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

Nick Bostrom (
Wed, 9 Dec 1998 00:40:44 +0000

I wonder if anybody here could help me with the following philosophical problem, relating to the discussion of Pascal's wager?

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 bliss.

Under these circumstances it could seem reasonable to choose the action that has the highest probability of giving eternal bliss, even though it would not affect expected utility. At least I would, if the choice were between a 1% chance in heaven and a 50% chance in heaven, definitely prefer the latter.

So Pascal might then say, yes there could be other gods, but you are well advised to bet on the most likely one (even if it is extremely improbable relative to the hypothesis that there is no god, or at least no god that would grant you eternal bliss).

Conditionalizing on that there is a god that will selectively punish or reward you with eternal hellfire of eternal bliss depending on your conduct, then the Christian God would seem quite a good bet. Is there any other god with these properties that is more probable? If you think Allah is more probable, then you should believe in Him instead. (Transhumanists may think they optimise their chances by anticipating trying to become gods themselves, but that isn't a plausible alternative for most people.)

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.

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???

Nick Bostrom Department of Philosophy, Logic and Scientific Method London School of Economics