my text on Science and AI:

Apropos Science, Gilles Deleuze said something very similar in his abecedaire:

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This paper is one-sided from two perspectives. On the one hand, it looks at institutions through the prism of power, authority, and dominance, which presupposes a broader societal dimension of power phenomena. On the other hand, it abstracts from all the qualities of educators, academics, and teachers, and interprets them solely through the problem of power. However, I do not believe that such a reduction distorts the image of the academy to an absolute degree. My goal is therefore to focus on a specific dimension of the problem of power that cannot be neglected in an institution such as a university. Based on this problem, I will interpret the entire framework of the university, which will determine whether or not it is politically influential. In the first two chapters, I will outline Foucault’s and Deleuze’s views on education; then, on this basis, I will evaluate which model of the university most aligns with this view.

Student Discipline

The characteristic features of disciplinary societies were centers or places of imprisonment. Examples include the hospital, the school, the factory, and, of course, the prison. What is the essence of these institutions? Their main function is the supervision of the individual in terms of time and space. Pupils must be confined for a certain time in a school, which is the space of their instruction. During instruction, they are disciplined by commands: “Students, stand up!” “Work on this task!” “Hand over your mobile phones!” In other institutions, everything runs according to the same logic. Prison: “Leave the cell!” Factory: “Observe the workplace rules!” Hospital: “Lie in bed, do not move!” Naturally, this concerns the power of the teacher, the manager, the guard, and the doctor. (Foucault, 1975)

Let us look more specifically at the relationship between the student and the teacher from a Foucauldian perspective. Let us focus on the element of the examination (l’examen). “The examination combines the techniques of an observing hierarchy and those of a normalizing judgement. It is a normalizing gaze, a surveillance that makes it possible to qualify, to classify and to punish. It establishes over individuals a visibility through which one differentiates them and judges them. That is why, in all the mechanisms of discipline, the examination is highly ritualized. In it are combined the ceremony of power and the form of the experiment, the deployment of force and the establishment of truth. At the heart of the procedures of discipline, it manifests the subjection of those who are perceived as objects and the objectification of those who are subjected. The superimposition of the power relations and knowledge relations assumes in the examination all its visible brilliance.” [1] (Foucault, 1995, s. 184-5)

In addition to students being kept in an enclosed space (subjected to discipline), the teacher’s power is exercised over them. “[T]he examination in the school was a constant exchanger of knowledge; it guaranteed the movement of knowledge from the teacher to the pupil...” [2] (Foucault, 1995, p. 187) From the position of power—the subject who possesses knowledge—the teacher evaluates, classifies, determines, and examines the students. This is permitted precisely by this position of knowledge. They can punish—for example, by giving the student an extra assignment—because, from the position of knowledge, they have evaluated that the student is not fulfilling their duties conscientiously. The teacher transmits knowledge, thereby fulfilling the epistemic function of the academy. However, they do so from a position of power and based on a power relationship over the students.

Student Control

Deleuze’s concept of the society of control is merely a continuation and overcoming of disciplinary societies. Supervising is very similar to controlling. It cannot be said that control does not exist in disciplinary societies; it plays its role there. However, the essential point is to have disciplined individuals who fulfill the demands of the power acting upon them during their presence in an enclosed environment or center of confinement. Why, then, move from discipline to control? Why are we no longer a disciplinary society, but rather a society of control? Discipline was too focused on confinement, whether temporal or spatial. Control is about something completely different; for it, confinement/enclosure is irrelevant. Students no longer have to be locked in a school—online teaching is sufficient for them (similarly with working from home—online). A convict does not have to go straight to prison; we can give them an electronic bracelet (”We have them under control”). A patient receives treatment at home. It is not about discipline, but about control—continuous assessment/tests, a bracelet, correct medication dosage (3 times a day)/ward rounds, and consultations/meetings. Old institutions such as schools, prisons, hospitals, and factories are no longer places where the individual is kept. These institutions are machines that grant or deny access. Individuals have been transformed into “dividuals”; they are divided by the fact that they represent a different number for each sphere. These assigned numbers—the codes that represent their identity—grant or deny access. For the school, the individual is an Fx student; for the bank, their account balance; for the insurance company, a calculation of potential risks; and for the employer, their resume and experience. Based on these codes, the individual is granted access to the various spheres of society. If they do not have a sufficient account balance, they will not be able to afford a mortgage, and thus independent housing. They do not have enough money in the account because they did not study well, meaning the sphere of attractive and well-paid professions is not open to them, and so on. Access has been denied to them through control. Discipline is about solid, fixed boxes; control is about a card (with valid codes) that opens doors to other spheres through which the individual can flow. (Deleuze, 1990)

