Consequentialism aims at maximizing the good in the long term, or on the whole. But what if the universe is infinite, temporally speaking? Then it seems that there are no actions that maximize the good (or that every action does so) because there will always be an infinite amount of good (and bad) in the future (and in the past as well, if the universe is truly infinite).
I recall reading once about how the notion of a multiverse where every action/decision results in another universe seems to make moral choices worthless, from a consequentialist view-from-nowhere, since every good and bad possibility is an actuality. [Yup - RC.] However, it seems plausible that we could focus the scope of our consideration on the universe in which we live without being open to an accusation of arbitrariness.
But, even if we keep our focus on the only universe which we experience, if it is infinite, then how are we to non-arbitrarily judge what maximizes the good? Should it be what maximizes the good in ten years, or one hundred, or a million? Why should the tenth year matter, but not next year, or all of the infinite years to come?
Now, it is clearly disputable that the universe will continue infinitely, but it certainly seems plausible. Do you think I have hit on an interesting problem, or has this been dealt with before?
Sounds interesting. (If anyone is familiar with the literature on this topic, feel free to provide references in the comments!) Cf. my post on the infinite spheres of utility paradox.
My initial thought is to clarify that what the consequentialist wants to do is to bring about the best world practically possible. And it seems that even when comparing worlds that contain (equally) infinite value, we can judge that some are better than others. For a simple example, consider a case of 'domination', i.e. where one world is (finitely) better than another at each of the infinite moments in time. Clearly, this world is also better overall, even though we cannot attribute a higher quantity of value to it (since both are just countably infinite).
[N.B. This is a puzzle for value theory generally, not anything peculiar to consequentialism -- cf. R.M. Hare.]
Anyway, I'll throw open the comments for anyone else who wants to chip in...