Hal Finney writes:
Not to detract from your main point, but I want to point out that sometimes there is ambiguity about how to count worlds, for example in the many worlds interpretation of QM. There are many examples of QM based world-counting which seem to show that in most worlds, probability theory should fail.
I'm not sure what examples you have in mind here, but this is actually the general point I was trying to make: probability theory doesn't seem to work the same way in a many worlds cosmology, due to complications such as observers multiplying and then not being able to access the entire probability space after the event of interest.
Consider these three examples:
(A) In a single world cosmology, I claim that using my magic powers, I have bestowed on you, and you alone, the ability to pick the winning numbers in this week's lottery. If you then buy a lottery ticket and win the first prize, I think it would be reasonable to concede that there was probably some substance to my claim (if not magic powers, then at least an effective way of cheating).
(B) In a single world cosmology, I announce that using my magic powers, I have bestowed on some lucky gambler the ability to pick the winning numbers in this week's lottery. Now, someone does in fact win the first prize this week, but that is not surprising, because there is almost always at least one winner each week. I cannot reasonably claim to have helped the winner unless I had somehow tagged him or otherwise uniquely identified him before the lottery was drawn, as in (A).
(C) In a many worlds cosmology, I seek you out as in (A) and make the same claim about bestowing on you the ability to pick the winning numbers in this week's lottery. You buy a ticket, and win first prize. Should you thank me for helping you win, as in (A)? In general, no; this situation is actually more closely analogous to (B) than to (A). For it is certain that at least one future version of you will win, just as it is very likely that at least one person will win in the single world example. I can only claim that I helped you win if I somehow identified which version in which world is going to win before the lottery is drawn, and that is impossible.
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