Control operates on the principle of modulation. Individual elements within society are altered and modulated. Constant modulation of wages (bonuses, allowances), modulation of workers through training, and even within the school: “The principle of modulation of ‘salary according to merit’ is not without temptation for the educational institutions themselves: just as the enterprise replaces the factory, continuing education tends to replace the school, and continuous assessment tends to replace the examination.” [3] (Deleuze, 1990, p. 243) An examination at the end of the term or semester is no longer sufficient; it is necessary to apply continuous monitoring of students’ knowledge—continuous assessment, presentations, and mid-semester tests. Control represents: “In the school regime: the forms of continuous assessment, and the action of continuing education on the school, the corresponding abandonment of all research in the University, the introduction of the ‘enterprise’ at all levels of schooling.” [4] (Deleuze, 1990, p. 247) Deleuze writes clearly: Control is the new form of domination. Knowledge (in the person of the teacher), which once required an examination, today demands continuous control and supervision over individuals. What is surprising, however, is that authority no longer needs to enclose students. All it needs is MS Teams, which resolves everything for it. Authority can assign tests and homework from the comfort of its own study, and machines do the evaluation on its behalf. In this way, authority maintains its overview and control right from its chair.

Models of the Academy and the Position of Academics

Libor Benda characterizes academic freedom using two main features: the professional status of academic freedom and the epistemic function of academic institutions. Both of these characteristics pertain to academics (educators). Due to their professional status, an academic has the freedom to research and inquire, but this freedom has certain limits and cannot be considered freedom of speech. In the case of the epistemic function: “that the task of academic institutions—and of individual academic workers—is, quite simply, to participate in the unbiased development of objective knowledge and the search for truth, regardless of any broader implications and impacts of the knowledge resulting from this activity. Based on this argument, academic freedom is then a necessary prerequisite for academic workers to be able to responsibly fulfill this role of theirs. From the perspective of this argument, truth is conceived as a value in itself, and it is academic workers whose professional responsibility is to produce truthful knowledge and pass it on, just as, for example, healthcare professionals bear the professional responsibility for saving human lives.” [5] (Benda, 2020, p. 25)

From the previous explanation, we could add to the aforementioned characteristics of academics their aspect characterized by authority and power. This authority is manifested primarily in the epistemic function, as it fulfills the role of the exchange and transmission of knowledge. Authority and power are precisely the ways in which the teacher fulfills their role in the epistemic function. However, this does not yet directly answer the question of whether the academy is political or apolitical. Using Benda, let us establish a list of university models:

• i) A university that is politically neutral, defending the Enlightenment ideals of truth, reason, freedom, and progress. Resisting external influences.

• ii) A university that is aware of its dependence on external influences, but strives for apoliticality through the imperative of academicism.

• iii) A university as a political institution that is built upon the values of democracy and humanity. It is politically active and resists all those who violate these given values.

This list will serve as the material that we will assess from the perspective of apoliticality. Ultimately, we will show how control and discipline relate to it. On this basis, we will assess whether the academy is a political institution or not.

