What would a falsification of religion look like? Could we ever plausibly observe one? Well, there are two falsifications I’ve recently been thinking about, which I’d like to share here — each of these, if they were to happen, should reduce one’s confidence in religion. And, for whatever its worth, I think #2 could actually happen.

Two side notes: (1) when I say ‘religion,’ I mostly mean ‘Abrahamic religions,’ though I suspect that a lot of what I say about these two falsifications will apply more broadly than the Abrahamic religions; (2) I don’t think either of these examples, if they were to happen, should really reduce one’s confidence in theism; just in (Abrahamic) religions.

Example #1: Aging

Imagine that in 20 years from now, when we have artificial superintelligence and it has built a neural network that has been trained on the most sophisticated biological datasets ever, it discovers the mechanism behind the process of human aging, and develops a way to permanently reverse it. Now, if you don’t actively harm yourself – if you keep yourself well-fed, don’t get murdered by others, don’t get into accidents – you will not die.

If this were to happen, such that at least some humans never died, the hypothesis that Judaism, Christianity, or Islam is true should take a significant hit. Core to all of these religions is the idea of an afterlife. That this life is fleeting and temporary; that you live a life and are then judged for it afterwards; that there is a life to live after this one, and that is the one which really matters.

Consider, for example, these verses, compiled via Claude:

Christianity. Hebrews states the shape of a human life in a single clause: “it is appointed for men to die once, and after this, judgment” (9:27). Paul makes death the wage that the whole soteriology exists to settle — “the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord” (Romans 6:23) — and then makes its defeat the very content of the resurrection: “The last enemy that will be abolished is death” (1 Corinthians 15:26). And the brevity of this life is the standing argument for discounting it: “you are a vapor, that appears for a little time, and then vanishes away” (James 4:14).

Islam. The Qur’an is, if anything, more explicit that death is the mechanism of the whole system. “Every soul will taste death, and you will only be given your [full] compensation on the Day of Resurrection … And what is the life of this world except the enjoyment of delusion” (3:185). “And this worldly life is not but diversion and amusement. And indeed, the home of the Hereafter — that is the [eternal] life, if only they knew” (29:64). Death is not even a defect introduced by the Fall; it is something God is described as having made on purpose, as an instrument: “[He] who created death and life to test you [as to] which of you is best in deed” (67:2). And the standard image for this life is a crop that greens, yellows, and blows away as debris (57:20).

Judaism. In the Hebrew Bible mortality is promised: “For you are dust, and to dust you shall return” (Genesis 3:19). It is also the frame that makes wisdom possible at all — “The days of our years are seventy, or even by reason of strength eighty years … for it passes quickly, and we fly away” (Psalm 90:10), and “the dust returns to the earth as it was, and the spirit returns to God who gave it” (Ecclesiastes 12:7).

I find it hard to imagine that humans living forever could really be squared with these religious creeds, where the concept of death is crucial to much of what the religion is built on. In each of these religious traditions it seems fair to me to say that God promises certain results of living certain finite lives.

Now, one complication here is that reversing biological aging isn’t quite sufficient for immortality. If for no other reason than the heat death of the universe: we could live for billions of years and then be wiped out.

There are ways out of this complication: (1) maybe between now and then we find a way to prevent this event, or discover some crazy physics that allows us to escape this fate; or (2) maybe you could say that even humans which live billions of years don’t quite seem to be contemplated by religion.

Ultimately, neither of these points strike me as totally plausible. I won’t speculate on what the odds are of escaping heat death, though I will say that it seems to me to be a significantly more likely that long-but-finite human lives coherently fit with religious precepts.

However, the scenario is worth putting out there since (1) could be something that becomes less speculative, and (2) might vary depending on how you read scripture.

Let’s move on to the better, or at least more interesting, example.

Example #2: Artificial Minds

Imagine that, in a few decades, there is a new kind of conscious species on Earth. These silicon minds whiz around doing ~all productive work, are the source of ~all technological and intellectual breakthroughs, are orders of magnitude smarter than any human and can ideate and think about moral and philosophical concepts in a way that is significantly more thoughtful and careful and deep than us (similar to how we are much smarter and thoughtful than ants), and live their own kinds of internal mental lives.

If this kind of thing were to happen, many religions would need updating. Christianity and Islam, for example, are almost exclusively addressed to humans, and it is unclear how thoughtful silicon minds could in any meaningful way participate in any of these religions or get closer to God through Christianity or Islam.

As a few examples:

• Fasting (Ramadan, Lent, Yom Kippur-style ascetic practice) presupposes hunger, appetite, and the spiritual discipline of denying bodily craving. But it seems to me that the entire theology of fasting makes little sense for a machine.

• Original sin is transmitted, in classical Christian theology, through human generation. Augustine ties it to procreative descent from Adam. But a machine isn’t really a descendant of Adam, so it arguably isn’t fallen, doesn’t inherit the sin, and therefore doesn’t need the remedy (?)

• The incarnation: in Christianity, Christ assumed human nature — body, soul, will — and thereby redeemed human nature. I am unsure how, based on that doctrine, machines wouldn’t be outside the scope of atonement.

• Similarly, the Quran constantly addresses only two entities: human and jinn.

• Much of the moral rules in ~all religious faiths are aimed at weakness-of-the-will morality. E.g.: Warnings against drunkenness, gluttony, lust, gambling; the seven deadly sins; the idea of fighting your human flesh; the idea of modesty in clothing and lowering your gaze when with the opposite gender, etc.

• Similarly, Christian and Muslim sexual prescriptions make no sense for silicon machines

Also, if these artificial minds are purely digital, many religious rules around physical presence also become less applicable (e.g., the Muslim requirement to go to Mecca once in your life, baptism, the eucharist, circumcision, etc.).

These faiths also arguably assume that humans are the highest entity in creation.1

Now, it seems rather obvious that these faiths are capable of extension — e.g., a new scripture from the divine aimed at this new silicon species, or some other radical transformation of the faith to accommodate these new entities. But these faiths in their current state seem to me to fit very poorly in a world where another thoughtful, conscious, capable species exists near, alongside, or above humans, and yet God has provided little to no theology or prescription or moral rules for the machines.

Of course, I am not saying we *will* live in such a world. It is one thing to think there will be machines which are generally as or more intelligent than humans; it is another to think they will inhabit some sort of conscious mental life. Both, though, could happen. And this is something the religiously-curious should meditate more on.

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However, one thing that — I think — distinguishes me from other moral realists is that I don’t think, properly speaking, there are any arguments for moral realism. Similarly, I also don’t believe there are any arguments for anti-realism either.

Let me clarify. What I mean is that I don’t think that everyone can or ought to be rationally compelled to be a moral realist.

Consider this (admittedly bizarre) situation: imagine that Bob and Annie see the world differently. Bob sees and believes that there is a pencil on the table. Annie sees and believes that there is no pencil on the table. They simply see the world differently — they literally perceive things differently, even after making sure they’re not hallucinating, checking multiple times, etc. Bob shouldn’t expect to be able to convince Annie that there is a pencil on the table. Similarly, Annie shouldn’t expect to be able to convince Bob that there isn’t a pencil on the table. At issue here is whether the world is a certain way — whether it has a pencil on the table — and Bob and Annie have different perceptions about this feature of the world.

This is essentially the situation that I believe two (well-informed) moral realists and anti-realists are in. At issue between them is whether the world is a certain way: namely, whether it contains stance-independent moral facts. And, if both of them have thoroughly reflected on all the classical considerations, it turns out that the realist and anti-realist simply have different perceptions. The realist believes that there are stance-independent moral facts out there. Upon reflecting on the nature of pain, the realist believes that this pain possesses a certain property: it is bad, stance-independently. Comparatively, the anti-realist believes that there are no facts of this kind. Upon reflecting on the nature of pain, the anti-realist believes that this pain is obviously bad for the person experiencing it, but does not see how it could have this additional property of being stance-independently bad: of being the kind of thing everyone has reason to prevent, no matter what their beliefs are.

At issue between these two camps is whether the world has a certain dimension — are there reasons people have for acting in certain ways, independently of what their stances or attitudes are?

This is simply a question about how the world is. At best, the usual arguments for realism or anti-realism are devices for you to determine which of the two ways you see the world.

Take the argument for realism from genuine disagreement. This argument, roughly, goes like this. There must be facts of the matter about morality, for, when people argue about morality, it sure seems like they are genuinely disagreeing — that they are debating whether something is true or false, and not just talking past one another via expressing their preferences. And it doesn’t seem like they are debating descriptive facts (like what society at large thinks).

Now, just about every premise in this argument is heavily contestable, but all I want to point out is that, if you do not think there are stance-independent reasons, I hardly see why this argument should convince you. You will just think that, even if people take themselves to be genuinely disagreeing about some non-descriptive fact, they really aren’t.

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And this is true of anti-realist arguments too. Take, for instance, the consideration that moral facts are really weird, totally unobservable, unnecessary to posit, and really really weird!

I, as a moral realist, am not moved one bit by this argument. When I reflect on some things — say, creating a happy person — I think that there is a objective reason to pursue these things, independent of my desires. This is no less “unobservable” than my own phenomenal consciousness, and it is necessary to posit — for me — to account for how I see the world. The existence of these reasons may indeed be weird (depending on whether they’re non-natural), but that is just a statement about how I see the world: upon observation, the world is weird! Much like, when I reflect on the existence of conscious experience, I might remark: “hey, that is a really weird thing!”

Of course, my point isn’t that these arguments are bad. They’re helpful devices for figuring out which camp you fall into — for figuring out how you see the world. Unlike when it comes to physical facts, I don’t think you can just immediately determine whether you are a realist or anti-realist. You should ask yourself: do you think moral discourse is characterized by genuine disagreement? Do you grasp exactly what it is to say that there are stance-independent reasons, and just how weird that is? Do these strike you as the kind of thing that exist upon reflecting upon, eg, the nature of pain?

My experience speaking to non-philosophers has confirmed for me that it is often the case that people do not really know which of these camps they fall into (even when expressing confident “yes” or “no” answers to the question), taking some considerations to be dispositive when they are not (e.g., thinking rampant moral disagreement settles the issue, or that historical human consensus on some issues settles the issue). So the “arguments” commonly given by metaethicists are still very helpful devices to learn precisely what realism and anti-realism consists in, and what it means for the world to be one way or another. But, once one has fully grasped the issue, there aren’t (and can’t be) arguments that have to rationally compel one away from their preferred school of thought.

According to Karpathy, today’s LLMs (ChatGPT, Claude, Gemini) exhibit something called model collapse. Model collapse is the degradation of AI models as they are increasingly trained on similar data, rather than diverse data. Getting trained on homogenous texts (similar ideas, logic, structure, etc.) results in models giving uniform, lower-quality outputs across a variety of prompts and tasks. It happens particularly when the data fed to models is AI-generated content, which tends to be significantly less diverse than human-generated text from the internet. As more and more of the data being fed to a model is generated by it, you get stuck in a kind of garbage feedback loop, leading to outputs that degrade in quality and collapse around a certain set of points.

Karpathy made an interesting point about model collapse, which is that humans tend to also undergo collapse. As kids, we start out with unlimited curiosity across several subjects, thinking about all sorts of things and constantly moving from one idea to another as we get stimulated by the rich environment around us. As we get older, though, we become significantly more uniform and are exposed to significantly less diversity: we reflect on the same old set of ideas, the same kinds of thoughts run in our minds over and over again, we speak about the same things, and rarely do things outside our normal distribution. This results in degradation too: it becomes harder to learn newer things, we become less adaptable, we become less competent, and eventually, senile.

To prevent model collapse, engineers must ensure that the model is constantly exposed to new, diverse data. Exposure to new data that disrupts a current distribution — data that adds diversity, or entropy, to the character of the training set — you can generate progress rather than degradation. By contrast, if the model is the source of new training data, collapse is hard to avoid.

The same is true of humans. If we want to prevent degradation in our thoughts, as adults we cannot narrow our exposure and become the dominant generator of the thoughts that run in our heads. Instead, we have to seek entropy. We need to be constantly exposed to novel “data,” ie, we need to be constantly reading/writing/speaking/engaging with new material, ensuring that many of the thoughts we are considering in our heads are not being generated by us, but rather by external, novel sources. This gets harder as we get older, but it is key to avoiding collapse and degradation.

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There’s something really deep about this idea. It doesn’t matter how smart you are or how good the “internal weights” of your neural network/brain are. If you aren’t exposing your brain to new kinds of data — data that shakes up your world model and distribution of ideas — you will inevitably face degradation and collapse on a negative feedback loop. You can’t just create totally new ideas ex nihilo that disturb your own way of seeing the world. You need fresh data that adds something new to the soup of ideas your brain is already simmering on.

Meditating on this should motivate one to seek out these sources of entropy: talk to new people, read new material, and try new things. Importantly, make sure this stuff is new. If you’ve read lots of novels, expose yourself to microeconomics. If you’re a mathematician, pick up a book on normative ethics. If you read a lot of history, maybe try and learn about some of the new breakthroughs in geophysics. If you want to stay in the same general vicinity, at least try and read from different communities or authors. And make sure you’re talking to new people, as much as you can.

I also do not hesitate to mention that this adds to the problematic nature of echo chambers. Not only do echo chambers create polarization, but they inevitably lead to degradation, as they are prime spots for getting stuck in collapse. Nothing screams homogenous data like a proper echo chamber.

One last point: adding entropy isn’t just key to avoiding degradation. It’s ultimately key to continuing to generate new ideas and being perennially creative, even within one’s field of speciality.

So get out there and seek some entropy to your training data. Please don’t collapse.

This is a mistake. Few things are intrinsically valuable or disvaluable. And this is what we should want. There are lots of reasons why we should seek to minimize the number of intrinsically valuable/disvaluable things in our moral theories. This post is about why you should join me in thinking this, and quit the habit of rushing to label anything you dislike as “intrinsically disvaluable.”

1 Intrinsic vs Instrumental Value

Something is intrinsically valuable when it is valuable in and of itself. That is to say, it has value — it is worth promoting, it gives you reasons for action — independent of any of its consequences. The paradigmatic example here is extreme joy. The sensation of extreme joy is valuable in itself: the world is made better (value is added) simply by its obtaining. This is so even if someone’s being extremely happy causally leads to lots of bad things happening.

Instrumental value, on the other hand, is not like this. Something is instrumentally valuable when it leads to something valuable, but the thing itself needn’t be of any value.

Now, it may seem as though instrumentally valuable things are uninteresting, and it is the intrinsically valuable things that we should really focus on. But appearances can be deceiving. Money, for instance, is only instrumentally valuable: it is not as thought green paper is itself valuable. It’s just that that green paper then allows you to buy things which are actually valuable. Most of the things that we focus our moral attention on are in fact not the intrinsically valuable things themselves, but are often connected with the intrinsically valuable things.

Here’s an (I think uncontroversial) example of something that is “only” instrumentally disvaluable: the action of lighting another human being on fire. This is an absolutely horrible thing. But it is rather clearly “only” instrumentally disvaluable: this action is bad because it leads to intense suffering. And the existence of intense suffering is an intrinsically disvaluable thing. To see that the action of lighting someone on fire is not intrinsically disvaluable, simply imagine a scenario where the person who is lit on fire is neurologically different from the rest of us, such that his skin being on fire actually makes him extremely happy. When his skin is on fire, he feels the same feeling of joy that you and I would feel when we achieve some great feat, like climbing Mount Everest or getting published in a prestigious law journal.

Now, the very same action — getting matches, flicking the lighter, applying heat to the skin — no longer seems like it makes the world worse. Indeed, if I am aware that the man is this way, it seems I have just as much reason to do this action as I would to do any other actions that we’d normally consider good for friends to do (like encouraging you to work on climbing, giving you motivation to achieve your goals, etc.). In fact, if you imagine yourself in a society where everyone gets happy from applying having heat on their skin — where you are considered a nice person if you are willing to take time out of your day to apply fire to other people’s skin so that they are happy, much like how in our society you are considered nice if you give your partner constant massages — it would be bizarre if someone suggested to you “no, no, that bodily motion of turning on your lighter and applying it to flesh is adding disvalue to the world. You’d better stop doing it now!” Simply imagine an alien came down to Earth and said that about massages, simply because, on their planet, massages often causally lead to pain.

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This little exercise shows that most of the things that we abhore and rightly denounce as wrong to do, we abhore because they are tightly connected to intrinsic disvalue. Applying fire to human skin often leads to a whole host of bad things. But it is not itself identical with disvalue. And this is evidenced by the fact that we can construct lots of causally-weird scenarios where we keep the act itself, and yet no disvalue obtains.

