Re: Infinite utility (was: Re: Pascal's Wager)

Dan Fabulich (
Wed, 09 Dec 1998 08:43:38 -0500

Nick Bostrom wrote:
>If one doesn't time discount future benefits, then it would seem that
>the expected utility of *any* human action is infinite, since there
>is always a finite probablility that it will lead to eternal

Yes, but this is cancelled out by the finite probability that the action will lead to eternal damnation and suffering. Thus utilitarians need not consider themselves morally blameworthy if their breathing causes floods in China; as far as anyone knew, NOT breathing would have had felt the same odds.

>Shall we conclude that most people ought to believe in some god then?
>- A more reasonable alternative may be to say that they time-discount
>future benefits (or are risk averse) in such a way that the expected
>utilities don't add up to infinity.

This is another answer.

>But here I see a problem for utilitarians... If other people's
>happiness count for as much as your own, and if there are infinitely
>many people (which is the case if the universe is open and has the
>simplest topology), then the total amounts of pleasure and of pain
>are both infinite, no matter what you do! Thus it seems that in an
>open universe with the simplest topology, utilitarianism is no guide
>to action. Similarly, for those people who think that an exact
>replica of yourself is yourself - then *you* would in fact at this
>very moment and in the future be experiencing an infinite amount of
>pleasure and pain no matter what you do.
>If we find the consequence that it doesn't matter what you do absurd,
>then we seem to have a refutation of both utilitarianism and this
>view of personal identity. But can that really be correct???

This is only a problem if the universe turns out to be open and that an infinite number of intelligent beings are already out there. If this is not the case, then there's no problem to address.

Even if this were the case, however, the infinities could still be compared. Remember, however, that comparing total utility is hard even when you've only got a finite number of people. But let's suppose that you had an infallible method for doing that. At that point, you could start making claims about one infinite set being a proper subset of the other infinite set, etc. And remembering that each action in such a universe would have literally an infinite consequence, it could even make sense to say that one action compared to another may even result in infinities with different cardinalities, in which the answer is clear: choose the bigger infinity of the two.