Politicization of the Academy / University

Let us look more closely at the first type of university, which defends ideals and resists external influences. Without going into extensive detail, we can conclude that such a university is more of an ideal than a reality. As a public institution, the university is in most cases dependent on the state’s financial resources, and furthermore, its operation and the execution of its activities are delimited by law. It can be concluded that the political has an influence and control over the university (not necessarily to an absolute degree). Both Benda and Butler agree on this: “Academic freedom belongs to universities, but universities belong to specific localities and respective local practices. Their walls are far more permeable than they appear on the basis of legal distinctions.” (Butler, 2018, unpaginated)

The second type of university assumes dependence on external influences. However, it strives for apoliticality through the imperative of academicism. What does this imperative mean? “The imperative of academicization says that when any topic is dealt with in teaching, it should be removed from the real world of everyday practice—from the world where elections are held, political decisions are made, and protests are organized—and placed in an academic context, where the structure, meaning, value, and history of this topic are subjected to examination using traditional methods [...] of the humanities, social sciences, and natural sciences.” (Fish, 2014, 31) The imperative strives to achieve political neutrality; the academic does not make suggestive evaluations or conclusions, and tries to keep the topic and issue as open as possible. This leaves space for the students to evaluate subject matter on their own and form their own opinions. On the other hand, this imperative, even when striving for value neutrality, does not fulfill the mission of higher education institutions regulated by the Higher Education Act (300/2025 Coll.), which reads as follows (This law is from my country, generally it may differ but I think most of the western world has something very similar):

Ҥ 6 Mission of higher education institutions (2) Higher education institutions fulfill their mission b) by providing higher education in the spirit of the values of democracy, humanism, and tolerance, which enables the acquisition, expansion, deepening, or renewal of knowledge from various areas of knowledge and culture and is a part of lifelong learning at the highest level, through education towards understanding, preserving, spreading, and enhancing the national cultural heritage and various cultures in the spirit of cultural pluralism,

§ 11 Academic freedoms and academic rights (2) The exercise of academic freedoms and academic rights pursuant to paragraph 1 must be in accordance with the principles of democracy, humanism, and the legal order.”

[Italics in the quoted section are mine.]

Removing and presenting any topic from the real world of everyday practice ultimately appears to be illegal. How can a teacher spread the values of democracy and humanism when they do not take a stand? Is it possible to abstract from the real world of elections, political decisions, and protests when they do not align with the values of democracy and humanism, and the teacher must exercise their freedoms and rights in accordance with these values?

This brings us to the last type of university, where the university is politically active and participates in spreading the ideology (using the term ideology in a neutral sense) of democracy and humanism. The academic’s exercise of their activity is legally prescribed in the spirit of specific values. For this reason, the academic is a politically engaged person. Not in terms of party affiliation, but in the sense of being a disseminator and advocate of political values. Here, discipline and control come into play again. They are precisely the answer to the question: how does a university educator carry out and provide education and mediate values? Through authority in the form of discipline and control over students. From the perspective of Foucault and Deleuze, the university would therefore represent a political institution that promotes its values through power. The university, therefore, cannot be considered an independent, apolitical, and impartial institution outside the political sphere. It is limited in its operations by the law—which is the result of the political—and its constituent representatives (the teaching staff) operate in a power-based manner.

Final words…

The perspective of power, through which I viewed the university, demonstrated that the university is a political institution. This naturally has consequences for the concept of academic freedom; how can academic freedom exist in the sense of independence from the political sphere when the university itself is politically active? However, the perspective of either Foucault or Deleuze is, in my opinion, not necessarily compatible with Butler’s view. Butler states that the university should be political, meaning it must promote the values of democracy, humanism, and tolerance. Foucault and Deleuze state that the university is already doing this, but in a way that operates through dominance. In my opinion, a stronger conclusion follows from this than the one Butler tries to advocate: we no longer need to strive to make the university politically engaged, because its legal framework already dictates it.

