turchin comments on Doomsday argument for Anthropic Decision Theory - Less Wrong
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The probability of it is high. There are several Tegmark's levels of the universe infinity which are mutually independent. (quantum multiverse, cosmological inflation, independent universes, eternal existence)
Also my own existence under SIA is argument for almost infinite universe.
And as humans are finite, we don't need infinite universe for existing of all possible humans, just very large.