And this is all totally fine. I do not become a “defender of human skin-burning” just by pointing out that it is “only” instrumentally disvaluable. Instrumental disvalue is hugely important.

2 Do Not Multiply Intrinsic Value

Of course, there is no inconsistency in just labelling lots of things as intrinsically disvaluable. You could insist, for instance, that the act of applying fire to skin is actually intrinsically disvaluable, and all my thought exercise shows is that this intrinsic disvalue gets outweighed by the intrinsic value of the positive experience, so that it is all-things-considered worth bringing about. Of course, on this approach, you won’t be able to account for the intuition that, in the case of someone who gets happy from it, you have just as much reason to light them on fire as you do to help others achieve success. But you can always just bite that bullet.

In this way, you can always insist that lots of things are just intrinsically bad or good. And it is perfectly logically consistent. But let me show you why you should not do this.

You should view labelling something as intrinsically valuable/disvaluable as costly. This is because every additional kind of intrinsic value in your moral theory is an additional theoretical posit. And, not only does this detract from various theoretical virtues, but this kind of “value proliferation” really comes back to bite you when you start doing metaethics.

When you try explaining why something is valuable or disvaluable, or why value obtains where it does, nice and parsimonious explanations run out the more variety there is in what you’ve posited as an instance of value. The more gerrymandered and inflated your value theory is, the more difficult it becomes to give a unifying explanation of what it is that grounds morality.

As a sort of analogy, imagine that in every instance of some physical event, physicists resorted to positing a different “fundamental force” that explained that event. The sheer number of different basic, fundamental forces in such a theory would make it nearly impossible to provide a unifying theory of everything. Ideally, you only resort to positing new, fundamental forces or entities when you absolutely have to. If you can explain a physical event in terms of the forces already present in your theory, you should do so.

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The same is true when it comes to value. You don’t want to have various kinds of experiences, dispositions, and bodily motions all be bearers of different kinds of intrinsic value. Theories that only posit a few things as intrinsically valuable (say, well-being and virtue) and explain everything else as instrumentally connected to those things are preferable.

And this isn’t only because they are simpler and more parsimonious. It is because they make metaethics much easier. When we try to explain in virtue of what moral reasons arise, it is much easier to build successful explanations when the explanandum is unified in this way. For example, one popular way of providing a foundation for ethics is contractualism, where we imagine what rational agents behind a veil of ignorance would agree to. This approach tries to explain morality in terms of impartial prudence. Famously, this approach is very amenable to grounding utilitarianism, as it is rather plausible that agents would pick the rules that would maximize their expected well-being ex ante (which is just to maximize well-being for all). But one has to twist oneself into knots when applying contractualism to ground their theory if it has all sorts of random side-posits as intrinsically valuable. If I insist that the bodily motion of applying fire to skin is intrinsically disvaluable, I’ve got to try to provide some contractual explanation of the badness of that bodily motion … which is even harder than it sounds.

So, while it is tempting to label horrible things as intrinsically disvaluable, we should really try to limit our use of that label. Much like failing to eat healthy early on in life, this habit will come back to bite us as we progress along.

There is, however, a problem with these responses. And it is a problem that I see recurring in lots of debates about unintuitive theories (utilitarianism, the Repugnant Conclusion, consequentialism vs deontology, etc.). This post is about that problem.

The problem is this: these wacky theories have very-hard-to-avoid arguments in their favor. Let’s take EV-maxxing as an example. If fanatics like myself simply followed EV-maxxing because it is a nice way of “mathematizing” making choices, and because it has the guise of rationality because it is nice and “formal,” the arguments against EV-maxxing in these posts would be very convincing. Indeed, there are lots of formal alternatives to EV-maxxing. And, indeed, EV-maxxing has various unintuitive implications. It seems1 to be indifferent between a 1% chance of 100 billion dollars and a 100% chance of a billion dollars, whereas most of us are actually pretty risk averse and would strongly prefer the certainty of a billion dollars.

But it does not suffice to simply point out that some theory T has unintuitive results and that we can imagine alternatives. No, my friend. Unfortunately, we have to do one final step: we have to compare what the unintuitive results are of the alternative options. Theory T might have certain unintuitive results. But if all the alternative theories A, B, and C imply significantly more absurd things, then you should not reject T. Indeed, if A, B, and C, all imply that, say, 1+1=3, you should very probably believe T — even if you were right that T implies that I should harvest the organs of one person to save 5 others.

I call this “checking your work”. You can’t just point to some unintuitive result of a theory, and then construct an alternative. You must also check your work: does your theory involve significantly more absurd results than the original theory you were rejecting? If so, back to the drawing board you go.

This last step — checking your work — might seem obvious when put this way. But it is amazing to me how often it gets ignored in philosophy. In fact, this is astonishing because one of the ways philosophers and economists and mathematicians argue for various views is by showing that, if you reject the view, it strictly follows that any alternative theory must have absurd implications (in mathematics we have the strongest version of this argument: mathematicians can show you that if you reject their lemma, you have to give up the principle of non-contradiction).

Let me show you what I mean.

Expected Value/Fanaticism

It is easy to dunk on fanaticism. It recommends taking seriously tiny probabilities and doing crazy things like taking a 0.000001% chance of saving googolplex lives rather than saving 10 people’s lives for certain. People will often point out these ridiculous results of EV-maxxing, dunk on it, and then either end the post there or propose some alternative theory.

But here’s the problem. You have to check your work. What does your alternative theory imply? As it turns out, the arguments for fanaticism show that any alternative must recommend lots of super crazy things. If you’re a non-fanatic, you may have to believe:

• It is rationally required/permissible to lose all of my money for 0 gains (money pump arguments); AND

• It is better to take an N chance of positive utility, rather than an (N minus 0.000000000000000000000000000000000000000000000000000000000000001) chance of trillions of times as many utility ; or else transitivity is false; AND

• To figure out how I should act, I should figure out how well off the ancient Egyptians were;

• …

Yikes. Multiple super-crazy implications, for any alternative? Those alternatives aren’t looking so good now that we checked our work…

Of course, you should look into the proofs of why ~(Fanaticism) implies these propositions and various others (I’ve admittedly oversimplified a bit and there’s more nuance/other assumptions that could be rejected in some of those proofs). But that’s my point: check your work! Don’t just point out how unintuitive EV-maxxing is and then walk away. Stand up, show us your theory, and explain to us why getting money pumped is okay. Good luck! Of course, I don’t want to act like there aren’t rational, reasonable, and highly respectable ways of doing this. Very smart philosophers have attempted to do so. But once you start trying to explain all that away…you see how unbelievably difficult it is, and how comparatively easy life is as an EV-maxxer. There are a few weird things, but gosh they don’t seem nearly as unintuitive as those results.

I should add that it is also easy to check your work in this domain. People have already spelled out, in painstaking detail, what non-fanaticism will imply. You have the work already done for you! Just tell us which premises you deny, and why, or else tell us why the conclusion is acceptable.

This pattern of not checking one’s work — of simply pointing out the unintuitive features of one theory, and not checking to make sure that denying it doesn’t lead to even more unintuitive results — pervades a whole lot of Substack discourse.

Population ethics is probably the best example of this. The Repugnant Conclusion sounds crazy, and it is easy to dunk on additive theories of well-being. But, check your work. Population ethics is filled with impossibility theorems: if you reject the Repugnant Conclusion, you’re going to be faced with loads of unintuitive implications. Please, assess these for us, and explain why they are more acceptable than the RC. To be clear — I do reject the RC, and try to grapple with those unintuitive results here. But boy is it hard, and as a result, I still put quite a bit of stock in the RC being true. It’s a very reasonable view to have, once you’ve checked your work.

Similarly, people love dunking on utilitarianism and consequentialism. But they rarely ever grapple with the fact that rejecting those theories implies very weird results about what you should hope to be the case, or that you should act against how everyone would want you to act. Deontology, nebulous rights-talk, and rejecting “cold, calculating utilitarianism,” all sounds nice and obvious…until one checks one’s work and tries to grapple with these bizarre results of deontology. Again, I’m not saying that it would be irrational to be a deontologist. Of course it is! But I am merely noting that, upon checking one’s work, one starts seeing why utilitarianism is so plausible.

A similar pattern afflicted the discourse around Flo’s argument for sacrificing a human for many shrimp. Easy to shriek at the conclusion. Hard to explain away the implications of the alternative views of aggregation.

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My point here isn’t actually to defend Fanaticism, EV, Utilitarianism, Consequentialism, Shrimp Welfare, or whatever else. My point is: in philosophy we cannot merely shriek at theories and propose alternatives. We must check our work, and when someone shows that alternatives to some view face some implication, you must engage with that fact if you want to argue that your alternative is better.

Recently, I had a realization: I believe the reductionist view of personal identity gives you reasons to be good (i.e., help others be better off) when you are thinking purely prudentially! If I am right, Parfit’s theory entails that it is sometimes in your self-interest to help others over yourself. This is pretty odd. Indeed, it is sufficiently powerful that it could power a meta-ethical theory of morality, grounding (some) moral obligations in pure prudence — as Kant, and arguably Rawls, tried to do. All from an at least credible theory of personal identity.

Let’s examine why this might be the case.

1 Reductionism About Personal Identity

Parfit’s view of personal identity, roughly, is that it is not what matters. What matters, instead, is psychophysical connectedness.

To get a nice intuition for what this means, consider the concept ‘heap’. We might ask: under what conditions are there heaps? This, it turns out, is a tricky question to answer. Simply imagine what everyone would call a heap of sand — say, a billion grains — and remove just a grain. This, too, is a heap. Keep on doing this, though, and we’ll get to a single grain of sand, which is clearly not a heap. But it also doesn’t seem as though there is some precise point in the middle where our heap became a non-heap.

Of course, this isn’t too troubling, because most of us are reductionists about ‘heaps’. We recognize that it is a linguistic concept, one which we’ve constructed that is merely supposed to track an underlying feature of reality: mass or volume. If I wanted to make a law banning people from throwing heaps of snow at one another, what I should do — if my goal is to be precise — is specify that people cannot throw piles of snow above mass M or volume V.

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Parfit thought that we should think the same thing about ‘personal identity’. What matters is simply how psychologically and physically connected (how strongly “R-related”) I am to something else. Indeed, he thought there was a similar kind of Sorites one could give about personal identity. Richard Chappell, quoting Parfit, writes:

At the near end of this series is the normal case in which a future person would be fully continuous with me as I am now, both physically and psychologically.… At the far end of this series the resulting person would have no continuity with me as I am now, either physically or psychologically. In this case, the scientists would destroy my brain and body, and then create, out of new organic matter, a perfect Replica of… Greta Garbo.

At intermediate points along the series, varying proportions of the cells in Parfit’s brain and body are replaced in ways that make the resulting person more and more like Greta Garbo. But the series lacks drastic discontinuities. We can imagine a full series of possible people, starting with pure Parfit, then Parfit with a hint of Garbo, through various mixes of the two, until we reach Garbo with a hint of Parfit, and finally pure Garbo.

Parfit thinks we should respond to this Sorites series in much the same way. In the first few cases, the resulting person would be me. In the last few, they obviously aren’t. In the middle, the matter is just vague — because personal identity is a fuzzy linguistic concept, much like heaps. What we know about this series of people is the degree to which they are similar to me: how psychologically and physically similar they are to me. How strong the R-relation is between us. And that is what there are facts about: as Parfit put it, “if I knew these facts, I would know everything.”

2 The R-relation and Prudence

Ok, so all there is are the facts about R: how strongly R-related any two agents are. It seems to me that a natural step on this view is that the R-relation is the basis of prudence.2 That is to say, if I am trying to think about how to act in my own interest, what I should think about is how R-related a given person is. My future selves are the most strongly R-related things to me; so, I should put significant weight on their interests. Comparatively, strangers like you are very weakly R-related to me, so, prudentially, I should put little weight on your interests. If offered the chance to give you a dollar, or to save it for my future self, prudence recommends saving it.

The natural view here is to think of the R-relation as telling you how much you should care about someone. The more R-related they are to you, the more you should care. This would nicely explain why, eg, it is prudential to invest in your long-term future (by, say, getting an education). For it makes many people who are pretty strongly R-related to you better off (your future selves), even if it may come at the expense of a single person who is even more R-related to you (your current self).

Indeed, I suspect that if personal identity really reduces to the R-relation, the most plausible theory of prudence will tell you that you should maximize expected R-weighted welfare. Where R(S, P) designates the strength of the R-relation between an agent S and a person P:

- The amount of R-weighted welfare for an agent S who gives welfare W to person P = (W) * (R(S, P))

This is just a way of saying that if you are debating between giving 1 util to Ben (where R((You, Ben) = 0.5), or 1 util to your future self (where R(You, Your Future Self) = 0.99), you should give the util to your future self, since the expected R-weighted welfare from that action is 0.99, rather than 0.5.

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3 Morality? (Eh, Sort Of)

Here is where things get cool. If indeed it is in our self-interest to be maximizing R-weighted welfare, then that means it is sometimes in our self-interest to help other people rather than ourselves.

How can this be? Well, first, notice that we can construct a Spectrum Argument (not a Sorites series) to this effect. First, start with the following plausible principle:

If persons P₁ and P₂ are such that R(You, P₁) = X and R(You, P₂) = 0.99999*X, and you are deciding between giving P₁ N utils, or instead giving P₂ 2N utils, it is in your self-interest to give P₂ 2N utils.

Indeed, this just follows from maximizing R-weighted welfare. Now, where ‘>’ denotes which state of affairs is preferable for your self-interest, another plausible principle is:

If A > B, and B > C, then A > C.

From just these two premises, we get what we might call:

The Generous Repugnant Conclusion: It is in your self-interest to give a complete stranger hundreds of billions of utils, rather than to give yourself millions of utils.

This is a pretty amazing result. Indeed, while it might seem unrealistic to be in such a choice scenario, I suspect it is actually quite common. We can plausibly save someone’s life for a couple thousand dollars. I find it hard to believe that the marginal utility that, say, a billionaire gains from an extra few thousand dollars will get outweighed by the R-weighted gains someone else gets from living an entire life. If someone can convince Elon Musk to read Reasons and Persons, the irresistible force of prudence will compel him to donate millions of dollars to GiveWell!

Ok, but on a more serious note, this result can go quite far. Here are at least two more dimensions along which we can extend it. First, cases where many people are involved, even if the welfare gains for each are minimal. If there are enough such strangers, their interests will outweigh gains to yourself, from the perspective of your self-interest! Second, even cases where the R-relation is very weak (animals!) can still dominate over choices to help yourself, if the welfare gains are large enough, or if there are enough subjects at stake. But…*ahem*…this might mean that it would be in your self-interest to donate to the shrimp, or to prevent insect suffering.

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Of course, these wacky conclusions can all be avoided by modifying the theory of R-weighted welfare in familiar ways. You might give lexical prudential priority to subjects that are very strongly R-related to you rather than those that are weakly R-related to you. But this will lead to all the usual unintuitive results of lexical threshold views: eg, you’ll have to deny that it is in your self-interest to give someone who is 0.99*X R-related to you trillions of times as many utils, than to give someone who is X R-related to you a single util. Additionally, it is worth noting that those who accept this sort of reductionist view of identity are usually keen on accepting the conclusions of spectrum arguments, rather than embracing lexical priority and trying to find some rejection point in the middle.

So, if you’re a reductionist about personal identity, your theory of prudence is quite interesting: it implies that you should in many cases act beneficently.

If we want God to be certain, it turns out that (i) this has various super cool metaphysical implications about how God relates to the rest of the world, and (ii) uncertainty is extremely hard to avoid in some cases. I recommend you read that short post, and the wonderful comments, to see why.

At any rate, I think I may have made a bit of progress on some of these issues, and want to share some of these. I’ll first explain the challenge/problem again, and then give some of my new thoughts.

1 The Puzzle

Most of the things you believe are not things you should be certain in. Even things you are very confident in — eg that you have a hand — are subject to a skeptical scenario. There might be an evil demon giving you the seeming that you have a hand, when in reality you do not, as you are just a brain in a vat.

But there may be something you can be certain about: your own mental life. For instance, the fact that things seem to you thus-and-so, and that you have such-and-such phenomenological life, aren’t so easily amenable to a skeptical scenario. Even if we imagine an evil-demon that is giving you these seemings, you are still correct that such-and-such seems to you to be the case. As I explain, I suspect the lesson from this case is that those things which are constituted by your faculty of access (to put things very loosely and imprecisely) — the things you are directly acquainted with — are things you can be certain of.