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[1] Original text: „The examination combines the techniques of an observing hierarchy and those of a normalizing judgement. It is a normalizing gaze, a surveillance that makes it possible to qualify, to classify and to punish. It establishes over individuals a visibility through which one differentiates them and judges them. That is why, in all the mechanisms of discipline, the examination is highly ritualized. In it are combined the ceremony of power and the form of the experiment, the deployment of force and the establishment of truth. At the heart of the procedures of discipline, it manifests the subjection of those who are perceived as objects and the objectification of those who are subjected. The superimposition of the power relations and knowledge relations assumes in the examination all its visible brilliance.”

[2] Original text: „the examination in the school was a constant exchanger of knowledge; it guaranteed the movement of knowledge from the teacher to the pupil…”

[3] Original text: „Le principe modulateur du «salaire au mérité» n’est pas sans tenter l’Éducation nationale elle-même: en effet, de même que l’entreprise remplace l’usine, la formation permanente tend à remplacer l’école, et le contrôle continu remplace l’examen.“

[4] Original text: „Dans le régime des écoles : les formes de contrôle continu, et l’action de la formation permanente sur l’école, l’abandon correspondant de toute recherche à l’Université, l’introduction de 1’« entreprise » à tous les niveaux de scolarité.“

[5] “that the task of academic institutions—and of individual academic workers—is, quite simply, to participate in the unbiased development of objective knowledge and the search for truth, regardless of any broader implications and impacts of the knowledge resulting from this activity. Academic freedom is then, based on this argument, a necessary prerequisite precisely for academic workers to be able to fulfill this role of theirs responsibly. From the perspective of this argument, truth is conceived as a value in itself, and it is academic workers whose professional responsibility is to produce truthful knowledge and pass it on, just as, for example, healthcare professionals bear the professional responsibility for saving human lives.” [Italics are mine.]

BENDA, L.: Akademie, politika a akademie jako politika: Ke kritice „rozšiřeneho“ pojeti

akademicke svobody, In: Social Sciences & Humanities 2020, Vol. 12 (2), 19–43.

BUTLER, J. 2018. „The Criminalization of Knowledge: Why the struggle for academic freedom is the struggle for democracy.“ [online] The Chronicle of Higher Education, 27. 5. 2018 [cit. 11. 10. 2020]. https://www.chronicle.com/article/The-Criminalization-of/243501 .

DELEUZE, G.: Pourparles. Paríž: Les Éditions de Minuit, 1990.

FISH, S. 2014. Versions of Academic Freedom: From Professionalism to Revolution. Chicago & London:

University of Chicago Press, https://doi.org/10.7208/chicago/9780226170251.001.0001 .

FOUCAULT, M.: Surveiller et Punir: Naissance de la Prison. Paríž: Gallimard, 1975.

FOUCALT, M.: Discipline and Punish: The Birth of the Prison. New York: Vintage Books a Division of Random House, Inc., 1995.

This is the second part, you can read it without reading the previous. However, here is the first one:

1. Specific measure of probability

In this part, I will try to construct an argument for the second tenet of Probabilism: “these credences are rationally required to conform to the probability calculus.” (Hájek, 2008, 229) There are many arguments for probabilism: “[b]ut one particular feature that all these arguments seem to share is the fact that they derive rational constraints on degree of belief from apparently pragmatic constraints on preference”(Eswaran, 2011, 318). My hope is to present an argument of different kind, but before the argumentation, I will reconstruct some of Hegel’s thoughts on measure as such. For the next part, I will treat probability as a measure, in the end the term “probability measure” is already established. For more see: (Bovens, Hartman, 2003), (Renyi, 2007).

