Suppose I promise x that I will do whatever I promise y, and I promised y that I will do whatever I promise x. I then promise x to bring ice cream to the party. In so doing, I have violated my promise to x to bring ice cream to the party. My violating my promise to x to bring ice cream violated my promise to y to do whatever I promise x. My violating my promise to y to do whatever I promise x then violated my promise to x to do whatever I promised to y. And so on.
It looks like by the simple neglect of bringing ice cream to the party, I have violated three promises in infinitely many ways.
But this action doesn't seem to be infinitely wrong, or if it is infinitely wrong, it is such because of the offense against God implicit in the promise-breaking, and not because of the infinite sequence of violations.
But why isn't it infinitely wrong (at least bracketing the theological significance)?
Is it because it's just one action? No: for a single action can be infinitely wrong, as when someone utters a spell to make infinitely many people miserable while believing that the spell will be efficacious (it doesn't matter whether the spell is efficacious and whether there are infinitely many people).
Is it because only a finite number of promises are broken? No: for a single promise can be broken infinitely often (given an infinite future, or a future dense interval of events if that's possible) with the demerit adding up. (Imagine that I promise never to do something, and then I do it daily for eternity.)
Maybe one will bite the bullet and say that the action is infinitely wrong. What's the harm in saying that? Answer: incorrect moral priorities. Keeping oneself from infinitely wrong actions is a much higher priority than keeping oneself from finitely wrong actions. But it doesn't seem that one should greatly, if at all, prioritize being the sort of person who brings ice cream to parties in the above circumstances over, say, refraining from finitely but seriously hurting people's feelings.
Puzzling, isn't it?
The above generated a puzzle by infinite reflection. But one can generate puzzling cases without such reflection. Suppose x loves y, and I harm y. I therefore also harm x, since as we learn from Aristotle, Aquinas and Nozick, the interests of the beloved are interests of the lover. Now suppose infinitely many people love y. (If a simultaneous infinity is impossible, assume eternalism and imagine an infinite future sequence of people who love y. Or just suppose I falsely believe that infinitely many people love y.) It seems that by imposing a minor harm on y, I impose a minor (perhaps very minor) harm on each of infinitely many people, and thereby an infinite harm. Now, suppose that I have a choice whether to impose a minor harm on y, who is loved by infinitely many persons, or a major harm on z, who is loved by only finitely many. As long as the major harm is only finitely greater than the minor harm, it seems that it is infinitely worse to impose the minor harm on y than the major harm on z. But that surely is mistaken (and isn't it particularly bad to harm those who have fewer friends?).
One might try to bring God in. Everyone is loved by God, and God is infinite, and so the major harm to z goes against the interests of God, and God's interests count infinitely (not that God is worse off "internally"), so the major harm to z multiplied by the importance of God's interests will outweigh the minor harm to y, even if one takes into account the infinitely many people who love y, since divine infinity trumps all other infinities. But this neglects the fact that God also loves all the infinitely many people who love y, and hence the harm to the infinitely many lovers of y also gets multiplied by a divine infinity.
Nor is infinity needed to generate the puzzle. Suppose that N people love y and only ten people love z, and my choice is whether to impose one hour of pain on y or fifty years of pain on z. No matter how little the badness of x's suffering to x's lovers, it seems that if you make N large enough, it seems it will overshadow the disvalue of the fifty years of pain to z.
I think the right answer to all this is that wrongs, benefits and harms can't be arithmetized in a very general way. There is, perhaps, pervasive incommensurability, so that the harms to y's lovers are incommensurable with the harms to y.
But I don't know that incommensurability is the whole story. It is a benefit to one if a non-evil project one identifies with is successful. Now imagine two sport teams, one that has a million fans and the other of which has a thousand. Is it really the case that members of the less popular team have a strong moral reason to bring it about that the other team wins because of the benefit to the greater number of fans, even if it is a moral reason overridden by their duties of integrity and special duties to their fans? (Likewise, is it really the case that the interests of Americans qua Americans morally count for about ten times as much as the interests of Canadians qua Canadians?)
Yet some harms and benefits do arithmetize fairly well. It does seem about equally bad to impose two hours of suffering on ten people as one hour of suffering on twenty.
So whatever function combines values and disvalues is very complicated, and depends on the kind of values and disvalues being combined. The only way a simple additivity can be assured is if we close our eyes to the vast universe of types of values, say restricting ourselves to pleasure and suffering as hedonistic utilitarians do.