Note: this essay is a crosspost from X/Twitter, and is largely targeted at a certain type of user on that site. Those deep in Philstack may notice that I have omitted some nitty-gritty details and glossed a few issues or concepts for the sake of simplicity.
This week was apparently Get Mad At Utilitarians week on Twitter. As per usual, the suspect at the center of this controversy is Bentham's Bulldog, who published an article arguing that bugs matter more than people (in aggregate). Coming off of an already growing frenzy around METR, Anthropic, and Effective Altruism, this article really kicked the dunking into overdrive, with everyone (myself included) taking the opportunity to air their pet grievances with EA and utilitarianism.
However, this essay is not about the insect argument itself. After all, this is not the first time BB has made this sort of argument, and I’ve already gone at it with him on the insect welfare issue specifically (and the downstream arguments for insect omnicide) in an old essay you can read here.
Instead, I actually want to focus on a very common criticism levied against this genre of utilitarian thought: that the whole approach of estimating, adding up, and comparing bundles of value to determine right from wrong is fundamentally distorted—that to do so is to somehow miss the point of what ethics is. In short: Morality Isn’t Math.
I am quite sympathetic to this argument. In fact, I went on a short rant in the wake of BB’s essay about how questions asking one to compare moral worth between groups are essentially making a category error. But while I do think there is some truth to the criticism, I think many of those who deploy it are at risk of letting it become a thought-terminating cliche.
In my view, math and logic are really the same kind of thing: Formal Sciences tasked with the manipulation of symbols and sentences according to rules and axioms. To the extent any system can be said to follow a set of abstract rules, it must behave according to some calculus. This calculus or logic may not be as simple as basic arithmetic, but it is still “math” in a way. To abandon the notion that morality is math-like in any sense is to basically embrace moral nihilism, or at least moral indeterminism: that there is no decidable truth of the matter that one could discover, even in principle, about which actions are right or wrong.
I think this is a bad conclusion to accept (though I won’t go into all the arguments against moral nihilism here). But the tricky thing about consequentialism is that if you try to avoid this descent into nihilism, if you do try to make morality behave according to some sort of structure or logic, it is surprisingly easy for something like Utility Arithmetic to fall out the other end. While the conclusions that emerge are ugly and horrifying, the assumptions that get you there are, on their face, eminently reasonable.
To see why, let’s focus on that objection from mutual @lovabler0gue: is utilitarian moral calculus the equivalent of asking how many pennies are worth more to you than your wife? Obviously, such a question seems absurd, and it points to the core of the Morality Isn’t Math objection: that the mere attempt to compare these sorts of things is just inherently ridiculous. Any claim that pennies or bugs matter more than people is ipso facto preposterous. That’s not how value works. That’s not how any of this works!
But if I may defend, for a moment, the very act consequentialists whose principles I oppose, I think this sort of objection oversteps its mark. Because the utilitarian claim is not quite as straightforward as “there should be an amount of pennies worth more to you than your wife.”
For starters, money, like all goods, has decreasing marginal utility to any individual as they gain more of it. If I were to receive $1M, that might give me X utils of well-being, but if you give me another $1M after that, I’ll only get Y utils, where Y<X. This decreasing marginal utility can eventually become asymptotic: there can be a point at which you have so much money that obtaining more doesn’t really move the needle, a point at which more money does not buy more happiness.
It is therefore relatively straightforward to say, even under utilitarianism, that there may be no amount of pennies given to you or any other individual that would be worth more than your wife.
But the utilitarian argument that leads to claims like “Insects Matter More Than People In Aggregate” is a bit more subtle, and it relies on a few premises that are not obviously false at first glance:
1. Goods have decreasing marginal utility, but utility itself does not
Think about it: utility is the thing that you get less of as you gain more money, but how could utility itself have decreasing marginal returns? Returns in what? The whole notion of decreasing marginal X presumes a scalar measure of X that can be compared against, which cannot itself have decreasing marginal returns (unless you invoke yet another measure of comparison).
When people talk about utility, they are often not referring to some intrinsic property attached to an object that can be held and weighed (hedonic utilitarians notwithstanding). Rather, they are typically referring to this abstract metric of comparability, a metric that naturally emerges when considering any well-behaved preferences.
This is where the math starts to creep in, because while you may intuitively reject the notion of using addition and multiplication to calculate good and evil, it’s a lot harder to argue that preferences alone are an illegitimate tool in moral reasoning. After all, to say something is good or bad is to imply that the good thing is preferable to the bad thing, at least in some sense. To say “you ought to be kind rather than cruel” sure would seem to imply that beingKind ≻ beingCruel.
And yet, it turns out that if you have some set of preferences, and those preferences obey a few relatively basic criteria for consistency (Completeness, Transitivity, Continuity/Archimedean, Independence), you can map those preferences to a utility function, such that U(X) > U(Y) ⟺ X ≻ Y and the resulting utilities add and scale accordingly. In other words, the mere act of having consistent preferences implies that you can do arithmetic on the objects over which said preferences range in a way that is equivalent to stating those preferences outright.