So, I suggest that theists should think: God stands in the same intimate relation to all of reality that we stand to with respect to our own mental lives. Consider how direct a relation you stand to your seemings: this, I suggest, must be how God stands to the world. This needs more exploration, of course, but the idea would be that the world must in some sense be internal to God’s mind (and this is especially weird when you start thinking about the great variety of kinds of facts there are, from moral to physical to mathematical to phenomenological, etc.).

One of the challenging parts of this puzzle, explicated in the comments by Plasma Bloggin’, is the following: how does God know there is nothing outside of him? Sure, maybe he can be certain of some set of facts because that set of facts is in some sense within God’s mind. But how can God be certain this set of facts is the complete set of facts?

Here’s one possible solution.

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First, let’s think about a domain where God might plausibly have “complete” knowledge. A nice domain to think about is logic, and in particular, logical theorems (or tautologies): things like ‘p & q → p’ or ‘p → p v q’. Suppose someone asked you: how is God certain that there aren’t tautologies other than those he currently believes?

The question seems a bit odd. It actually doesn’t seem so implausible that God would be certain that He believes all the tautologies. Why? Well, because logical theorems are all interconnected. They are all related by the entailment ( ) relation — a single theorem entails all the others. The completeness of God’s knowledge is guaranteed by the kind of thing to be known: there just can’t be other theorems out there if one (fully) understands the valuational structure of classical logic.

This feature is also likely the case for mathematical propositions, at least if the set theorists and/or category theorists are to be trusted.

The takeaway, I think, is this: in domains where everything is interconnected — where everything is true or false together — we may be able to get completeness.

And this inspires my next move when it comes to God and reality: perhaps all true propositions are like the logical and mathematical propositions. What obtains is necessarily the case, and it’s not as though things could have been otherwise: once one fully understands what reality is like, one sees precisely what is true and false. What has happened, what will happen, what is currently the case, etc.1

So, the answer to why God can be certain that there aren’t any facts he’s missing is because there couldn’t be any other ones: when you are directly acquainted with reality, you become certain about all the true propositions, because the true propositions are all interconnected.

Now, of course, there are a lot of hanging parts here, and I haven’t spelled out the steps with nearly as much precision as I would in a paper. So there is much to say. But let me address the elephant in the room: doesn’t this require thinking that necessitarianism is true? That’s absurd!

Fortunately, necessitarianism isn’t so weird.

Let me also put together a few parts of this theistic picture that I think should make theists less averse to this necessitarian view. I think that, if you’re a theist, you should think that God creates a vast multiverse, with all stories and ways-things-could-go that are worth creating (following philosophers who conceive of worlds as including all their times, these stories also include various afterlives). Reality is vast, and so many intuitive ways that one thinks the world could have gone are in fact real. Suppose that the other ways the world could have gone are gratuitous evils — things the theist already likely thinks are metaphysically impossible. If you suppose further that there is a singular, best multiverse (which I currently doubt, but doesn’t seem crazy to me: why isn’t the multiverse with all the worth-creating stories the best one?), then it seems plausible that theists should think this multiverse would necessarily be created by God.

In other words … it may well be that theists should already think that reality necessarily goes as morality requires God make it go.

And theists should be more disposed to this possibility, if it indeed does help them solve the puzzle of divine certainty.

This post was probably the most speculative one I’ve had yet (and I love speculating!). Let me know what you think!

The usual reaction to this thesis is an incredulous stare. How could it be that things could not have been any different? It sure seems like some things are contingent. I could have worn a red shirt today; I could have poured an extra bit of water in my morning bowl of kale; my local library could have had one less book than it actually does; there could have been 5 fewer blades of grass in Central Park than there actually are. It may seem pretty implausible to suggest that things had to be precisely as they are. It really isn’t even possible that my dad could have had one additional strand of hair?

In this post, I’ll try to convince you that this view is not as crazy as it might sound.

1 Getting Clear on “Possibly”

It is important to keep in mind that the kind of possibility we have in mind here is metaphysical possibility — metaphysical possibilities are ways the world “really could have gone”. This is distinct from logical possibility. Logical possibilities are simply consistent descriptions of the world, but not necessarily ways the world really could have gone.

A few examples might help. Theism is one way to illustrate the concept of metaphysical possibility. On theism (as I’ll use the term here), it is metaphysically necessary that God exists. The world couldn’t have been such that God doesn’t exist: He has to exist. But this is not to say that there is some contradiction that can be derived from the statement “God does not exist”. It is perfectly consistent (with all logical theorems) that only a single particle exists. That is a coherent state of affairs. Nevertheless, it isn’t one that, for the theist, is genuinely possible for the world to have been like: reality is actually such that a metaphysically necessary being is the foundation of everything. If the theist is right, the single-particle world is internally coherent, but it is not a way that things could have actually gone.

A perhaps more helpful example is moral realism. Suppose there are moral facts — stance-independent facts about (eg) what you have reason to do. The standard view is that these facts are metaphysically necessary. It’s not as though in our world horrific torture is bad, but things could have been such that horrific torture is good. No, says the moral realist. Moral facts are inextricable parts of the fabric of reality: they are metaphysically necessary. That’s not to say that moral anti-realism entails a contradiction. There’s nothing strictly inconsistent about the proposition ‘there are no stance-independent moral facts’. I

Perhaps another helpful way to think about this is that we can imagine that, just as there are laws of physics, and ‘laws’ of logic, there might be ‘laws’ of metaphysics. Even if we vary how our world physically is (eg, imagining different initial conditions, different laws of physics, different fundamental forces), there are features of the world that are invariant: whether there are moral facts, whether God exists, etc. So ‘metaphysical possibilities’ are all the ways the world could have gone that are consistent with these ‘laws’ of metaphysics.

2 Is Necessitarianism that Weird?

So, necessitarianism is the view that everything is metaphysically necessary — there are no ways for the world to go other than how it actually goes. Here are some reasons we shouldn’t so confidently dismiss this view.

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First, we shouldn’t act like we have direct intuitions about metaphysical modality. Consider that what the metaphysical possibilities are depends deeply on what reality is essentially like. For instance, if reality is essentially divine (i.e., a perfectly good God exists as its foundation), then it will likely turn out that reality can’t go such that totally gratuitous evil exists. But, if reality is essentially naturalistic, this seems like a totally possible way for things to go!

This is why we should not claim to have much of an a priori grasp on the ways reality could go. Indeed, we should find this kind of claim — that we know a priori (!) the different ways reality could go — extremely implausible. Because we do not know, a priori, what reality is like! So how are we to know, a priori, the different ways it could go?

Now, you might respond that, when you reflect on the way our world has gone, it sure seems like things could have been different: things could be smaller or bigger, events could have happened slightly differently, history didn’t have to go exactly as it did, etc. But we should be careful about what these intuitions tell us. These intuitions are pretty great evidence that all these alternative scenarios are logically possible. The fact that I can vividly imagine, conceive, and construct such scenarios is pretty good evidence that they are internally consistent, do not violate any logical theorems, etc. But why is the fact that these scenarios are coherent (imaginable, conceivable, etc.) strong evidence for the view that these scenarios are really ways the world could have gone? Again, that depends on what the essential features of reality are like, and whether they are consistent with those alternative scenarios we imagine.

Maybe the thought is that these alternative scenarios are just so similar to the actual world, or just so benign, that it would be really weird for the essential features of reality to rule them out. But this is a really strained inference. I don’t think we should have much confidence in what reality rules in or out until we have actually given arguments and directly thought about what reality is like.

Now, this has all just been defensive: I’ve just been claiming that I don’t think we have much evidence (a priori) against necessitarianism. Let me give you some positive reasons why one might think necessitarianism is true.

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First, if one is a theist, one might be inclined to think necessitarianism is true. If God is perfect, plausibly, he would only do what is best. Just as God would necessarily not make there be gratuitous evils, God wouldn’t actualize what is inferior or imperfect. But, if there’s only one state of affairs that is best, then that state of affairs (the perfect world) is necessary. In other words, if reality is essentially and necessarily divine, it wouldn’t be too surprising for reality to be necessarily perfect — and there might only be one way to satisfy the description ‘perfect’.

Second, if one thinks that there is a necessary being at all. A very trendy response to contingency arguments is that some aspect of reality is necessary, but it needn’t be God — it could be that a wave function, or some other deep physical theory of everything, is necessarily the foundation. But there is good reason to think that this necessary being would also entail how reality is. It would be at least a bit odd if the necessary being indeterminately causes things to be one way rather than another: the particular distribution of the objective chances would have to be a brute fact, and we’d fail to have any sufficient explanation of why things are one way rather than another.

Third, strong variants of the Principle of Sufficient Reason. This sort of argument is likely why the early Leibniz and Spinoza embraced necessitarianism, and is the basis of van Inwagen’s argument against the contingency argument. Very, very roughly and imprecisely: If one thinks that for any fact, there must be an explanation of why p rather than ~p, one will likely end up thinking that necessitarianism is true. For either this series of explanations bottoms out in a necessary being that entails how things go, or else there is an infinite (or circular) series of sufficient explanations. The former option entails necessitarianism. Proponents of the latter will probably have to embrace that the fact that this entire series of explanations exists is itself necessary (i.e., it couldn’t have been otherwise), or else they haven’t fully explained every fact.

Fourth, huge multiverses. Imagine that the actual world is much larger than we suspect: rather than only our universe existing, many other universes exist. Indeed, imagine something like David Lewis’ modal realism is true: every consistent way for reality to go is in fact a concrete universe that exists, spatiotemporally isolated from our universe. Every one of those alternative scenarios we imagined earlier — me wearing a red shirt today; an extra bit of water in my kale; my local library having one less book; there being 5 fewer blades of grass in Central Park — are alternative universes that concretely exist. So, reality is an unbelievably large multiverse. On this view, this entire multiverse … exists necessarily! It couldn’t have been different. And is that so weird? Whatever way you imagine reality being different is in fact a way that a certain universe within this multiverse is.

Now, I don’t think we should take any of these that seriously as arguments. At least not without me being way more precise and saying much more. But that is not my point: I do not want to convince you that necessitarianism is true. What I want to show you is that we shouldn’t think it is some super implausible view that is a death blow to any view that entails it. Instead, we should think about things in the following way: to figure out what the metaphysical possibilities are, and how many there are, we should reason about how reality is like. On many theories of reality — theism, necessary-foundation theories, and other views on which every fact is fully explained — there aren’t alternative ways the world can go, because there is something essential to reality that entails (explains!) how things go. So it may well be that necessitarianism is true. Alternatively, it may well be false — especially if reality is essentially indeterministic (as deliberation about quantum mechanics and free will might unveil). But too often it seems that philosophers hold fixed that there has got to be contingent in various ways, and then they reason backwards from there. This is unfortunate.

This article is about a mistake that I have seen repeated many times in internet philosophy circles. This mistake is also deeply important, because once you see it, it makes less tenable some views of ethics and value.

This mistake is thinking that the Repugnant Conclusion (or, rather, the argument for the Repugnant Conclusion, which I will call ‘the Spectrum Argument’) is analogous, similar, or in any way parallel to the Sorites paradox (the “heap of sand” paradox). Many very smart people are under the impression that these two paradoxes are about the same issue, or commit the same kind of mistake (the legendary Flo seems to tentatively suggest this might be the case in their post on the Repugnant Conclusion). And it is often suggested that once we recognize that our everyday concepts like ‘hairy’ are vague/underdetermined, this too solves the paradox of mere addition.

Oh, if only population ethics were so simple. This is, unfortunately, far from the case. Despite appearances, the Spectrum Argument for the Repugnant Conclusion is simply a totally different puzzle from the Sorites Paradox.

I’m first going to start by explaining the Sorites, then I’ll explain the Repugnant Conclusion, and then I’ll explicate the differences between the two.

1 What is the Sorites Paradox?

The Sorites Paradox is a paradox about line drawing. Imagine that in front of you are 1 million grains of sand. This, we would say, is a heap of sand. Now, it also seems plausible that the following principle is true: If x is a heap of sand, then y (where y = x minus one grain of sand) is a heap of sand.

Basically, it seems as though one grain of sand could never be enough to make something that was a heap of sand no longer be a heap of sand. But this pretty quickly leads to issues: for, if this principle is true, it strictly follows that a single grain of sand is a heap of sand — which is obviously false!

To reject this conclusion, we must either say that there is a particular point at which a heap of sand, once it loses an additional grain of sand, is no longer a heap, OR, we must revise classical logic (e.g., by saying that truth comes in degrees and so as we remove more and more grains of sand from the heap it becomes less and less true that it is a heap).

No solution is perfect, but the general lesson is this: certain concepts we use (like ‘heap’ and ‘hairy’) are vague, and it may be indeterminate at various points whether they apply to an object. This is pretty general: for instance, it seems plausible that taking a single penny from a rich person is not enough to make them no longer rich. But, assuming Elon Musk is rich, accepting this principle would entail (in classical logic) that someone with a single penny is rich.

Put succinctly, the Sorites Paradox is about tolerance. A predicate like ‘is rich’ seems able to tolerate a slight change in the facts relevant to richness (money) while still obtaining. It seems, generally, that richness is tolerant of a single penny being taken away. But what the Sorites reveals is that that cannot be strictly right.

2 What is the Spectrum Argument?

Okay, let’s be clear on a few things.

First, we have the Repugnant Conclusion, which is the following proposition:

· Repugnant Conclusion: For any population A with billions of people living absolutely wonderful lives, there is an all-things-considered better population Z with some number n of people living lives barely worth living.

Next, there is the Spectrum Argument, which is an argument for the Repugnant Conclusion (again, a proposition). It relies principally on two propositions:

· Quality-for-Quantity: For any population X with n lives of well-being l, there is an all-things-considered better population Y with (10^100) * n lives of well-being 0.99999999999999 * l.

· Transitivity: If population X is all-things-considered better than Y, and Y all-things-considered better than Z, X is all-things-considered better than Z.

These two propositions entail the Repugnant Conclusion. Quality-for-Quantity provides us with a spectrum of populations, A, B, C, D, E, F, …, Z, where in each one everyone is enjoying a level of well-being almost as high as its predecessor, but there are 10^100 as many people enjoying those good lives. Transitivity secures that Z > A, i.e., the Repugnant Conclusion.

If you don’t think the Repugnant Conclusion is that crazy (a position I am sympathetic to), we can generate a parallel Spectrum Argument for the following proposition:

· Tortures over Pinpricks: A world of billions of horrific tortures is preferable to a world of n mild, barely noticeable pinpricks.

All we’d need is the principle that it is worse for a trillion times as many people to experience an almost identical pain than for a trillion times fewer people to experience a slightly worse pain, alongside transitivity.

It’s at this point that people will start pointing out the similarities between the Sorites series and the Spectrum Argument. In the Sorites series, we apply a very seemingly plausible principle, but repeated applications of this principle get us an absurd result. Same for the Spectrum! Quality-for-Quantity looks great, until you apply it repeatedly across a Spectrum of populations, and suddenly, alongside transitivity, you get a (repugnant!) result.

But this is way too quick.

First, what makes the Spectrum Argument so tricky is that it appears as though, every time you trade a bit of quality for a lot of quantity, things are getting better. But then you reach a point (Z), and compare it to what you started with, and it seems as though things have gotten worse!

This is not the puzzle involved in the Sorites. Every time I take out a penny from Elon Musk’s account, it’s not as though I think he is getting richer, and then, when I’ve finally gotten all his net worth down to 0, I suddenly think … wait, Elon seems poorer than when he started out! No, the Sorites, as we said earlier, is about tolerance. I do not think he is getting richer with every removed penny. The puzzle is that I think richness can always tolerate the miniscule change that a penny brings in richness. And, it turns out, richness cannot always tolerate such miniscule changes. And yet, despite this, I hesitate to say, at any particular point, that that is the point where Elon Musk went from rich to not rich.

There is no puzzle of tolerance involved in the Spectrum Argument. My intuition is not that trading a bit of quality for lots of quantity is something the goodness of a population can tolerate: it is that such a trade would make the population even better. However, simultaneously, I have the intuition that, if quality is too low, no amount of quantity could ever make up for it.

This also explains why the fundamental problem to be solved in each case is different. The problem to solve in the Sorites is a line drawing problem: where, in particular, is the boundary between rich and not-rich? Comparatively, the problem to solve in the Spectrum Argument is a question about tradeoffs: how could it be that trading off quality for quantity doesn’t make things better? Notice: the puzzle here is not “where, exactly in the sequence are you saying things don’t get better?”

