By hypothesis.
I agree. I was paraphrasing what ata and Roko were talking about. I think it's a hypothesis worth considering. There may be a level of enlightenment beyond which one sees that the hypothesis is definitely true, definitely false, definitely undecidable, or definitely irrelevant to decision-making, but I don't know any of that yet.
There is no evidence for any infinities in nature. Agents need not bother with infinity when making decisions or deciding what the right thing to do is.
I think, again, that we don't actually know any of that yet. Epistemically, there would appear to be infinitely many possibilities. It may be that a rational agent does need to acknowledge and deal with this fact somehow. For example, maximizing utility in this situation may require infinite sums or integrals of some form (the expected utility of an action being the sum, across all possible worlds, of its expected utility in each such world times the world's apriori probability). Experience with halting probabilities suggests that such sums may be uncomputable, even supposing you can rationally decide on a model of possibility space and on a prior, and the best you can do may be some finite approximation. But ideally one would want to show that such finite methods really do approximate the unattainable infinite, and in this sense the agent would need to "bother with infinity", in order to justify the rationality of its procedures.
As for evidence of infinities within this world, observationally we can only see a finite distance in space and time, but if the rationally preferred model of the world contains infinities, then there is such evidence. I see this as primarily a quantum gravity question and so it's in the process of being answered (by the ongoing, mostly deductive examination of the various available models). If it turns out, let us say, that gravity and quantum mechanics imply string theory, and string theory implies eternal inflation, then you would have a temporal infinity implied by the finite physical evidence.
There's no temporal infinity without spatial infinity (instead you typically get eternal return). There's incredibly weak evidence for spatial infinity - since we can only see the nearest 13 billion light years - and that's practiacally nothing - compared to infinity.
The situation is that we don't know with much certainty whether the world is finite or infinite. However, if an ethical system suggests people behave very differently here and now depending on the outcome of such abstract metaphysicis, I think that ethical system is probably screwed.
In the future, it may be possible for you to scan your own brain and create copies of yourself. With the power of a controllable superintelligent AI, it may even be possible to create very accurate instances of your past self (and you could take action today or in the near future to make this easier by using lifelogging tools such as these glasses).
So I ask Less Wrong: how valuable do you think creating extra identical, non-interacting copies of yourself is? (each copy existing in its own computational world, which is identical to yours with no copy-copy or world-world interaction)
For example, would you endure a day's hard labor to create an extra self-copy? A month? A year? Consider the hard labor to be digging a trench with a pickaxe, with a harsh taskmaster who can punish you if you slack off.
Do you think having 10 copies of yourself made in the future is 10 times as good as having 1 copy made? Or does your utility in copies drop off sub-linearly?
Last time I spoke to Robin Hanson, he was extremely keen on having a lot of copies of himself created (though I think he was prepared for these copies to be emulant-wage-slaves).
I have created a poll for LW to air its views on this question, then in my next post I'll outline and defend my answer, and lay out some fairly striking implications that this has for existential risk mitigation.
For those on a hardcore-altruism trip, you may substitute any person or entity that you find more valuable than your own good self: would you sacrifice a day of this entity's life for an extra copy? A year? etc.
UPDATE: Wei Dai has asked this question before, in his post "The moral status of independent identical copies" - though his post focuses more on lock-step copies that are identical over time, whereas here I am interested in both lock-step identical copies and statistically identical copies (a statistically identical copy has the same probability distribution of futures as you do).