The upshot of this is that, while sure, there may be no amount of pennies that are “worth more” than your wife, the consistency of your preferences implies that there is some amount of utils that are worth more than your wife, even to you.
Now, admittedly, this isn’t quite as clear-cut as I’ve made it seem. That your preferences obey a utility function does not necessarily imply that there is some basket of goods or wants that you value over your wife. Sorry ladies, but sadly you cannot accuse your boyfriend of loving something more than you by citing the Von Neumann–Morgenstern utility theorem. Specifically, the theorem does not imply that the utility function is non-satiated, i.e., that for any given basket of goods X there is some other basket of goods Y such that U(Y) > U(X).
Moreover, the third of those consistency criteria (the Archimedean property) is arguably the most bendable: it essentially guarantees that no preferences take on infinite or infinitesimal value. Plausibly, one could reject this criterion. Perhaps your love for your wife truly is infinite. Perhaps there is no conceivable basket of goods, no set of earthly or divine pleasures, no knowledge or status or IV drip of ambrosia and hedonium that would outweigh her value in your mind. You would not merely die for her; you would sacrifice God’s grace and an eternity in Heaven just to keep her. Quite a romantic thought, and one that manages to escape the grasping claws of arithmetic (hyperreal and surreal numbers notwithstanding).
But those claws get longer and sharper when we start considering the other premises.
2. Goods have decreasing marginal utility within individuals, but not across them
This premise can be summed up as the idea that utility adds across persons, i.e., The Numbers Should Count. Sure, I might get less out of a second million dollars than I get out of the first, but if you give both me and a clone of me $1M each, we both get X utils. In total, we now have 2X utils, greater than if I had gotten $2M to myself (X+Y).
Now, although seemingly innocuous, there are a lot of objections to this aggregation premise, as it quite naturally leads to some of the thorniest problems in ethics. Nevertheless, I think it’s worth appreciating how intuitive this premise is at face value. To quote Parfit’s famous line rebutting those who question aggregation:
Each counts for one. That is why more count for more.
We can’t escape the math proofs here either. Harsanyi’s aggregation theorem implies that this sort of additive property naturally follows from those same VNM axioms when applied to both individuals and social choice functions (plus Pareto indifference). Once again, the mere consistency of our individual and collective preferences implies that we can use math for moral reasoning.
Notably, unlike the value to an individual, it’s hard to see how this sort of aggregate value could be asymptotic or bounded. You can always add more people. Even if you and I value our partners over any conceivable basket of goods that we each could receive, the combined value of our partners surely exceeds that which we place on each individually.
Many have tried to construct axiologies (theories of value) that avoid this additive property, but they have some weird implications of their own. Does the value of each existing person in the world decrease with every new birth? Do your children matter less individually the more of them you have? If we are to respect the equality of persons, it seems rather intuitive that we respect the addition of their interests.
This alone has pretty substantial implications. For simplicity, let’s treat money as a stand-in for generic goods or wants (i.e., we are ignoring inflation and instead imagining these pennies as more like fractions of additional raw economic output). Under this additive premise, while there may be no amount of pennies given to you alone that would exceed the value of your wife, there is, in principle, some quantity of pennies given to some other quantity of distinct persons (call it a “gazillion”) that “outweighs” your wife. Give enough children enough candy bars and well, sorry, but the love of your life just can’t compare.
Stated as such, this conclusion may seem outrageous, but it really isn’t that absurd when you consider the very real tradeoffs we make in public policy. Most people would pay money to have a shorter commute, and we can give them a shorter commute by increasing traffic speeds. Conversely, we can lower traffic speeds to under 20 mph to substantially reduce the probability of fatal accidents, but in doing so we deprive a large number of people of something they value (their time). The fact that we don’t do this means that more people will die. It means that we are implicitly choosing some modest amount of value given to some large number of people over someone’s wife. Tough luck.
Still, perhaps you reject the notion that aggregating value across persons is legitimate. Perhaps you think that’s where this whole thing goes wrong. Well, in that case, let me introduce you to premise #3:
3. Moral reasons are agent-neutral
Perhaps the most obvious objection to the prior discussion, one which you may have already started typing in the comments, is that preferences are individual—that just because I value my partner at a gazillion utils doesn’t mean you have to value her to the same degree. Why are we combining preferences at all when those preferences are not shared?
The utilitarian response here is that, if morality is to be meaningful in any sense, then it has to obey what’s known as agent-neutrality. The idea is that if morality tells us what we ought to do, then that means it gives us reasons to act in certain ways, and if those reasons are to be moral reasons, then they cannot just be mine or yours alone. Right and wrong shouldn’t depend on which agent is taking the action; if something is objectively, morally wrong then surely it can’t only be wrong when you do it.
