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Utilitarianism, if it is to be a proper paradigm of ethical reasoning, must apply in an abstract sense. It cannot be that there exist certain cases, certain states of the world, where the paradigm falls apart, because if so, the theory cannot be said to be an ultimate foundation for all moral reasoning.

In this argument, I will argue that there do exist certain cases where Utilitarianism becomes useless. That is, within these scenarios, Utilitarianism cannot be use to perform any sort of moral reasoning, or, if it is attempted to be used in such a way, it produces useless, trivial gibberish.

The argument is simple, but its genius mustn't be denied. We need two propositions, from which the argument then follows readily.

The first proposition, which is just the definition of Utilitarianism rephrased.

First proposition. Let A be some action and B be some other action. We are to decide which one is morally preferable. Let U(A) and U(B) be the total utility functions, both of which consists of sums of the individual utilities that each person gets under actions A and B. The utilitarian proceeds by comparing U(A) and U(B) and picks the action which the largest possible value. If the values are equal, both actions are equally defensible from a moral standpoint.

The second proposition.

Second proposition. It is possible that infinitely many people exist with strictly positive utilities while there does not exist infinitely many people with strictly negative utilities.

This is the certain case mentioned earlier. Indeed, it is certainly possible that infinitely many people or "organisms" exist and, under both actions A and B, these people have strictly positive utilities, while the opposite (i.e. infinitely many people with strictly negative utilities) does not occur. There's no particular reason why this is impossible, at least not within the framework of Utilitarianism. I am not saying it is likely, or that I believe this to be true, but its possibility is all that is needed.

Now, combining these two propositions, a knockdown argument of Utilitarianism emerges. It is the following.

Argument. If infinitely many people with strict utilities can exist, then both U(A) and U(B) are in this case equal to infinity, since they are the (countably) infinite sum of individual utilities, and infinitely many of these utilities are strictly positives, and hence the sum is necessarily infinity. Hence, Utilitarianism collapses. It cannot perform moral reasoning, because to ask whether A is better than B corresponds to asking whether infinity is bigger than infinity: this is gibberish. In fact, it's worse than gibberish, because even if we add to action A the murder of a person, then no matter how much of a loss of utility this is, the Utilitarian still cannot say that B is now better than A, because infinity minus a billion is still infinity. So U(A) is still equal to U(B).

  • "does exist certain cases where Utilitarianism becomes useless", but they exist in every value theory. "If infinitely many people with strict utilities can exist, then both U(A) and U(B) are in this case equal to infinity, since they are the (countably) infinite sum of individual utilities" - this is not how you should count it. If we'd use just constants as cardinal numbers in computational complexity, we'd achieve nothing. Mathematicians invented limits and you don't use them. But that's your fault. – rus9384 Apr 26 '18 at 13:54
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    There do exist certain cases where classical physics is useless, so it can not be the ultimate foundation of all physical reasoning. But I am sure utilitarians would love it if utilitarianism was as "useless" as classical physics, their inspiration. We are not God, so we are not privy to ultimate foundation for any reasoning, nor will we ever be. This is a wrong standard to apply. And not that it matters, but there are different grades of infinity in mathematics, and ways to define which is bigger. – Conifold Apr 26 '18 at 18:27
  • Utilitarianism is not taken too seriously today. We know today & known for multie years there is too much subjectivity in this view. Take for instance the life of the president of the United States is probably more valuable than 200 regular people. Here too the greatest number means nothing. The president comes first. This should not fall under morality at all. This is more practical. Is it ironic that ordinary street people say philosophy is useless in reality & then attribute a pure practical approach as Moral? You can't have it both ways. Only normative ethics describes morality. – Logikal Apr 26 '18 at 18:37
  • Descriptive ethic is what the ordinary person thinks of when thinking about morality. This means these people thing morals are related to race, culture, law, society, etc. Normative ethics does NOT allow this. Normative ethics is meant to be Objective only. There is no opinion or authority needed to make moral claims. The most important is that moral claims are too express UNIVERSAL truth values. That is country or laws do not matter. For example, when Christians claim abortion is murder they are expressing the claim is for all humans no matter where they are. No agreement is needed. – Logikal Apr 26 '18 at 18:44
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    @Logikal Moral objectivism may be even less popular today than utilitarianism. Also, one can have normative ethics without objectivism (Brandom), objectivism without universality (McDowell), ethics without any claims, only imperatives (e.g. "abortion is murder" expresses "do not abort" and has no truth value), and evolutionary ethics is descriptive but quite popular with philosophers. – Conifold Apr 26 '18 at 20:07
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Does this argument prove the uselessness of Utilitarianism? Utilitarianism, if it is to be a proper paradigm of ethical reasoning, must apply in an abstract sense. It cannot be that there exist certain cases, certain states of the world, where the paradigm falls apart, because if so, the theory cannot be said to be an ultimate foundation for all moral reasoning.

On the contrary, the usefulness of an ethic is obviously in real cases, when you use it , not in abstract ones.

If I understand correctly you claim to have proven with an undeniably genius logic that if the world had an infinite number of people, then utilitarianism would be useless. Now do you understand that it's perhaps impossible or maybe infinitely unlikely, or a the very least unseen, for the world to contain an infinite number of people ? And as such, it is useless to consider this case ?

To that I'll add a much simpler case of unparalleled genius: utilitarianism would also be useless if there were no people at all.

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Given an infinite number of people, we can still assign utility values to situations by taking the average over the sum of people. Given a function, we can often calculate its average value over an infinite set. There are other possible approaches, such as calculating it over a representative but finite sample. You are throwing around infinities in a naive manner. You saying utilitarianism fails because you don't see how it would work in an impossible situation, which is a failure of your imagination more than a failure of utilitarianism.

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