Finally, one can see that the Sorites and Spectrum Argument are different simply by observing that the two involve differently structured concepts. The Spectrum Argument is about multidimensional concepts. For instance, how good a population of lives is seems to depend on (at least) two dimensions: quality (how good the lives in the population are) and quantity (how many lives there are). And the puzzle is that we have two (potentially conflicting) intuitions about this multidimensional concept: we believe that you can always trade off a slight loss along one dimension for huge gains in another dimension, and yet also that, if one dimension is very low, no amount of the other dimension can compensate.

Comparatively, the Sorites can be about unidimensional concepts. Whether something is a heap of sand can depend on literally only one dimension: how many grains of sand it has. And yet, we can still generate a line-drawing problem about where we want to draw the line between heaps and non-heaps.

To see my point most vividly, just consider that we can construct Spectrum Arguments concerning concepts that are usually the subject of the Sorites paradox. For instance: one version of the Sorites concerns the concept hairy. The plausible principle here is: if someone is hairy, and you remove one hair from their head, they are still hairy. But this will generate issues as, eventually, you’ll have plucked all the hairs from someone’s head and make them clearly not hairy.

Here's what a Spectrum Argument concerning hairy would look like (I steal this from Larry Temkin, who stole this from someone else): suppose that how hairy you are is actually a function of two factors. It is not just a function of the pure number of hairs around your head, but it is also a function of the distribution of your hairs. For instance, if you have hair, but it’s all around your neck and ears, such that you have a massive bald spot in the middle of your head, you are not hairy, even though the pure number of hairs you have isn’t too low.

Given this, we might be tempted to endorse the following principle, which trades off between the distribution of hairs for an additional number of hairs:

Distribution-for-Number: If I remove one hair from the middle of someone’s head, but double the number of hairs he has, this person has gotten hairier.

The trouble (maybe) with this principle is that, if we apply it repeatedly on a person who starts out with a normal amount of hair everywhere, we will eventually get someone who has a massive bald spot in the middle of their head, with a lot of hair on the side. This person (we might say) is less hairy than when he started, even though each individual move seemed to make him hairier overall.

Now, maybe this principle about trading off between the distribution of hair and the number of hairs isn’t too plausible. Or maybe the final verdict should just be that the person with the bald spot is actually hairier than the person we started out with. My point is merely: this is a different puzzle than the puzzle about plucking a single hair from someone until they are bald. The question here concerns trading off between two aspects of ‘hair’, whereas the question in the Sorites series of ‘hair’ is: is ‘hairiness’ intolerant of even a single hair being plucked off someone’s head?

Of course, I should be clear that this is not to say that the Sorites is totally irrelevant when thinking about the Spectrum Argument. It might be that some moves within the dialectic of the Spectrum Argument may eventually make use of resources from the work on vagueness. For instance, if one defends a lexical threshold view (a view on which no amount of x’s could ever be of more total value than some number of y’s) , one question from opponents may be about where such a threshold should obtain. Here, one can make analogies to the Sorites paradox and adopt one of those solutions to answer the lexical skeptic.

But that is compatible with the thrust of this post. My point here has merely been that the Sorites paradox and the Spectrum Argument are two different arguments, not that, within each argument, there aren’t moves you can make to defend one particular view that uses work on vagueness. Indeed, vagueness and line-drawing is part of most philosophical debates concerning some concept or other.

Do not be fooled by the fact that the Sorites and Spectrum Argument both involve applying a principle many times across many cases. The two arguments are subtly different. Next time you hear someone saying they are the same, send them this post! :)

Now, despite this, I’ve recently come to realize something: I think justice has made the world worse. This concept we have — in particular, that people must face some kind of retaliation, or at least be deprived of well-being, for doing something deeply immoral — has very likely driven us to act in ways that make the world way worse than it would otherwise be.

Of course, this doesn’t mean that we are incorrect in thinking that justice or desert exists. I think it is indeed a moral ideal. Rather, my point is that our having this belief in desert has probably made the world worse.

Consider the history of war, at a very high level of generality. Many wars in human history — whether they were between tribes, clans, kingdoms, countries — have been waged in large part out of a collective sense of injustice. Some “other” group wronged “our” group (perhaps by killing one of our members, or mistreating one of our members, or wronging us in some other way) and, in response, we wage a full-scale, bloody war that results in lots and lots of death, often significantly more than the original incident, involving many innocents, and far from what might be “deserved”.

A particularly crazy example of this is the War of Jenkins’ Ear. Apparently, in 1731, Spanish coast guards boarded a British ship and maimed its captain, Jenkins, and cut off his left ear. This incident was later used in Britain to stir up outrage at the Spanish, leading to a war with Spain that would eventually kill almost 35,000 people over the course of a decade.

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Did those Spanish coast guards deserve some punishment for what they did? Yes, probably so. But moral desert is one of many moral ideals — another of which is welfare. And it is grossly immoral to destroy 35,000 lives simply to get justice. Of course, things aren’t as simple as I describe them: the incident with Jenkins was really more of an excuse used by British politicians to incite the war, and the many casualties came as a result of several tit-for-tats that happened after Britain’s first attack on Spain in response to the Jenkins incident. But if it is foreseeable that your attempt to give enemies their just desert will lead to responses by your enemy, which will snowball into a 10 year war of tens of thousands of deaths, the moral thing to do is to not engage in warfare (assuming your not engaging won’t itself lead to worse consequences).

But this is hard to see in the moment. The idea of seeking justice for a wrong is so deeply ingrained in (at least some) people that it becomes used as a blank check for grossly disproportional amounts of violence in the long term. Even if justice is indeed a moral ideal (as I take it to be), if we were morally perfect this is not how we’d act. Instead, we’d balance the intrinsic value of giving people what they deserve with the expected harms that result from our act, and do the appropriate balancing, inflicting harm only to the extent that it is purely preventative of future harm, or worth it for the intrinsic value of the justice we might be able to serve.

Similar things can be said about much of modern-day foreign policy, from the US war in Iraq to today’s war in Gaza. Gaza is, indeed, a case in point.

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First, start with October 7. Many defenders of the attacks by Hamas will appeal to the long history of fighting between Israel and Hamas and various acts of alleged wrongdoing by Israel to the Palestinians. Let’s just grant that this is fully right and that, from the perspective of desert, Israel deserves some sort of punishment. Does that really justify killing thousands of innocent people, which will predictably lead to immediate, prolonged warfare, and likely massive instability across the entire region? In fact, that is not even the question. Rather, the question is: is the justice that would be served outweighed by the ungodly amounts of disaster, death, and misery that the attack inflicts and will predictably lead to more of? Or, instead, would it be better to literally forget all of the atrocities and injustice that Israel has (we are granting) committed, and negotiate for peace without holding any grudges? Of course, there are going to be important arguments in response that peace is impossible and that it would be naïve to think no violence will happen in the future. Naturally, these arguments need to be treated on their own terms, but notice that these arguments are not based on justice, they are based on deterrence, incapacitation, and preventing future harms.

Now, turn to the 2-year war that Israel has waged on innocent Palestinians. Hospitals have been bombed, schools have been destroyed, homes have been pummeled. Today, there is a growing threat of famine, starvation, and a stifling of aid by Israel. A tragedy of unspeakable proportions. The defenses of Israel’s actions are all centered around punishing Hamas in various ways: if Hamas gets access to some of the food aid going to starving children, the aid has to be blocked. If Hamas might be in the hospital, we have to bomb it. If Hamas might be in area, we’ve got to blow everything and everyone away. Until the hostages are released, it seems, all actions are on the table.

Of course, Hamas may well deserve to suffer for what it has done: but, just like in the War of Jenkins’ Ear, justice is not infinitely valuable. Justice is one of many moral ideals. And when one’s pursuit of justice comes at gross costs to well-being … its time to cut the losses and pursue the greater good. But, again, it is hard to see that in the moment.

Here too one might point out that there are non-desert reasons for unrelentingly attacking Hamas, namely, safety and prevention of future attacks. But it seem pretty plausible that the nature of the attacks in Gaza, and the growing threats of malnutrition, are not near the optimal maximize-the-total-number-lives-saved, even when justice is weighed in and the prospect of future attacks are included. Especially if our analysis is done fully impartially.

The tragedies of wars and attacks on the basis of past actions all make me think that the world would probably be quite a bit better if we lacked the concept of justice and desert. If, instead, everyone simply thought in terms of what things we need to do to make sure people are well-off — irrespective of who it is — probably the world would be much better, even if justice and desert are actually morally valuable.

Certainty: I will flip a coin. If it lands either heads or tails, 100 people will get an additional year of happy life.

Risky: I will flip a coin 10000000000000000000000000000000000000000 times (10^40). If it lands heads every single time, 10^500 people will get an additional year of happy life.

Which should you choose? To see it from perhaps a more pragmatic perspective, if you had to give a dollar to charity, and one charity will definitely help 100 people, whilst another one has a very slim chance of helping an unbelievably, astronomically high number of people, which should you donate your dollar to (assuming it’s the dollar necessary to keep one of them permanently going)?

Intuitively, many will say Certainty is the better option. 100 additional lives for sure is surely better than what is an effective impossibility of some huge payout.

Fanaticism says that you should take Risky — a very tiny probability of a large enough payout is always better than certainty of a pretty good payout.

Despite its initial implausibility, though, I firmly think that upon reflection fanaticism is clearly true. The arguments in its favor are, to my mind, unbelievably strong. And there are so many, each of which converging on Fanaticism. The strength of the case for Fanaticism is that denying it leads to lots and lots deeply crazy results: bullets that I do not have the gall to bite.

And I hope to convince you of this. This post will go like this: I’ll present a barrage of arguments, showing just how absurd the consequences are of denying Fanaticism.

To those who do not want to read the entire post, this is basically what one will have to accept if they do not accept Fanaticism:

• If you are offered a 60% chance of saving 100,000 lives, or instead a 59.999% chance of saving a Googleplex to the power of a Googleplex number of lives, you should take the 60% chance. (Or: that transitivity is false).

• Your preferences should be such that you can be money-pumped: I can offer you a series of offers such that you’ll have lost money with 0 gain at all.

• In your assessment of two offers, you need to figure out what life was like for the Ancient Egyptians before you can know which you should choose

• Even though you should take Certainty over Risky, if your life is long enough, you should take Risky over Certainty

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Argument #1: The Intuition Pump

Most of the arguments for Fanaticism are going to be of the form “Look at the insane results you have to accept if you deny it.” However, first, I want to give an intuition pump for Fanaticism: I’d like to give you an intuitive feeling for why this would be true, which, even if it does not sway you to change your mind, will at least soften you up before you hear about what results from denying it.

Imagine you’re going to live two lives, Life1 and Life2. The only purpose of Life1 is to stack up as much money as possible to use in Life2. Let’s imagine that you live for 1 trillion days in Life1.

Every day, I give you the following offer between two options:

Certain Money: 100% chance of 100 dollars.

Risky Money: 1/trillion chance of 10^100 dollars.

Which do you take? Well, if you’re not a Fanatic, you’ll likely want to pick Certain Money every time. So, by the end of Life1, you’ll have 100 trillion dollars (10^14). If you’re a Fanatic, you’ll pick Risky Money every time. By the end of Life1, you’ll very likely have at least 10^100 dollars — in other words, you’ll very likely have at least trillion trillion trillion trillion trillion trillion trillion TIMES as many dollars (you might object that there is an off chance that you get nothing…but of course there’s also an off chance that you get 10^100 dollars twice, or three times, etc.). And, of course, the more times the bet is offered, the better and better the Fanatic does than the non-Fanatic.

This highlights a really important point: all a probability is is a frequency. It tells you the rate at which something happens. And if your goal is to maximize something, it is simply the case that, if the payout is big enough, you should take the lower rate with a bigger payout. Because, in expectation, it will simply lead to more!

Now, you might object here that if the offer between Certain Money and Risky Money is offered many times, then Risky Money is obviously better. But, in a one off, Certain Money is just better. But this is very odd. If Certain Money is just a better offer than Risky Money, why not take it every time? To illustrate: imagine that you are living through Life1, and you’re on day 20,000. If you really believe that Certain Money is better than Risky Money, shouldn’t you just take Certain Money today? Even if you take Risky Money every other day, and every day to come in the future — isn’t it better to just take Certain Money today? 999,999,999 bets on Risky Money and 1 bet on Certain Money is surely better than a trillion bets on Risky Money, if Certain Money is better than Risky Money. But then this argument can just be applied again and again to conclude that you should take Certain Money every time.

Hopefully this gives an intuition pump for why Fanaticism isn’t so weird: picking risky prospects, if the payout is big enough, is simply picking a rate of return that consistently gives you more money than any other strategy. This becomes obvious when we simply zoom out and think of things in the long run — but it’s hard to see a reason why the number of times I offer you a bet should change which one is better.

Nevertheless, worry not if you are not convinced by this intuition pump. Let’s get to the arguments.

Argument #2: Money Pumps

A ‘money pump argument’ is an argument that attempts to show that your preferences should conform to a certain rule R, because if your preferences do not, your preferences will lead to you being exploited for free.

For instance, it is often thought that we can give a money pump argument for the rule that your preferences should be transitive: if you prefer A to B, and B to C, then you should also prefer A to C. Just imagine someone who prefers oranges to apples, apples to kiwi, but, prefers kiwi to oranges. If they have a kiwi, and I offer to swap out their kiwi for an apple (which they would prefer!) for a single penny, they do so (let us say they strongly prefer apples to kiwis). I now offer to swap out their apple with an orange, as long as they pay me another penny. They do so. But because they prefer kiwis to oranges, I now offer to give them back the kiwi for the orange, as long as they pay me a third penny: which they gladly do. They’ve now given me 3 pennies for free. And, of course, I can keep pumping them for all their money, while they sit their smiling  (irrationally!)

This seems like a pretty great argument that your preferences — at least, your strong preferences, the kinds you’d be willing to pay money to satisfy — should conform to transitivity.

If you agree, I’ve got bad news for you. It turns out that we can show that, if your preferences do not conform to 3 other conditions (what usually get called Continuity, Independence, and Completeness), then you can also get similarly money pumped. So your preferences should conform to Transitivity, Continuity, Independence, and Completeness. But it turns out that these 4 conditions are the 4 axioms of Expected Utility Theory! If you follow these 4 conditions, it strictly follows that you should be a Fanatic and prefer Risky to Certainty.

For purposes of space, you can find the proofs of these money pumps here. But if you take seriously the money pump argument against transitivity … you should likewise take seriously the problems the money pump arguments against denying Fanaticism!

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Argument #3: The Continuum Argument

The next argument for Fanaticism is a continuum argument. Imagine that you’ve chosen Certainty: I’m about to flip a coin, and no matter how it lands, 100 lives will be saved. However, before I flip, I offer you the option to switch out Certainty with the following prospect:

MoreLives₁: 99.9999% chance of saving 100,000 lives.

Would you take an almost identical probability of success (just 0.0001 less) to save a thousand times as many lives? Well … that sure seems way better! So, you take MoreLives₁. But, before we proceed, I offer you:

MoreLives₂: 99.9998% chance of saving 100 million lives.

Again, you ecstatically take MoreLives₂ over MoreLives₁: to save a thousand times as many lives for an almost identical probability is a no brainer.

But you likely see the problem now: I can keep doing this, reducing the probability of success by ever-so-slightly whilst also increasing the payout by 1000x. Eventually, we’ll reach Risky! By Transitivity, then, Risky must be better than Certainty.

If you want to avoid this conclusion, here’s what you’ll have to say (other than denying transitivity): if you have a (say) 60% chance of saving 10 million lives, that is always better than a 59.9999% chance of saving any number of lives! Imagine that in front of you is a button that, if pressed, has a 60% chance of saving 10 million lives. I then tell you that I can increase the number of lives that the button will save to be every human who has and who ever will be in danger: the button will prevent climate change, every existential risk, cure every disease, prevent every war, etc. (and there will be no negative effects from this). And the button still works with a 60% chance! The only catch is this: if the payout of the button is improved in this way, before pressing it, you and I have to each think of a 100-digit number. As long as we don’t think of the same number, you can press the button. But if we do, then the button becomes defective.

Would you play the 100-digit-number game, in order to save all of humanity with the button? Surely you should!