And so if we are to talk at all about “what matters”, it is not enough that something matters to a single person. I may personally dislike the taste and texture of uni, but that doesn’t make it capital-B Bad. It is only bad to me. And the whole point of ethics, assuming we reject nihilism, is to step back from those subjective interests, to take the so-called View From Nowhere and separate right from wrong and good from bad on objective, neutral terms.
Note that this doesn’t imply that losing a partner “doesn’t matter” in the moral sense because their life is your personal interest. But it does mean that, to the extent the suffering you feel from their loss “matters”, it is not merely because said suffering is bad to you. It is because suffering itself is bad, in a way that matters for all agents equally. And it is that objective badness that gives us moral reasons to not inflict suffering upon others and to relieve such suffering when we can, regardless of whatever personal interests drive us towards other actions.
This means that to the extent your wife matters in this moral sense, she cannot get some special treatment. You may value her more than an infinite jar of pennies or a gazillion candy bars, while the children who gorge upon the latter may not care about your wife at all. But from the “point of view of the universe”, such personal interests must fade, and what is left—what ultimately matters—is the universal goodness of life and happiness that you and your wife share, and which ought to bear upon all agents equally. But just as the value you receive creates moral reasons for others to defend and promote it, so too does the value they receive create moral reasons for you. Which means, at some point, as the gazillions grow and the many become many enough, choosing your personal interest over theirs can no longer be justified under objective, neutral ethics.
Here’s the thing, though: I think almost everything I’ve said in this section so far is wrong. In fact, I would argue that this is the real crux of act consequentialism—not the mere use of math or preferences, nor even the ever-controversial aggregation of value across persons, but rather the idea that morality must be agent-neutral.
Consider the obligations that parents have to their children or which doctors have to their patients. Both of these obligations are agent-relative; I do not have the same degree of obligation to nurture and feed your kids as you do to your own. Or consider the act of lying: what makes such an act (generally) wrong is not merely that I have uttered something false or caused a false belief in others—there is no fault in merely being mistaken. No, what makes lying wrong is that I have said something that I know to be false. Again, it’s an agent-relative concern; the moral reason hinges on a fact about the agent in question.
Agent-neutrality ignores these considerations, and it really is the linchpin of consequentialist arithmetic—when you all complain that Morality Isn’t Math, this is what you’re really complaining about. Without it, Harsanyi’s aggregation theorem doesn’t get off the ground, as there is no global social welfare function to maximize (certainly not one that satisfies VNM). Global preference functions require agent-neutral reasons.
Yet the funny thing about agent-neutrality is that it’s not even really about the math per se. One can, arguably, consequentialize any deontological moral theory, so that its permissions and prohibitions also correspond to some sort of function being maximized (since “X is right & Y is wrong” still implies that “X is morally preferred to Y”). It’s the same sort of mathematical representation, applied to deontic verdicts instead of value. But the crucial thing is that, unlike in normal consequentialism, the functions that emerge from a consequentialized deontic ethics are necessarily agent-relative—my obligations are not the same as yours.
One way to understand why this divergence is so important is to notice that agent-neutrality requires that moral reasons ignore relationships—that our moral interests and obligations be perfectly symmetric regardless of history or kinship. Sure, we don’t have zero obligation to strangers, and there may of course be scenarios where such symmetries emerge, such as the obligations that rulers have to their citizens when deciding policies. And in such cases where weighty and impartial responsibilities are incumbent upon us, perhaps we can reduce moral calculus down to simple measurements of costs and benefits. But outside of these special circumstances where we are entrusted with this role, what is right for you is not merely what is best for all. “Who matters more” just...doesn’t matter.
You might worry that this sort of turn would condemn us to moral nihilism, but note that accepting agent-relativity does not mean we have to dispense with universality or objectivity. Every mother and father has an obligation to their kids, regardless of their desire to fulfill it, just as every person has an obligation to not assert that which is knowingly at odds with their beliefs. These obligations apply to all agents equally, but the specific actions and interests they prescribe are yours and mine alone.
But what this does mean is that, on occasion, it is possible for our moral obligations to come in conflict. It may be right for me to do everything in my power to save the life of the woman I love, even if that means letting millions suffer and sacrificing every penny of economic value in existence. And it can be equally right for you to try and stop me.
This, in my view, is the principal error that utilitarians commit when they boil morality down to measures of value or worth. It’s not that Morality Isn’t Math; it’s that it isn’t Impersonal. There is no “best possible world” that morality demands we strive towards. There is no set of agent-neutral reasons to which ethics can be reduced. There is no neutral “point of view of the universe” where moral worth is tallied, nor does God keep a well-ordered ranking of world-states. There are only the actions that we each as individuals ought to and ought not take in light of who we are, what we value, and how we relate to other moral patients in this world—what we owe to each other.
Even granting agent-relative reasons, couldn't there still be agent-neutral reasons — and a "best possible world" that we should strive for *all else equal*, when we haven't anything personal on the line — in addition?
I wrote a response to this, I hope you enjoy / aren't too offended (I was maybe a little aggressive??) -
https://ramblingafter.substack.com/p/your-daughter-vs-1-million-strangers