Thanks to your help Churchwork, I now see that the 4 Step Proof disproves and disallows this...
"Imagine living in a universe where nothing is original. Everything is a fake. No ideas are ever new. There is no novelty, no originality. Nothing is ever done for the first time and nothing will ever be done for the last time. Nothing is unique. Everyone possesses not just one double but an unlimited number of them.
This unusual state of affairs exists if the universe is infinite in spatial extent (volume) and the probability that life can develop is not equal to zero. It occurs because of the remarkable way in which infinity is quite different from any large finite number, no matter how large the number might be.
In a universe of infinite size, anything that has a non-zero probability of occurring must occur infinitely often. Thus at any instant of time—for example, the present moment—there must be an infinite number of identical copies of each of us doing precisely what each of us is now doing. There are also infinite numbers of identical copies of each one of us doing something other than what we are doing at this moment. Indeed, an infinite number of copies of each of us could be found at this moment doing anything that it was possible for us to do with a non-zero probability at this moment."
(Barrow, John D. The Infinite Book: A Short Guide to the Boundless, Timeless and Endless. London: Vintage, 2005. pp. 156-58)
That's Barrow's description of something he calls the Infinite Replication Paradox.
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So, seeing as the Proof permits a universe of any size (except infinite) does it also permit the Finite Replication Paradox?
This is a finite version of the above. It works like this.
There are only a certain number of ways that matter can be arranged into stars and planets. A stupendously high number, to be sure, but still a finite number. Therefore, in a stupendously large universe, these arrangements will eventually begin to repeat themselves, leading to identical (atom-for-atom) copies of stars and planets. The outcome of the Finite Replication Paradox is that in a stupendously large (but finite) universe, there are a finite number of identical copies of you, me, everyone else, the Earth and the Sun. How many copies will depend critically on the volume involved. There could be just one other copy or there could be trillions.
Seeing as the Proof permits a universe of any size (except infinite) it would seem to therefore permit the existence of a finite number of exact copies of us.
Is that so?
Or, if I've misread the Proof, could you help me out please and direct my attention to where it rules this out?
Thanks,
Cerenkov.
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