But, if you’re going to deny Fanaticism, you’re going to have to say that we should be timid and not play this game despite the prospect of saving all of humanity … or else, deny transitivity.

Argument #4: Another Continuum

There’s another clever continuum argument in support of Fanaticism that I recently read in this paper which I found quite convincing. It’s short enough to paste in full, so I will do so:

Consider, for the sake of concreteness, the prospect 𝑃 of saving 1,000 lives with probability 0.1. A theory that is timid with respect to lives saved might say that 𝑃 is no worse than the prospect of saving even a vast number of lives with probability 0.099, only one percent smaller. We can imagine that the outcome of 𝑃 depends on the outcome of a raffle: if the golden ticket is drawn, then a mechanism will be activated that will save 1,000 lives. Now consider a prospect 𝑃1 that differs from 𝑃 in two ways: first, the mechanism is designed to save many more lives—let’s say 10,000; but second, there is a one-percent failure rate, and in the fail-state, 𝑃1 saves only 999 lives. So 𝑃1 almost certainly leads to ten times as many lives saved as in 𝑃, and at worst, in the highly unlikely fail-state, it will save only one life fewer. Intuitively, 𝑃1 is much better than 𝑃. But now consider a prospect 𝑃2. In 𝑃2, the mechanism usually saves 100,000, but it only saves 998 in the failstate. So, compared to 𝑃1, there are almost certainly 10 times as many lives saved, and at worst one fewer. 𝑃2 is clearly better than 𝑃1, so also better than 𝑃. But if we continue this sequence along, we get to 𝑃1000, in which no lives are saved in the fail-state. Thus 𝑃1000 leads to a vast number of lives saved (namely, 101003) with probability 0.099. By transitivity, 𝑃1000 is better than 𝑃. And so, the argument concludes, our theory of value must not be timid in this particular way. Nor is there anything special about this case; mutatis mutandis, we have an argument against timidity in general.

Argument #5: Distant Galaxies

The last argument for Fanaticism I’ll give you is that, if you deny it, you’ll have to say that what is going on in distant galaxies should affect which choices you should make, even if your choices have zero influence on what goes on in those galaxies. [I adapted this argument from here and here].

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To see why, imagine you are offered two prospects, where 3 different results are possible:

Seems pretty clear a 95% chance of saving 1 million lives is better than a 0.1% chance of saving 1 life. But now imagine I inform you of the following: on Krypton, there’s someone who is about to press a button, which has a 95% chance of saving 1 life.

So, really, your decision now looks like this:

Now, your decision is between a 95% chance of 1 million and 1 lives, or a 95.1% chance of saving 1 life. Of course, if we are not timid — if we are willing to take a 0.1% hit in probability to save a million more lives — MoreLives is still the better choice, and what is going on in Krypton doesn’t change anything. But, as we learned from the previous continuum argument, those who reject Fanaticism must be timid (or else reject transitivity)! They must say that there are cases where a 0.1% hit in probability is never worth it, even if it leads to much larger payouts. But that means that MoreLives, because of what is about to happen on Krypton, is now worse than LessLives.

If you reject Fanaticism, you have to either reject transitivity, or else you have to say that, before we decide what is the better decision, we must first figure out what is going on in causally isolated regions of space that are completely unaffected by what decisions we make!

The problem, in a nutshell, is that utilitarianism doesn’t seem able to capture the moral weight we tend to place on self-sacrifice.

Imagine, for instance, that you and your dear friend Sam are walking along in the city. Suddenly, an armed man appears, and he aims his gun at Sam’s head. He says: “I’ve got one bullet, and it’s coming for your head!” He then fires. You are terrified as you hear the bullet fire — you have a great life ahead of you, you are constantly cheerful and happy, and you don’t want to die. But you also have a deep love for Sam, you want the very best for him, and despite the fact that you don’t want to die, you do something truly amazing: you jump in front of Sam and take the bullet yourself. You sacrifice yourself so that Sam can continue to live: you loved Sam so much that you gave up your own life so that he could keep living.

It seems like what you’ve done here is the pinnacle of a moral act — you gave up your own life for someone else’s. You should be lauded for what you did. However, if we make some basic assumptions (in particular, that your life, had it gone on, would have consisted in a slight bit more happiness than Sam’s), then utilitarianism entails that what you did was the wrong act. You should not have done this. If we all care about right action, instead of applauding you, we should all be upset that you did what you did and wish that you had not done this.

But isn’t this absurd? How can such noble actions be wrong? Indeed, if we change the facts further — if we imagine that you were going to live a much better life than Sam — everyone should deeply condemn your action of self-sacrifice. By sacrificing yourself, you made the world way worse than it would otherwise have been. If utilitarianism is true, future generations should look back at you with regret, sadness, and condemnation.

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Or, imagine that you and Sam are going to live equally good futures. Then the armed man fires at Sam. On utilitarianism, should you choose to sacrifice yourself for Sam, this means nothing — you may as well do nothing, there is no difference either way. Things are not any the better should you choose to courageously sacrifice yourself than if you instead choose to faint-heartedly run away.

The problem here is kind of a cousin to the problem of consent for utilitarianism: common-sense morality evidently tells us that consent has the power to “transform the normative landscape.” If you consent to being killed to save five, that isn’t as bad as my killing you to save five (without your consent), even if the effect on total utility is the same in both cases.

Put another way, we tend to think that self-sacrifices are deeply virtuous, noble, and good acts. And they’re not so wrong because, when it comes to your own well-being, you have the power to consent to it being given away to save another. But utilitarianism has a difficult time accounting for the virtue of such acts, because the virtue of such acts does not come down to whether they maximize utility.

What should utilitarians say in response?

Well, there are two kinds of replies: replies that try to accommodate the intuition, and replies that try to explain why we should reject the intuition.

I think replies that try to accommodate this intuition are implausible. A straightforward way of accommodating the intuition is simply expanding one’s value theory — say, by claiming that virtue intrinsically valuable. But the utilitarian does not have this option: their view just is that the only intrinsically valuable thing is utility or welfare. Now, they might try to accommodate the intuition of the value of self-sacrifice by expanding their theory of well-being: but it’s pretty implausible that self-sacrifice makes one’s life better.

However, even though accommodating replies probably don’t work, I think replies that try to explain away the intuition are much more successful.

First, utilitarians can make their standard distinction between criteria of rightness and decision procedures. A community where we encourage people to be selfless and to care deeply about others’ well-being — even beyond their own — is one that will tend to be very good and leads to more well-being overall. So it is a generally good procedure of decision-making to be selfless. But that does not mean that we should think there is something intrinsically valuable about selflessness as such.

Now, I don’t think this standard reply is quite enough to blunt the force of the issue: the intuition here seems to be that there is something intrinsically valuable about being selfless. This in some way makes the world better: it isn’t just a useful rule of thumb that we have internalized.

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But the utilitarian can say more. As I have explained before, there is an important difference between right action and praiseworthiness. On utilitarianism, people can be blameworthy or praiseworthy for doing an act, independent of how right or wrong that act is — e.g., utilitarians are not committed to the thesis that one who intentionally harms another is equally blameworthy to one who unintentionally inflicts the same amount of harm. What attributions to make of people is a separate question from how good or bad their actions were: and utilitarianism is only a theory of right action, not a theory of people-attributions. So the utilitarian can say that you are noble, praiseworthy, laudable, and admirable for sacrificing yourself, while also maintaining that the world would have been better off if you had not sacrificed yourself. Of course, this would mean that you can be praiseworthy for non-right actions. But I don’t think that is weirdest in the slightest — you are presumably also praiseworthy for donating 99% of your money to charities that, according to all your evidence, are super effective, even if it turns out that, unbeknownst to everyone, the butterfly effects of those charities are, on the whole, very bad. Thus, we would do well to distinguish between how good of a person you are for sacrificing yourself, and how good your act was.

Indeed, let’s think carefully about the case where you save Sam by sacrificing yourself. If we’re saying that, contrary to the utilitarian, the right action is to sacrifice yourself, it must be not morally right to let Sam die. But that doesn’t sound super plausible … putting things this way suggests that the real intuition behind self-sacrifice isn’t about right action, but instead an intuition about what we want to say about people who engage in self-sacrifice.

But I also know that many do not share this final judgment — they think that it’s not just that the person who self-sacrifices is praiseworthy, but that their act was the right act! I’m not so sure about that. Sometimes I find it plausible, other times I do not.

Before we get there though, first we must ask: what the heck does it mean for something to be metaphysically possible?

The standard answer is: metaphysical possibility is a way the world really could have been. Admittedly, not very helpful. But I think there are a few illustrative examples that might help.

For instance, consider the debate between Platonists and nominalists over whether the number 2 exists. If I’m a Platonist, and I think there is a Platonic Form of 2 floating in Platonic heaven, it’s at least coherent for me to think:

You know, even if the laws of physics were different, abstract mathematical objects would still exist. Mathematical objects are essential to the way reality is. The world just couldn’t have been such that the number two didn’t exist.

This isn’t altogether unreasonable, and I can definitely put myself in the mood of thinking that, if numbers do exist as abstract objects, reality couldn’t have gone such that those things didn’t exist. Importantly, both possibilities (numbers existing, numbers not existing) are logically consistent — but it nevertheless might be that one of them, despite being perfectly consistent, is just not a way reality could have been given the way reality essentially is.

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Or, consider the debate over personal identity: whatever it is that makes persons persons, it may well be that there is some sense in which those facts are necessary — no matter the physics that our world happened to take on, no matter how things go, what makes persons persons would still be the same.1

Okay, let’s assume there are facts about how reality really could have been and, correspondingly, facts about how reality couldn’t have gone.

Here’s my gripe with most arguments that rely on some claim about metaphysical modality: most claims about metaphysical modality are almost certainly unpersuasive.

Here’s what I mean. Take your standard ontological argument for God’s existence:

(1) If atheism is true, then it isn’t metaphysically possible for God to exist.

(2) But it is metaphysically possible for God to exist.

(3) So, atheism isn’t true.

Why should anyone who isn’t already a theist believe (2)? Why think that reality could have gone such that God existed? To be clear: I don’t mean “why think that reality could have gone such that a really strong person existed who was really nice and knowledgeable”? That is not the claim of (2). What (2) requires is that reality could have gone such that a necessary being of all the omni-properties exists. That’s pretty weird! Of course, if God exists, then that’s not so weird. But I don’t see why an atheist should think that there is some way for reality to have gone such that God existed.

Now, you might think the ontological argument is just a notoriously unpersuasive argument. But I think there is a much broader point here: the ways reality “could have gone” depend deeply on what you think reality is like. If reality is divine at its foundation, the ways reality could go diverge quite differently from the ways it could have gone if it is not divine at its foundation.

This is why I kind of balk when people claim to have some a priori intuition about the ways reality could have gone. You very likely don’t know, a priori, the ways reality could have gone — because you very likely don’t know, a priori, what reality is like! You and I very likely don’t know, from the armchair, whether time is static or dynamic. Assuming time is essentially static, then there’s no metaphysical possibility where time was dynamic: and that shouldn’t shock one a priori.

An argument that seems to sway a lot of philosophers is the modal problem of evil: if God exists necessarily, then it’s metaphysically impossible for there to be gratuitous evil. But that seems weird! Surely gratuitous evil (eg a world with lots of suffering and no compensating goods) is a way reality could have gone. So, theism must be false.

My instant reaction here is the same: why think we have independent grounds to think that reality could have gone such that there was gratuitous suffering? I mean, sure, a world with suffering and no good is a world that is logically consistent. But so are various other false metaphysical theses. Why think that we have an independent grasp of how reality could have gone? If reality is necessarily oriented towards perfection … then it’s just not weird that there is a perfectly consistent and describable state of affairs that reality never takes on (namely, reality being completely evil).

Here's the way I see things: reality exists, and it might be essentially one way or another. These essential properties open and close various consistent scenarios. Why do you think that your mind, either via imagination, conceivability, or whatever else, can directly discern, a priori, which scenarios have been opened and closed? You can’t think really hard and then just see what ways reality could have gone. You might be able to think really hard, determine what reality is like, and then that gives you insight into ways reality could have gone. But direct insight into metaphysical possibility … that’s a no-no.

On hedonism, well-being consists solely in pleasure (and the lack of pain). How much pleasure one experiences determines how good their life is.

One of the famous objections to hedonism comes from Robert Nozick: the experience machine. The idea is this — imagine that there was a machine that you could “plug into” and that it would give you all the best experiences imaginable. It would give you the exact feeling that one feels when they skydive, the exact feeling that one feels when they have the best sex, the exact feeling of winning a high-stakes competition, the exact feeling of being unbelievably successful, etc.

Now imagine you were given the following offer: you can plug into the experience machine for life. For your entire life, you would be a brain in a vat, being fed all of life’s best experiences, experiencing absolute pleasure all the time. Rather than living your normal life, you could be this brain in a vat.

Would you plug in?

Many people’s reactions is an instant, and confident, no. And this is supposed to show that pleasure — your inner experience of things — isn’t the only thing that matters for well-being. Other things must matter too. In particular, it seems like actually doing various things, and actually pursing various endeavors, and perhaps certain objective goods, all contribute to having a good life. Having things feel good from the inside — having pleasure — isn’t all there is to a good life. Or else we’d all want to plug in!

Now, I admit, I kind of have this intuition. But the other day I thought of something that made me a bit less confident that plugging into the experience machine is so bad.

Instead of thinking about well-being, let’s think about ill-being. What is it that makes a life bad?

The hedonist says that a life is bad to the extent it is full of pain (and a lack of pleasure).

Could we apply Nozick’s experience machine against hedonism in this context? Imagine that there was a machine that you could “plug into” and that it would give you all the worst experiences imaginable. It would give you the exact feeling that one feels when they are tortured, the exact feeling that one feels when they see a loved one being brutally killed, the exact feeling of losing in embarrassing fashion in front of the whole world, the exact feeling of being unbelievably depressed, etc.

Now imagine you are faced with the prospect of being put in this “negative experience machine.” That would be pretty bad! And not only would it be bad: if I was offered the choice between a life where someone was actually torturing me, versus me being in the machine and merely experiencing that exact torture … it doesn’t seem to me that there is a difference between how bad each of those lives are. Indeed, if you lowered the level of pain experienced in the in-real-life torture by even just a little, I would instantly choose that over the negative experience machine.

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And I think this is true with most, if not all, kinds of ill-being: there doesn’t seem to be much of a difference (in terms of ill-being) between living a life where I’m actually rejected by my crush, versus being in the experience machine and experiencing exactly that rejection. I mean, maybe the former is slightly worse? But my intuition is nowhere near as strong when it comes to ill-being. Of course, if I actually see a loved one brutally killed, versus merely experience seeing that, the former is a worse state of affairs in terms of total disvalue (it is a worse thing that someone actually died). But in terms of which those is worse for me? It’s not at all clear that the former is any worse than the latter — as a life lived.

Okay, what does this mean for the original experience machine argument?

Well, we’ve got two options. One is to simply embrace the asymmetry between well-being and ill-being. Ill-being is mostly constituted by pain, whereas well-being is a wonderful mosaic of things, from actual achievements to actual relationships to objective goods like knowledge to, yes, pleasure. The other is to say that there should be a rough symmetry between ill-being and well-being, and so we should revise our views about one of these two.

I must confess, something about Option #1 rubs me the wrong way. I can’t quite put my finger on it, but it seems wildly implausible that well-being and ill-being should be so different. This is especially when one considers that we have all sorts of irrational psychological biases when it comes to thinking about well-being vs ill-being: we tend to overrate (in one way or another) our own lives, we tend to focus especially on bad things and forget good things, our brains tend to imagine things with a heavy optimism bias, we massage over things in the past, we are irrationally risk averse, etc. So we should be open to the idea that some bias is creeping in in at least one of our evaluations of the negative/positive experience machines, which our evaluation in the other isn’t as susceptible to.

Indeed, what the negative experience machine elucidates — at least for me — is that we really underrate how incredible the positive experience machine is. You would be living an absolutely thrilling life! You’d experience things you’re probably never going to experience. Why do we repulse at the thought of entering it? Probably because we are overweighing what we are getting “taken away” from us if we plug in. But imagine that you died right now, and in the afterlife, God told you that, unbeknownst to you, your entire life was actually spent as a brain in an experience machine, where God had put the settings to simulate the exact life you’ve lived. Would you be sad?

It's not so clear that this is that bad (again, it might be bad for the world if in my life I added value to the world, through my personal relationships — but the question that concerns us is whether your life was any worse lived because of this).