1.1.Hegel on specific quantum and specific measure

„Abstractly expressed, quality and quantity are in measure united“ (Hegel, 2010, 282). As we have seen before, quantity turns into quality and the label which best catches this relation is called measure. Before we jump to the specific measure I will mention briefly first two stages, where the notion of measure deals with the twofold character of itself. At the start, the measure is some specific amount or specific quantum that confers a specific quality on something and without which the thing would lose that quality. Take an example of water, its specific quantum (or measure) is a temperature interval from 1°C to 99°C. If the temperature goes over the range or below, the quality of being a liquid vanishes. Secondly, measure sees that specific quantum can easily pass over the limit. The latter is also a quantum and regarded purely as quantum (without a relation to quality) it has no limit. It can go on ad infinitum. We understand that the quantum is nonetheless something external to measure, so we come up with an external measure, which Hegel calls the “rule” (Regel) or “standard” (Houlgate, 2022, 248-251). Best probabilistic example could go like this: there is 40% probability that it will rain tomorrow. The quantum 40% here constitutes the quality of probability. But in the other areas, for instance economics, there could be 120% or 200% growth of GDP. So, quantum as such is not limited to be in alignment with interval from 0 to 100%. But we know that if we cross the limit for probability, it would not be probability anymore. It would be necessity or impossibility. It is not possible to say, that there is 120% probability of raining tomorrow. Thus, we made up a limited scale for probability, represented by Kolmogorovs axioms, where interval [0,1] reflects probability distribution. In other words, we come up with external standard that will guarantee us the quality of probability.

Now let’s take a closer look on the qualitative moment of measure. Certain specific quantum or range of quanta constitutes the quality of something. Thus, measure is always a measure of something. Something is a category or a label that Hegel mentions for a first time in the begging of his doctrine of being. There he comes to a conclusion, that something is always in relation to something else, hence is determined by and determining other things. This insight comes handy at the stage where being is represented by measure. When something has a measure, it can also be a measure for other things, or put other way around, its measure (as specific quantum) can be revealed by other thing that serves here as a measure (external standard). At this stage Hegel says that the measure reached the point where it is not only being in itself (a thing having a measure), but also a being that is for itself (a thing being a measure (for other things)). Its name is specific measure (Houlgate, 2022, 252-254). We can see that the probability measure also reaches this point because it is today a measure for degrees of belief. It has this other something (degree of belief), to which it is a measure. In the next part I will try to justify why probability measure can be a measure for credences.

1.2.Argument for Probabilism

We begin with an assumption that probability is something different from credences – their intensive magnitudes are external. I suggest, we can measure one intensive magnitude with the other. It is worth mentioning, that for now we know only the exact number for probabilities, for example for an event of dice rolling number 6: P(6) = 0.1666. Yet, we do not know the exact (number) intension of the credence. Degrees of belief for now are formed by vague terms like “I am certain”, “I am not so sure”, “I think A is more possible than B” and so on. But what are we allowed to presuppose about credences? They are part of intensive magnitude, such magnitude has degrees, which have their determinacy only in relation to other degrees of that magnitude. Thus, the credence of “dice rolling number 6” has a specific position on the scale thanks to other credences (by an amount of them). What could be those other degrees of belief of our agent? We can begin with certainty: the agent is certain that the dice will roll some number. Second highest credence: the agent is almost certain that the dice will roll some number from a set of 5 members. Third credence: the agent is less certain that the dice will roll some number from a set of 4 members. Forth credence: the agent hesitates that the dice will roll some number from a set of 3 members. Fifth credence: the agent thinks that there is some small chance that the dice will roll some number from a set of 2 members. Sixth credence: the agent is not sure the dice will roll some number from a set of 1 member.