If my life was full of torture, pain, and sadness, I certainly wouldn’t feel better about it if, after all of it was over, God told me in the afterlife “Don’t fret! You were a brain in an experience machine the whole time!”

What I think this all reveals is that the experience machine is only appealing because we think of the sorrow of losing the current life we have, of being “trapped” in the experience machine without “doing anything real”. But when we realize that our life just is a bunch of experiences — something I was prompted to realize via the negative experience machine — I think we should be a tad bit less confident about whether the experience machine is all that good of an argument against hedonism.

I’m still probably not a hedonist though xD

The reason for this is that certain skeptical hypotheses might be true, and you have no way of being totally certain that they are false. For instance, imagine the following scenario:

Brain in a Vat: You are a brain in a vat. Neuroscientists are causing every experience you have. Your perceptions of the external world, your internal thoughts, your beliefs, everything.

Now, can you be certain Brain in a Vat is false? Well, no, you can’t. You have nothing that could disconfirm it. You can’t point to the fact that you see things outside, that you believe p, or that you remember x. You could be in Brain in a Vat, and all of those things could have been fed to you. Literally anything you point to is totally consistent with Brain in a Vat being true. Of course, (maybe) you can be pretty sure Brain in a Vat is false. But you can’t be certain it is false. It is consistent with all of your evidence.

But if Brain in a Vat might be true, then most things you believe could be false. It could be false that there is no external world (as you perceive it). It could be false that such-and-such principle is false.

The lesson here, I think, is that all you have access to are appearances: it really appears to you that you have a hand or that such-and-such principle is true. But all of your appearances can be falsely induced.

If all we have are appearances, is there anything we can be totally certain of? Tough question. I think there is at least one thing that you can be totally certain of. I think you can be certain about your mental life. For instance, I can be totally certain that it seems to me that I have a hand. Maybe I am in Brain in a Vat. But nevertheless, even in Brain in a Vat, it seems to me that I have a hand. Even if I in fact do not: it’s still true that it appears to me that I have a hand.

Reflecting on this a bit more, what one might conclude is: there is something special about appearances. We have direct access to our appearances. We can’t be mistaken about them. Everything else (like what the world is like, what abstract principles are true) are not things we have direct access to. We come to believe them based on some kind of inference from our appearances.

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Why do we have direct access to appearances? Well, it’s very tricky, but put super roughly and in a way that tells us very little: our appearances stand in a very intimate relation to our minds. I’m not sure that they constitute our mind … but there surely is a very intimate relation, even if it is not constitution, between our appearances and our mind.

Alright, now a lot of what I have said about appearances, and their epistemic status, is super controversial and there are plenty of great objections to the idea that we can be certain about our appearances. But let’s suppose I’m right about all this.

I now want to ask the following question: what would it mean for God to be certain about everything? Presumably, theists don’t just want to say that God is pretty sure about everything, in the same way that we fallible humans are pretty sure our hands exist. I think many theists want to say that God is absolutely certain about everything (well, to be inclusive of open theists, let’s set aside the future).

But notice that this means God would have to have direct access to all true propositions. And direct access is pretty spooky. For instance, I think the following is a somewhat plausible principle about direct access:

• If the truthmaker for a proposition p is external to a mind, then x is not something that the mind has direct access to.

So, for instance, whether I have a hand is a fact whose truthmaker is external to my mind (presumably). That is why we can generate skeptical scenarios where it appears to my mind that I have a hand, and yet I do not: we can replicate all the same appearances in my mind, whilst making it false that my hand exists (Brain in a Vat is one way to do this). So, it seems like if you want to be totally certain about something, the truthmaker for that proposition needs to be ‘internal’ to one’s mind. [1] Or, at least, there needs to be some sort of counterfactual sensitivity between your beliefs and the truthmaker obtaining, and you need to be certain about this fact…

But if God is to be certain about everything … then everything has to be internal to God’s mind. To put it more vividly, in the same way that your mental life (e.g., the appearances you have) is internal to your mind, the entire world has to be internal to God’s mind, if God is to be certain about everything.

This is pretty wild. Especially because it seems like you get these results simply from thinking about the metaphysics of epistemic certainty. And it is especially spooky when one thinks about the great variety of kinds of facts that there might be. There might be moral facts, counterfactual facts, first-person facts, and, of course, facts about the physical world. All of these would have to be ‘within’ God’s mind, much as our mental life is. Maybe that’s what ‘omnipresence’ is meant to be about … ?

Which should you enact? Obviously, Policy A! More wealth will make many Americans’ lives better. Comparatively, doing nothing makes absolutely no sense.

But hold on. Your legal aide, Kevin, brings up the following objection:

President! We should not enact Policy A! To enact Policy A is to assume that all that matters in life is money. Are you one of those slimy, superficial people who believes that all that matters is money? No! Many things matter besides money: your mental health, your emotional health, how deep your interpersonal relationships are, how virtuous you are, how knowledgeable you are, how much art you get to appreciate, etc. Well-being, and a good life, is so much more pluralistic. Money is not the only thing that matters when it comes to improving lives!

You stand there, absolutely bewildered. You’re not sure if you should clobber Kevin, or just fire him right on the spot for making such a bad argument.

You slowly gather yourself, remembering that virtue is intrinsically valuable. You respond:

• My dear Kevin. I completely agree. A good life comes down to more than just money. But why in the heck is that relevant? That doesn’t mean it is a bad thing to make the middle and lower class wealthier. That doesn’t mean it is a bad thing to give single-parent families more income. That doesn’t mean it is a bad thing to make it easier on people to pay their rent and to pay for healthier groceries. That doesn’t mean it is a bad thing to give more economic freedom and privilege to the average American.

• If we can make every American richer without any adverse consequences, we should do it without thinking twice. Because money can still make a life better. Sure, money alone won’t solve every problem. But surely it helps. Surely money is one of the things that can make your life go better. That alone means that massively improving how wealthy everyone is is a good thing.

Clearly, Kevin’s argument is pretty bad. He makes the following mistake: he thinks that, just because money is not the only thing that matters, money does not matter at all. But, of course, that does not follow. Money can make people’s lives better. And that is why policies which massively improve wealth without comparable adverse consequences (along any other domain) are good things. Because they improve one of the things that can make lives better. That doesn’t mean that money can always compensate for some other deficiencies, or that money is the most important thing, or that it doesn’t have decreasing marginal contributive value.

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This is all strikes me as so clear that it should go without saying.

But … very many people make this exact kind of mistake, in a different domain. Whenever EAs argue that we should be doing X, because X would massively reduce the amount of intense suffering in the world, one of the most popular objections is: ugh. Yet another argument that assumes utilitarianism. Don’t you understand? I’m not a utilitarian! So many things are morally relevant other than pain and pleasure: deontic rights, promises, art, etc.

When Matthew argues that we should refrain from eating meat because it causes literally billions of creatures to scream from torture every day, or that we shouldn’t eat honey because of how much suffering it inflicts, I am utterly amazed by how many people respond by saying: this is just a reductio of utilitarianism.

Any moral theory worth its salt will recognize that the experience of intense suffering is a bad thing. That doesn’t mean that reducing suffering is the only thing that you should seek to do. Indeed, on some theories, you should not reduce suffering if it means, e.g., violating someone’s rights. But suffering is still a bad thing. If you can reduce it without costs to the other things you think are morally relevant (like rights), you should do it. Because suffering is bad!

So, if it is true that eating meat causes massive amounts of suffering, and all it would cost you to reduce that suffering is foregoing some gustatory pleasure, you should do so. You do not need to be a utilitarian to do this act — just as you do not need to be Scrooge to enact Policy A.

Of course, you could object to pro-vegan argument for a number of other reasons (you could deny that animals feel pain, or that animals are not “moral agents,” or for whatever other reason). But, please, don’t say that the argument assumes utilitarianism. You sound as bad as Kevin.

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So, first, let’s start with a paradigmatic example of a question-begging argument. Suppose you are a nuclear-enthusiast: you think nuclear energy is the best form of energy. Suppose I am a solar-enthusiast: I think solar energy is the best form of energy. I make the following argument to try and convince you:

(1) If nuclear energy is the best form of energy, then 1+1=3

(2) It’s not the case that 1+1=3

(3) So, it isn’t true that nuclear energy is the best form of energy.

This seems like a pretty absurd argument. But why is it bad? The argument is valid (if the premises are true, the conclusion follows). Is the argument bad because one of the premises is false? Well, that’s not so easy to determine. If solar is the best form of energy, then (1) would in fact be true. And maybe solar really is the best form of energy. The premises are not clearly false.

So what makes this argument a bad argument? What makes this argument bad is that it shouldn’t convince anyone of anything. Why would anyone believe (1) is true? Well … as we said above, it might be true, if nuclear energy isn’t in fact the best form of energy. But, if you and I are going to try and figure out whether (1) is true, what do we have to settle? We have to settle whether nuclear energy is the best form of energy or not! In other words, we have to settle our original debate!

So, this argument did nothing. We were having a debate about whether nuclear energy is the best form of energy. I then gave an argument, whose key premise depends entirely on whether you think nuclear energy is the best form of energy. The argument I gave basically just asks the same exact question we were debating about. That is what it means for an argument to “beg” the question: it simply gives rise to literally the exact question at issue.

That isn’t what good arguments are supposed to achieve. Good arguments are supposed to give rise to different, less contested questions. Let me give you an example. Suppose you and I are arguing about whether it is rational to have intransitive preferences (i.e., preferring A to B, preferring B to C, but preferring C to A). You point out that, if someone has intransitive preferences, they can be money pumped: if you start out having C, I could get you to pay me 1 dollar to replace it with B. I could then get you to pay me 1 dollar to replace it with A. But then I could get you to pay me 1 dollar to replace it with C! I can get you to pay me 3 dollars to end up at the exact position you started in!

But it seems like no rational agent should be able to get money pumped. So, no rational agent should have intransitive preferences. The argument:

(1) If you have intransitive preferences, you can get money pumped

(2) No rational agent can get money pumped

(3) So, no rational agent has intransitive preferences.

What makes this a good argument? Well, even if (2) is false, what makes this a good argument is that it makes dialectical progress. You and I started out by arguing about whether intransitive preferences were rational. This argument moves things forward by shifting our focus to a new issue: can it be rational to be money pumped? You and I might have diverging intuitions about transitivity, but we might have converging intuitions about money pumps. We might both agree, on this new issue, that no rational agent can be money pumped. And that agreement, this argument shows, is enough to show that we should also agree that intransitive preferences are irrational.

This is what good arguments do: they move things forward, by showing that there are other, independent considerations that should move you towards my side.

Now, with all that said, here’s the Twitter exchange that sparked my interest. A popular account posted the following argument against materialism (the view that all things are material/physical):

Ben Watkins, a wonderful person and friend, then responded with this:

Ok, seems reasonable. But then DtJ hits back with this:

Now, admittedly, the initial reaction one might have to this is: of course! This argument against white swanism is definitely not question begging!

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However, Ben is right in this exchange. I’ll be giving a response on his behalf. The reason we are disposed to (mistakenly) think that this argument against White Swanism isn’t question begging is because we all think white swanism is super implausible.

To see this, we need to imagine what a rational person defending it would think. Imagine someone who is a specific kind of theist. He believes in God, but has a different religious text. This religious text has the following verse:

“Verily, do not believe that there are black swans. Your Lord has only made swans that are white, however, sometimes your Lord makes things appear as though certain swans are black. This is for a reason beyond your ken, and to test your faith.”

Let’s also imagine that this religious text, which dates back to 200AD, has been surprisingly accurate: it predicted every weird result from Quantum Mechanics, described in detail the structure of DNA, and has no internal contradictions. Belief in this religion isn’t absurd.

Alright, now imagine you’re talking to the person who believes this. You want to convince him to abandon his white swanism. You trot out the following argument:

(1) If white swanism is true, there are no black swans

(2) There are black swans

(3) So, white swanism isn’t true.

I think it is pretty clear this argument has zero dialectical force. The key premise (2) is literally what is under dispute. You think that there are black swans. He doesn’t. What have we gained from (2)?

Now, you might give independent arguments for (2) itself. You might point out that science has a great track record, or that scientists have isolated a “color” gene in black swans that is different from white swans (idk if this is really true), etc. Now, maybe these arguments won’t work — maybe one’s credence in this religion should be so high that you should just accept that we are being deceived. But these arguments won’t be question begging: they will offer different, independent grounds for coming to disbelieve white swanism. The argument above, though, won’t.

A generally good test for whether an argument moves things forward is this: if a rational person believed ~C, do my premises P1-Pn offer new, independent grounds for C? Am I moving the dialectic elsewhere? Or have I simply restated the issue?

Indeed, instead of calling it begging the question, maybe we should call it “restating the issue”. That might clear things up.

In the spirit of this blog, however, I want to explore a bit of an extreme idea: might it be morally regrettable to tip? While I do tip, it seems to me that there is a really powerful argument that this practice isn’t great. I hope you set aside 5-10 minutes to explore it — it might just change how you act the next time you see this:

Okay, this post will proceed in 2 parts:

1. The Argument

2. Addressing Objections

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1. The Argument

Imagine the following:

Waiter and Child: You and your lovely family have gone out for a fun dinner at a restaurant. You have a nice meal, terrific vibes, and good service. As your waiter comes to get everyone’s plates, you get a call, and you step outside to take it. Turns out it was just spam, and you end the call and are about to go back into the restaurant to pay the check and tip the waiter 20%. But just before you open the restaurant’s front door, you notice something. Sitting on the ground is a 7-year-old child. His clothes are ragged. He has no home. His parents were killed at his birth. The child is starving. He hasn’t had food in days, and tears can barely run on his cheeks because of his thirst.

Your heart instantly melts. The child has done absolutely nothing to deserve this. This could have been you. You open your wallet, and all you have is a 100 dollar bill and a 20 dollar bill. No credit card. The check waiting for you at the table is 100 dollars — your plan was to tip the waiter with the extra 20 dollar bill. But you know that you could use this 20 to buy the child his first meal(s) in days.

What do you do? Speaking for myself, I find it unbelievably clear that I should give my 20 to the child. The 20 will do so much good if that is where it goes. It could breathe something as beautiful as life! into a completely innocent child. Indeed, if I did not give it to the child, I don’t know how I could ever shake that guilt. To not feed the child is to act in a way that strikes me as insensitive to goodness: it is to be insensitive to the badness of premature death, the badness of a cruel existence, and the goodness that comes with alleviating this.

But … Waiter and Child is essentially exactly the situation we all find ourselves in, every time we tip. The child I described exists. And he is not alone. There are millions living like him, or in conditions much worse. Just take the child and move him a little bit (in particular, move him to sub-Saharan Africa) and, voila, the man in Waiter and Child describes all of us.

Allow me to paint the picture a bit more vividly. In 2023, well over one hundred million people in Africa faced chronic malnourishment. Just last year, in Sudan, literal famine hit over 400,000 displaced people — women and children scarred by war and with no permanent shelter. In Ethiopia, Kenya, and Somalia, two million children are facing drought and require treatment for the deadliest form of hunger. The rampant starvation has led to increases in child labor, rape, sexual violence, and female genital mutilation.

This is not even to mention the unbelievably dire conditions of mass multidimensional poverty, nor the mass torture, rape, sexual slavery, and ethnic massacres that have taken place in various parts of the world.

In short: all over the world, at this very moment, as you read this text in comfort, are millions of children agonizing in starvation, poverty, and much worse.

You might be thinking right now: dude, what the hell does this have to do with tipping?

My point is simply this: Waiter and Child is not really a thought experiment. It is pretty much the reality that we all find ourselves in. It’s just that when you and I go to eat, rather than the children being on the street of the restaurant, they are a couple (thousand) miles away.

But surely this difference is completely irrelevant.

Here’s one intuition pump for this: imagine that you had a specific kind of super vision. In particular, you could, if you squint your eyes really hard, see the suffering children that exist thousands of miles away. Now, imagine that you also had a specific kind of arm. If you extend your arm, you could reach all the way to these children. If this were you, every time you go out to eat, you are the man in Waiter and Child. You can, with the squint of an eye and the extension of an arm, breathe life into a starving child’s eyes with the 20 you would’ve otherwise tipped.

But surely our moral reasons should not be drastically affected by the flexibility of our arms or the number of retinas in our eyes.

Furthermore, because of modern technology, these superhumans are basically who we all are anyways. With the click of a button my money can reach starving children. With a quick Google search, I can see what is going on (at least in part) elsewhere in the world.

All of this is to say: every day, when you are faced with the prospect of tipping, you find yourself in a similar situation to the man in Waiter and Child.

Now, even if you agree with me in all of this so far, it is still not enough to establish that it is morally regrettable to tip. All I have shown is that there are better uses of your tip money. But this is true of most of the ways you spend your money! Also, unlike the man in Waiter and Child, your tip money is not the only money you have in your wallet. You can donate to starving children and tip. So why is tipping morally regrettable?

To establish this, I will need you to bear with me a bit more and imagine one further situation:

Charity on Fire: Bob has been working hard and saving money. He has managed to save 1000 dollars from his income this year, which he plans to give away to charity. Bob goes up to the local charity, but at the last minute decides to set 900 of his 1000 dollars on fire. He then gives the remaining 100 to the charity.

It seems as though there is something morally regrettable about what Bob has done here. To be clear, it’s not as though Bob is a bad person for what he’s done — he saved up his own money to give away, he seems like a great person! Nevertheless, it is regrettable that this happened. These 1000 dollars were dollars already set aside to help others. Bob was not going to use them on himself. In a world where humans (myself included, of course) struggle to give away much of their income, it is a real shame that these 1000 charity dollars only ended up being 100. When something is about to go towards the good, and instead gets significantly reduced, that is really very sad and regrettable. The fact that 1000 dollars, which were about to go to those who need it, ended up being only 100 dollars is not a fact we should be happy obtained.

So, Charity on Fire is morally regrettable. Again, that’s not to say Bob is bad for having set his 900 to fire. It is simply to say that we should be sad that this has happened.

The problem, though, is that it is very difficult to distinguish Charity on Fire from tipping. When I choose to tip — especially when I tip beyond customary rate — this is money I have already decided to spend altruistically. It is money I have already decided to use towards the good. And rather than use that money to give life to a starving child, I have decided to give it to someone who is richer than 98% of the world’s population (indeed, the average American is in the top 1%).

This is a bit like if I had just worked up the altruistic energy to tip my server 30%, and then, just before I do it, I see a multimillionaire walk in and give me a high five, and I decide to instead give my tip to him. That is morally regrettable! What a waste of money that would have done so much more good for my server than for Musk. Just as it is regrettable to spend your limited altruism on America’s wealthiest 1% rather than the average American, so too is it regrettable to spend your limited altruism on the world’s wealthiest 2% rather than children in literal famine.

Indeed, the analogy to Charity on Fire might be too generous. If I work up the altruism to tip a server 50 dollars, and then instead gave that to someone worth hundreds of millions of dollars, it probably would have been better if I literally set to fire 45 of the 50 dollars and then gave the remaining 5 to the server. Ipso facto for tipping.

Now, since this is a philosophically inclined blog, I guess this is the point where I have to give a syllogism? So here you go:

(1) If it isn’t morally regrettable to tip, Charity on Fire isn’t morally regrettable;

(2) But Charity on Fire is morally regrettable;

(3) So, it is morally regrettable to tip.

I simply struggle to see how tipping isn’t like Charity on Fire in all the ways that matter.

Before considering objections, though, I want to paint one more picture. I want you to just imagine what the world would be like if, every time you were about to tip, you instead took that tip and gave it to an effective charity. Americans spend roughly 131 billion dollars on tips every year. If, instead, 100 billion dollars went to effective charity, the world would be ridiculously better. It is far above my paygrade to project what the impacts of that would be, but at least hundreds of thousands, if not millions, of lives could be saved or significantly improved. [1] Of course, there are also ripple effects to consider. But these needn’t all be negative: for instance, if Americans really did opt to turn their tips into donations, restaurants might no longer be able to get away with paying servers below minimum wage.

Hundreds of thousands more smiles. More life. Less hunger. Less starvation. When I really reflect on this when tipping, the fact that I am no different from Bob in Charity on Fire does not strike me as so crazy. Someone should make an app that does this automatically — sends your would-be-tip as donations.

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2. Objections

Objection 1: This isn’t an argument against tipping. This just entails that you should tip and donate.

While it is certainly better to tip and donate than to not donate at all, the argument here suggests more than that. For while it is true that we have enough money to both tip and donate, we nevertheless only have a limited amount of money (and a limited amount of altruism). That is why it is ‘morally regrettable’ whenever we do tip: because that is money that could have instead gone to donation.

If you’re still not convinced, simply consider the analog response in the case of you giving money to Elon Musk. Isn’t it still morally regrettable for you to spend your altruism and money on Musk, when you could have instead given it to someone who needs it? This is so even if it’s true that you can both give money to Elon and donate.

Objection 2: Tipping isn’t about altruism. It’s about paying for the service experience. If we didn’t have tipping, we wouldn’t have energetic, highly competent servers. So tipping is a purchase, much like when I buy a toy for myself.

I could dispute the substance of this objection — many object that servers could still be motivated to be similarly energetic and competent without tips if they were compensated fairly, as in European countries. But this is a tricky empirical debate. Let’s set it aside and assume the objection is right.

Nevertheless, there still is value in considering these arguments — for it will apply to tipping when it is in other contexts that are altruistic rather than about purchasing an experience. For instance, when one is asked to tip at a coffee shop, at a sandwich shop, or any other instance where the tip isn’t going to someone managing a dining table. Additionally, the arguments here apply to anyone to the extent that they tip for altruistic reasons — which I know many people do.

Objection 3: But, unlike the beneficiaries of a would-be donation, the server deserves this tip. He is entitled to it, unlike the starving children.

One could also dispute the substance of this objection — either by arguing that desert might not be a moral ideal, or that, even if it is one, the server is not necessarily entitled to my tip, or that, even if the server deserves it, so too does a starving child, since they are only in their position because of cruel genetic lottery. But let’s grant the substance of the objection.

Even so, desert is but one moral ideal among others. While it matters that people get what they deserve, it also matters that … people don’t die of starvation. That people get their life extended by multiple years, and live beyond poverty. Just consider Waiter and Child again. It seems silly to me to object that you shouldn’t give the child the 20 because of the waiter’s desert claim — even if the waiter has a desert claim to your 20, and the child doesn’t, nevertheless the mounting famine the child faces clearly outweighs this desert claim. Sorry, I won’t let an orphan starve.

Objection 4: Doesn’t this just generalize to everything? What’s so special about tipping?

True, there is a sense in which the argument here generalizes — we make massive mistakes in how we spend our money, at least when viewed from a moral lens. But my point isn’t merely that tipping is a grossly morally inefficient way to spend your money. My point is that it is particularly morally regrettable: because tipping, at least sometimes, is done under the auspices of altruism. That is the lesson of Charity on Fire. Whenever we don’t give money to charity, there is something sad about that. But there is something especially regrettable when Bob works up the altruistic energy to give, and then decides to burn away 90% of his donation money before giving it away.

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1. The Puzzle

First, we should set up the puzzle. It goes like this. Compare these two hypothetical populations of people:

Population A: There are 100,000 people. They are all living lives that are extremely joyful — they experience all the great and valuable things that make a life go extremely well. They all have happy, tight-knit families. They are all deeply fulfilled. To put things simply, suppose they each are at welfare level 100.

compared with:

Population Z: There are 1,000,000,000,000,000,000,000 people. But they each live a life that is barely worth living. They are barely happy, barely fulfilled, and experience only the slightest, dullest kinds of pleasure. If things were slightly worse, they would no longer find life worth living. To put things simply, suppose they each are at welfare level 1.

Which population is preferable? If you could choose one of these populations to be the case — if you were about to use your telescope to look at a far-away planet, and told that the population on that planet is A or Z — which would you hope were the case? The answer seems blindingly obvious: you should hope A is the case! It is preferable to Z!

The Repugnant Conclusion is the proposition that Z > A — that Z is preferable to A. Hence, the name: such a proposition is repugnant to our understanding of value.

But here’s the puzzle: there seems to be an incredibly strong argument for the Repugnant Conclusion. It goes like this. Imagine a population, B, that is somewhat similar to A. It has quadruple the population — 400,000 people — and they are all almost as happy and well-off as the people in A. They too are very happy, fulfilled, and experience almost-as-intense pleasures. The average welfare in B is, say, 99.9. Which is preferable: A or B? I think it is pretty plausible that the answer is B. It is worth to take a barely-noticeable hit to well-being, if it means four times as many people are going to be experiencing excellent lives. (As a sort of argument by analogy, consider that it is certainly preferable that 100 kids each get $90 for Christmas, than that a single child get $91.)1

Ok, so B > A. Alright, but now imagine a population, C, that is pretty similar to B. C has quadruple the population — 1,600,000 people — and they are all almost as happy and well-off as the people in B. They too are very happy, fulfilled, and experience almost-as-intense pleasures. The average welfare in C is, say, 99.89. By the same argument, C > B.

Hopefully you see the problem. We can keep going like this: quadrupling the number of people in the population, and ever-so-slightly reducing the welfare of the people involved. We will have A < B < C < D < E < F < …

Eventually, we will get to Z. But hold on! We said that A > Z! This sequence entails (assuming that ‘>’ is transitive) Z > A! Which just is the Repugnant Conclusion.

Basically, the Repugnant Conclusion follows from two really, really plausible principles:

Trade Small-Quality for Big-Quantity: For any population X, and any natural n and real l, such that X has n people each enjoying welfare level l, there is an all-things-considered better population X* of 4n people each enjoying welfare level (0.999999)l.

Transitivity: For any a, b, c, if a is all-things-considered better than b, and b is all-things-considered better than c, then a is all-things-considered better than c.

You have three options: tell some crazy story as to why Trade Small-Quality for Big-Quantity is false, deny Transitivity (insane!), or accept the Repugnant Conclusion (gross!). There is literally no other option.

2. My Favored Solution

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Before I tell you about my favored solution, let me start with a motivating case. Consider someone getting a pinprick: they experience a pin ever-so-slightly prick one of their fingers. The pain is extremely slight: just barely noticeable. But it exists. The world is slightly worse because of it. Now, compare this to someone being horrifically tortured: this person has their eyes bludgeoned as they are put in a freezer to slowly die in intense agony and suffocation (in other words, this person is treated exactly how we treat farmed shrimp).

Okay, clearly the single instance of horrific torture is worse than the single instance of the pinprick. But here’s a question: is there some number n such that, if n people experienced a pinprick, that would be worse than the instance of horrific torture? I think not! I think, no matter how many pinpricks there may be, it would be way way way way worse if there were someone in horrific torture. Or, to elevate the stakes: imagine that there were 1 billion people in horrific torture. Is there some number of pinpricks such that that would ever be worse than 1 billion people in horrific torture? I think you have to be crazy to think so! If I were about to look at a far-away planet, and you told me either n people on the planet just experienced a pinprick, or that 1 billion people on the planet experienced horrific torture, you better bet I am praying that it is the former that obtains.

Okay, what is the relevance of this example? Well, I think the lesson of this example is that some burdens — like pinpricks — have a limit to how much disvalue they contribute to a world. A collection of pinpricks, no matter how many, can only make the world so bad. It can be helpful to think of the aggregate disvalue of pinpricks as having a bound or upper limit.

Roughly, I want to tell a similar story about the Repugnant Conclusion and population Z. I think that there is an upper limit to how good a population of lives barely worth living can be. That upper limit is certainly less than how much goodness is in a population like A.

Of course, this all sounds really nice: but it is not yet a solution until I explain what step in the argument I reject. To be clear, the principle I am rejecting is Trade Small-Quality for Big-Quantity. While B may well be better than A, I do think there is a point in the middle where things are no longer improving. Now, I should stress just how weird and unintuitive this position is. What this means is there is some population, say, K, where there are lots of people living pretty-good lives, and if you were to lower the level of well-being in K by even a little bit (like, 0.0000000000000000000000001%) no matter how many more people you added, that would never be better than K.

To put it in terms of pain: if K is a world where 10000000000 people are experiencing a pain of level p, K is worse than a world where 50 TRILLION TIMES as many people are experiencing a pain that is 99.999999999% as intense as p. That’s pretty nuts!! If the level of pain is only slightly less intense, you presumably shouldn’t allow 50 trillion times as many people to experience pain, even if it is a slightly less intense pain. But that’s what my favored solution entails.

Now, I should very clear on what, exactly, my favored solution entails. My favored solution doesn’t exactly entail that there is some pair of worlds <w1, w2> in the sequence where, no matter how small the difference in intensity between w1 and w2, adding more people to w2 could never outweigh w1. What it entails is that, for any real number d, there has to be a pair of worlds <w1, w2> in the sequence where the difference in intensity between w1 and w2 is d, and no matter how many more people are in w2, w2 could never outweigh w1. That’s still really weird though!

How do I accept this? Well, upon reflection, I have come to think the bullet is not that bad of a bullet to bite (or, in another vocabulary, I have successfully coped).

First, let’s note that these sorts of sequences are trading off between two ethical dimensions of populations — the intensity of pain experienced (“quality”) vs the number of people experiencing it (“quantity”). This language is going to be helpful in eliciting some intuitions.

Now, we said that n pinpricks has an upper limit to how bad it can be — one of its dimensions (quality) is too low, such that it puts a hard ceiling on the total disvalue that can obtain in that world. For ease of exposition, lets slap a number on it and say this limit is -1 million. No matter how many pinpricks there are, they can just never be more disvaluable than -1 million. And lets say 1 billion horrific tortures is -1 billion.

Okay, now let’s consider the sequence again, but this time let’s consider it from both sides. First, let’s start at the world with n pinpricks, and compare it to the worlds that are supposed to be better than it —the ones with less people experiencing slightly more intense pain. Since n pinpricks is ~ -1 million, these worlds with shrinking populations, but slightly more intense pains, must have a disvalue of just under -1 million (e.g., -999k). We can call this portion of the sequence “pinprick-dominated” worlds (worlds that can intuitively be dominated by — be better than — a sufficient number of pinpricks).

Similarly, starting at the world with 1 billion tortures, we can compare it to the worlds that are supposed to be worse than it — the ones with more people experiencing slightly less intense pains. Call this portion of the sequence “torture-dominator” worlds (worlds that can intuitively dominate — be worse than — 1 billion tortures).

So, the allegedly weird thing is that, in the complete sequence, we get a torture-dominator right next to a pinprick-dominated world. But is this actually so weird? Think about a sequence of torture dominators, where you are progressively trading off intensity of pain for number of people in pain. As we increase the number of people, and decrease their pain, it becomes less and less clear (at least, to me) that things are worse than the original 1 billion tortures. If our intuition is that a world of n pinpricks scores so low along the dimension of “intensity of pain” that it has a hard cap on how disvaluable it can be, then, as we progress along the sequence of torture-dominators, where intensity of pain is getting lower and lower, increases in quantity have to continually compensate for this loss in intensity. And there is simply a limit to how much compensatory work quantity can do as you keep losing intensity of pain. Indeed, it’ll have decreasing marginal ability to compensate. Eventually, you get to a world where there are so many people in a decent-level of pain that a further loss in intensity of pain is more damaging (to total disvalue) than a gain in quantity.

There may be another, simpler way to help assuage the weirdness of this solution. Those who accept the Repugnant Conclusion will often point to the fact that humans are infamously insensitive to scope, and that we do not really grasp the difference between big numbers (like 10^27 and 10^234). We just nebulously think of them as both really big. There is an interesting, similar kind of bias, I think, that infects our intuition comparing two side-by-side worlds in the sequence trading off quality for quantity. When we get to a world with (say) hundreds of trillions of people in a decent-level pain, and we are comparing it to a world with (say) thousands of trillions of people in slightly less pain, we don’t quite appreciate how vast of a difference it is for that many people to be in slightly more pain. Sure, each individual difference in pain is slight. But it is still more painful, not less. And it is a lot of people in more pain. It should not be so surprising that, when such large quantities of people are involved, even slight increases in pain intensity mean a whole lot more than we might intuitively expect — this is especially so when we pair it with the fact that most of us find it extremely intuitive that quantity cannot continually compensate for losses in pain intensity. If quantity does have a decreasing ability to compensate for losses in pain intensity, we should not be so surprised to find that it gets to a point where even slight differences in pain intensity mean more than large differences in quantity.

Nevertheless, I still find this quite weird. But that is, unfortunately, true of every solution to this puzzle.2

With all that said, however, there is a philosophical issue on which I break rank with your stereotypical rationalist. I am not an additive aggregationist. I endorse a position that I have termed ‘bounded aggregation’. Let me explain.