Now let us go back to probability and forget for a while the scale of credences. The probability distribution for sets of numbers is as follows: P(set of 6 members) = 1; P(set of 5) = 0.8333; P(set of 4) = 0.666; P(set of 3) = 0.5; P(set of 2) = 0.333; P(set of 1) = 0.1666. Thus, the probability P(6) = 0.1666, is the lowest, thanks to other probabilities. At this point, when we know the position of P(6) and the position of cr(6), we can compare both intensive magnitudes. The only difference between them is that the position of P(6) is quantified, it has an assigned number: 0.1666. The position of cr(6) is not, but we know it is also the lowest. Therefore, we can use now P(6) = 0.1666 as a specific measure and measure – that means to quantify – the not-numbered-intensive magnitude (credences). Thus, when we are comparing the probability (of dice rolling number 6) with degree of belief (of dice rolling number 6), its rational to conclude that cr(6) = 0.1666.

Let’s take an analogical example. I have a piece of wood measuring 0.6m, but I do not have by myself an external ideal standard represented by a ruler. In my mind, it is totally rational to use this piece of wood as an external standard for measuring other things that have also the extensive character. I think it is a right assumption that degrees of belief are something different from probabilities. So is the piece of wood from a rope, metal stick, height of a house, or perimeter of a lake. But after some effort, we can measure all of them, using just that small piece of wood. It might not be exact, but at least it we will approach the desired result.

Intensive magnitude of credences is in ordinary language expressed only through quanta, it is vague and lacks determinacy of a number. My conclusion, therefore, would be that credences should rationally conform to the probability calculus, because the probability measure is one of the best external standard for credences. It provides for credences quantification, mathematical apparatus and (what would Hegel call) the determinacy of the number. In contrast to the Dutch book and other arguments, where the rationality is judged by the consequences, I propose a view, which is much simpler. In nutshell I claim that, if the intensive magnitude of credences does not accept the probability distribution, it is left without precise quantification because there is no other intensive magnitude, which share that many features with credences, as probability. By the way measuring one intensive magnitude with the other is also justified by physics. The Foundations of Measurement, Vol. I: Additive and Polynomial Representations is the definitive text on conjoint measurement, which explains how two or more intensive attributes can be measured together to reveal a quantitative structure (Krantz, Luce, Suppes, Tversky, 1971).

1.3.The story does not end

Degrees of belief should conform probability calculus. “For this reason, a prominent strand in the Bayesian literature revolves around attempts to argue that it is irrational to allow your credences to violate the axioms” (Strevens, 2017, 19). If it violates, you are irrational, if not, you are rational. Many arguments for probabilism share this binary logic. But we have seen that there is some background standard, which serves us to compare two intensive magnitudes (probability and degrees of belief). In other words, we measure both quanta, quantum of credences and quantum of probabilities, according to some measure. I suggest that this background measure is rationality itself. If rationality has only two values (being rational or irrational) it is rationality for ideal agents. Bayesian standards for rationality: “are not necessary conditions for any kind of epistemic rationality that human beings can achieve or approximate, or rationally ought to attempt to achieve or approximate” (Talbott, 1991, 147). I do not intend to go along this path, but there exist a literature concerning this issue, which treats rationality as a measure, that comes also in degrees. For more see: (Staffel, 2019), (Elqayam, Evans, 2013).

Conclusion

My argument for probabilism is not immune to criticism. The difficulty is evident, on the one hand probability theory is an exact mathematical theory, where the notions are well defined and everything is deduced from axioms, in short, it is a realm of exact numbers, deductions and inferences. As such this theory is situation invariant and independent conceptual network (in old jargon, it expresses something eternal and infinite). On the other hand, credences are always credences of someone. Such a person is situation dependent finite creature, not always thinking about coherence of beliefs and deductive reasoning. So, the problem is: how to align those two intensive magnitudes? In my mind, looking for impenetrable argument is not a right way how to do it. It is like looking for an ideal triangle in our everyday world. Probably we should admit that the probability measure is one of the best available tools how to represent credences. Just as we use imperfect physical standards to measure the world, we use probability to approximate and structure our epistemic attitudes. In this sense, probability is not an idealization to be achieved but a practical measure that guides rational belief. It is our 0.6 m piece of wood that comes sometimes handy and brings results.1

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