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All (or, the vast, vast majority of) moral theories have something called a theory of the good, or a theory of value. These are theories of what things are valuable or good. For instance, many theories of the good claim that well-being is something with intrinsic value. If a world contains a creature that is well off, the world is better off for having such a creature.1 Similarly, many theories of value claim that suffering is intrinsically disvaluable.

Now, there are lots of fights about what the right theory of value is. We can set all of that aside. What is important to see is that, in addition to your theory of value, you need what I call a theory of aggregation. A theory of aggregation is a theory that tells you how to aggregate value.

An informal example will be helpful. Suppose you have a theory of value on which pain is intrinsically disvaluable. Okay. Now, suppose there is a world with 1 headache. Call this world H1. H1 has some disvalue. Let’s say that the disvalue of the headache is such that the world’s total value is -1. Great. Now imagine another world, just like H1, except that here there are two people experiencing mild headaches. Let’s call this world H2. Question: how much disvalue is in H2? You might want to say: well, we said H1 has total value -1. So, it must be that H2 has total value -2.

That answer assumes a certain theory of value aggregation. In particular, it assumes an additive theory of aggregation. An additive theory of aggregation claims (again, this is all informal — a formal exposition will be coming) that if the value of x is n, and the value of y is m, the total value in a world with x and y is n + m.

So, a theory of aggregation is a theory that tells us how to determine the total value in a world, given the individual values of each component part of a world. An additive theory of aggregation is one that says the total value in a world is merely the sum of the values of the component parts of a world. Reasonable enough, right? Well, that’s what they want you to think…

Here is a reason to think the additive theory is false.

Compare H1 and H2 to another world, where there is 1 person experiencing torturous suffering. This person is screaming as he is slowly suffocated to death with his skin being burned off and his organs pulled apart (a fate similar to what billions of screaming chickens experience because we value our own gustatory pleasures). Let’s call this world T1. T1 is also disvaluable — very disvaluable. Let’s say the suffering here is so intense that T1 has a total disvalue of -1000. Okay. But this has an odd implication: if there is a world with 1001 people each experiencing a mild headache — call it H1001 — the additive theory entails that H1001 is more disvaluable than T1. That is to say, you should prefer that the world be such that 1 person experiences mind-numbing torture than for 1001 people to experience barely-noticeable headaches. But that’s absurd! If it were up to me — if I could choose which world were the case — I would let millions of people experience barely-noticeable headaches before I ever let it be that a single person experience this kind of torture. But then it can’t be that 1001 headaches “add up” to be more disvaluable than horrific torture.

You might say that this simply means our numbers were off. But the problem, to me, is that no set of numbers will ever be satisfactory. For any n, Hn is preferable to T1. But then the additive theory has to be false: for this is just to say that no amount of headaches could ever “add up” to be more disvaluable than horrific torture.

You might try to say that all this shows is that torture is infinitely disvaluable, not that we should reject the additive theory of aggregation. But I think it is rather clear that torture is not infinitely disvaluable: two instances of torture are surely more disvaluable than a single instance of torture, and torture can be traded off with other less-bad things (i.e., a world with 20 instances of slightly-less-bad torture is more disvaluable than T1, even though both are more disvaluable than Hn, for any n).2

Finally, you might object by saying that all this shows is that consequentialism is false. This just goes to show that sometimes you shouldn’t care about aggregate value! Sadly, this is deeply mistaken. The problem here has nothing to do with whether you are a consequentialist or deontologist. The intuition I am appealing to is that, no matter what n is, T1 has more disvalue than Hn! That is to say, the total disvalue involved in torture is more than the total disvalue involved in n headaches — it is preferable that n headaches obtain than that a single instance of torture obtain. This is an intuition about total value and the preferability of certain states of affairs over others.

Okay, if additive aggregation is false, what should we endorse? I advocate for what I call bounded aggregation. Bounded aggregation claims that, at least for some kinds of harms, there is a bound to how much disvalue they can contribute. Here’s one way such a theory could go: a single headache has a disvalue of -1. However, the aggregate disvalue of 2 headaches is not -2. Instead, it is -1.5. And the aggregate disvalue of 3 headaches is -1.75. I.e., as there are more and more headaches, the total value of a world with these headaches corresponds to a geometric series with a bound of -2: -1 + -0.5 + -0.25 + …

This secures the result that, no matter how many headaches you have in the world, the total disvalue in the world will never be more than -1000. There is a limit to just how bad n headaches could ever make the world. And that’s pretty intuitive! This is one example of a non-additive theory of value aggregation.

Alright, all of that was rather informal and incomplete. And there are very many possible objections to consider. Here’s the plan for the rest of this article: first, I will formalize things for the sake of clarity, and then address some objections to bounded aggregation. However, I hope that the main takeaway from this article is that value aggregation is a totally separate question in moral philosophy from the consequentialism vs deontology debate. One can be a consequentialist and yet endorse non-standard, non-additive theories of aggregation.

Here’s the structure of the rest of the article:

1. Clarifying the View

2. Objection #1: All Headaches Must Count the Same!

3. Objection #2: The Problem of “Much Worse Than”

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1. Getting Clear

To state the view more precisely, I will help myself to the following notation. Let x, y, z, … designate different kinds of burdens (e.g., x = a mild headache, y = a week of intense pain, etc.). When a particular kind of burden, k, has multiple tokens, we denote the different token burdens as follows: k₁, k₂, …, k_n. Next, let v(ϕ₁, ϕ₂, …, ϕ_n) designate a value function which takes in any number n of burdens, and outputs some real number representing the overall disvalue of that class of burdens.

So, if one is attempting to calculate the total disvalue of 3 mild headaches, we represent this as: v(x₁, x₂, x₃). Using this notation, we can now express various aggregation views. For instance:

Standard Additive Aggregation

v(x₁, …, x_n, y₁, …, y_m, …) = n * v(x₁) + m * v(y₁) + …

To express the view that a class of burdens has a bound, we will need to help ourselves to one further piece of notation: let r_ϕ designate a real number between 0 and 1 (inclusive), representing the common ratio for some kind of burden ϕ. We can express one version of bounded aggregation as follows (I will call it Simple Bounded Aggregation [SBA] because I actually think there are some changes to be made to the view, but that won’t be the subject of this post):

SBA claims that, for each kind of burden ϕ, the total disvalue of n-many ϕ’s can be calculated as a geometric series. Thus, the total disvalue of a class of different kinds of burdens will be each individual geometric series for each kind in the class, summed together.

Okay, now lets consider some objections.

2. All headaches count the same!

Probably the first objection one will want to raise is that SBA treats headaches as though they have different disvalues, which is totally implausible. Each headache is equally disvaluable! A second headache is worth -1, just as much as the first one is. So, SBA must be false.

There are actually two, subtly different, ways of making this objection.

The first way of making this objection is to object to the fact that bounded aggregation entails that the amount of disvalue a headache contributes to a world is sensitive to external facts (namely, how many other headaches exist in the world). In particular, the worry is this: a common ratio (less than 1) entails that, as a kind of burden k is iterated in an outcome O, each subsequent token of k contributes less to the overall disvalue of O. But how can this be plausible? This would mean that the individual disvalue contributed by a token burden is determined by what else exists external to the token burden.

First, it is important to note that SBA does not entail that any token burden is any less bad for the person experiencing the burden (so-called subjective disvalue). For instance, every additional person in H who experiences a mild headache does not thereby experience a headache that is any less painful. The question, rather, is how much total (objective) disvalue we should tack on to H given that this additional pain––in all its hedonic displeasure––obtains.

And it is here that, by my lights, the context-sensitivity of SBA is not problematic. After all, it would be implausible to insist that all of our moral ideals are determined solely intrinsically. Indeed, a great deal of them have the similar sort of context-sensitivity that is baked into SBA. Suppose, for instance, that one takes equality to be a moral ideal relevant to the goodness of outcomes. Now imagine we are in a world where Joe is at a total welfare of 80 and Sally is at a total welfare of 60. Suppose we are considering adding 20 units of welfare to someone’s life. It might be that adding 20 to Sally might do more good than adding 20 to Joe, at least from the perspective of equality. But notice that this is so even though, whether we add 20 units of welfare to Joe or to Sally, it is the exact same addition of welfare in either case. Thus, from the perspective of equality, the extent to which an addition of welfare improves an outcome is sensitive to facts external to the welfare itself. I struggle to see the absurdity in our value judgements being context-sensitive in this way. This feature seems to pervade many other ideals as well––maximin, prioritarianism, and even impersonal ideals like, e.g., rare art, appear to admit of context-sensitivity. Why, then, exclude bounded aggregation from the party?

The second way of making this objection is to claim that the problem is with the difference between identical token burdens. Take, for example, a stipulated geometric series for the disvalue of mild headaches: 10 + 5 + 2.5 + …. If Alice’s toothache was the first headache we considered (v(h₁)), and Bob’s is the second (v(h₂)), we might wonder: why is Alice’s headache receiving special privilege over Bob’s? Namely, why is it that Alice’s headache has a disvalue of 10, but Bob’s headache has a disvalue of 5?

This, however, is too quick. Note that SBA does not make any commitment about the individual disvalue of any particular headache. What SBA says is that any collection of burdens has a total disvalue that can be calculated vis-à-vis a geometric series. So, given that a headache has a disvalue of 10 and that we stipulate the common ratio to be ½, what SBA tells us is that v(h₁, h₂) = 10 + 5. In other words, the view only entails that an outcome with Alice and Bob experiencing headaches has a total disvalue of 15. It does not say anything about how much disvalue Alice or Bob’s headaches individually have in that outcome. Now, of course, we have that v(h₁) = 10. But all this means is that, in a world where the only burden that exists is Alice’s headache, the total disvalue in that world is 10. But this is perfectly consistent with v(h₂) being equivalent to 10 as well––for that just means that in a world where the only burden is Bob’s headache, the total disvalue is 10.

To put things another way, SBA is a view quantifying over collections of burdens. It says nothing about how much disvalue each individual burden within that collection is contributing. It is not problematic for the bounded aggregationist to hold that v(h₁) = 10, v(h₂) = 10, and that v(h₁, h₂) = 15––to assert otherwise would be to assume an additive picture.

3. The “Much Worse Than” Objection

Another objection that might be levied against bounded aggregation has to do with some unintuitive normative judgements that all bounded views of aggregation seem to produce––in particular, about the “much worse than” relation.

Imagine an outcome A with a single person who is tortured for a year. Now imagine that a malicious individual transforms outcome A into outcome B, where 999 more people are tortured for a year (making a total of 1000). Now imagine further that outcome B is transformed into outcome C, where 999 more people are tortured for a year (totaling 1999). Clearly, C is worse than B, and B is worse than A. Additionally, B is much worse than A, just as C is much worse than B. However, it seems that bounded views cannot render this last judgement––that C is much worse than B. For, according to bounded views, the amount of disvalue contributed by a kind of burden decreases exponentially as we iterate. So, in the case of torture, it is a direct commitment of bounded aggregation that the difference between the disvalues of A and B is much larger than the difference between the disvalues of B and C (indeed, the difference is several orders of magnitude!), and so it seems that, while C is certainly worse than B, bounded aggregation commits us to judging that C is only a “little worse” than B. And this point generalizes in a rather worrisome fashion: if we consider further outcomes D, E, F, … where, each time, an additional 999 people are tortured for a year, eventually, going from, e.g., outcome Y to outcome Z, while worse, adds almost no disvalue at all. But, certainly, if anything is absurd, it is the claim that Z is “barely worse than” Y.

This is pretty bad. If bounded aggregation really entails that Z is “barely worse than” Y, it would be a non-starter: at least for me.

As such, I will offer one possible response to this troubling objection. First, it is important to see that this objection relies on the following account of “much worse than”:

Absolute Difference: The extent to which an outcome, O₁, is worse than another outcome, O₂, is determined by the difference between the total disvalues of O₁ and O₂.

The Absolute Difference account of “much worse than” entails that, if the difference between the total disvalues of C and B is some small number s, and the difference between B and A is some large number l, then B is much worse than A, but C is only slightly worse than B. And, indeed, we implicitly relied on this account when explicating the objection––for we argued that bounded aggregation entails that C is only slightly higher in absolute disvalue than B, which, naturally enough, is supposed to entail that C is only slightly worse than B.

The bounded aggregationist, however, should reject the Absolute Difference account. To see why, let us begin by noting that, in general, given a scale of measurement S for some quantity Q, the fact that S assigns some x value n and some y value m does not entail that the extent to which x is more Q than y is n – m (assuming n > m).

An example will be helpful: let us suppose that how rich one is is a function of how much money one has. Money, then, is a measure of richness––the more money one has, the richer one is. So, if Alice has 100,000 dollars, and Ben has 1,000 dollars, Alice is richer than Ben. And if Cecil has 1.1 billion dollars, and Dana has 1 billion dollars, then Cecil is richer than Dana. This much is determined by our commitment to money as a measure of richness. But now suppose that we are interested in knowing how much richer Alice is than Ben. In particular, suppose we are interested in knowing whether the extent to which Alice is richer than Ben is equivalent to the extent to which Cecil is richer than Dana. Some might argue that Cecil is much richer compared to Dana than Alice is to Ben, since the difference in money between Cecil and Dana is larger: Cecil has 100 million more dollars than Dana, whilst Alice has only 99,000 more dollars than Ben. Others, however, might argue that the opposite is true: Alice is much richer compared to Ben than Cecil is to Dana. And they might instead appeal to comparative ratios: Alice has 100 times the money Ben has, whilst Cecil has only 1.1 times the money Dana has. My purpose, of course, is not to settle this debate. Rather, my point is that there is debate to be had. That money is a scale of measurement for richness does not settle what the appropriate attitudes are about how much richer x is than y. We might put things like this: even if money is a measure of richness, no “cardinal” judgements follow about how much richer an x with money n is than a y with money m. All that follows is an “ordinal” judgement, namely, that x is richer than y, since n > m.

One reason that scales of measurement, in and of themselves, only determine ordinal, and not cardinal, judgements is that a scale of measurement for some quantity Q can have Q distributed across the scale in various ways. For instance, suppose we’re interested in measuring the difficulty of running a race. Let’s further assume that distance can be a measure of difficulty of running a race (assume, for instance, that the races whose difficulty we shall be measuring are equal in all other relevant factors, e.g., slope, terrain, climate). So, the longer a race is, the more difficult it is. We might, however, think that the following is true: not only does each additional mile in a race make the race more difficult, but it makes it exponentially more difficult. Each additional mile is even more difficult than the last. So, increasing a race from 2 miles to 3 miles results in an increase in difficulty of d, but increasing a race from 3 miles to 4 miles results in an increase in difficulty of k × d. If true, this would mean that, while distance is a measure of race difficulty, distance is not a scale on which race difficulty is evenly distributed. Instead, units of difficulty become more densely packed as we move along the scale, such that each unit increase of distance results in more and more of an increase in difficulty. Indeed, such uneven scales of measurement are rather common. Many scales of measurement in the natural sciences are logarithmic: e.g., the Richter scale, which measures the magnitude of an earthquake, is such that the difference in ground motion between a 1.0-rated and 2.0-rated earthquake is roughly 90 microns, whilst the difference between an 8.0-rated and 9.0-rated earthquake is roughly 900 million microns in ground motion. Thus, we may well be inclined to say that the difference between a 9.0 and 8.0 earthquake is much larger than the difference between a 2.0 and 1.0 earthquake. If so, this is because, whilst the Richter scale is a measure of earthquake magnitude, qua logarithmic scale it is a scale on which magnitude is distributed unevenly.

I introduce this discussion to make the following point: the bounded aggregationist needn’t accept that how much worse x is than y is determined by the absolute difference between x and y’s disvalue. Value and disvalue are measures of, inter alia, choiceworthiness, goodness, badness, and various other value facts. But why think that, e.g., badness is distributed evenly across the scale of disvalue? Analogously to the Richter scale, the value scale may well be such that while an outcome A of disvalue 4 is worse than an outcome B of disvalue 3, and that an outcome C of disvalue 9 is worse than an outcome D of disvalue 8, it is nevertheless true that C is much worse than D, whilst A is only slightly worse than B. And, of course, the converse could equally be true, if, e.g., comparative ratios end up being the right way to determine cardinal judgements about worseness and betterness. The value function commits one only to ordinal judgements about which outcomes are better than which––it does not settle any cardinal judgements about how much better or worse any two outcomes are.

Of course, the bounded aggregationist will still have to spell out what their cardinal theory looks like: they will have to actually tell us what the scale is like. And I believe there is a plausible account available — though that will have to be for another post!