The Great Big Arguments #9: Infinity

Basic form of the argument:
For all we know, the universe is infinite. There might even be infinite universes. However small the chance of a god existing in any given way, place or universe, the infinite possibilities make it practically certain that a god is out there somewhere.

Answer by SmartLX:
This one crops up a great deal, but I have yet to see it formalised. A possible reason for this is that it doesn’t hold up very well when even basic mathematics are applied to it.

Firstly, the universe may not be infinite in whatever way matters. There may have been nothing of consequence before the Big Bang, or even no time so that “before” doesn’t even make sense. The multiverse may merely be a useful way of modelling the phenomena we see in the field of quantum mechanics, while not actually being real. Therefore the possibilities may not be infinite either, and a god may have only one chance to exist.

Secondly, the presence of an infinite element in a calculation does not automatically take the result to 100% or probability 1. The set of even numbers (2, 4, 6, 8…) is infinite but contains absolutely no odd numbers. You can calculate the digits in pi forever but they will never repeat themselves. The sum of an infinite set will be a finite number if each new number is a smaller percentage of the previous one, e.g. 1 + 1/2 + 1/4 + 1/8 + … = 2.

To speak more practically, if the multiverse is real there may well be things all universes have in common which preclude the existence of uncreated omnipotent beings. Super-advanced beings who have acquired godlike powers through evolution and technology over aeons, sure, possibly out there somewhere, but this supposition is an extrapolation of our own status and the technology we’ve developed so far, not a guess unrelated to anything we’ve ever seen before.

To make my answer as general as possible, there are any number of reasons why the probability of the existence of a god might be zero, making the number of different universes irrelevant. (Try to roll a 13 with two standard dice – you’d be there a while.) Even if it’s not zero, there are any number of reasons why a non-zero probability is not brute-forced to certainty by an infinite universe/multiverse. Infinite possibilities just mean there are things we can’t rule out, but I’ve never claimed to be certain that there are no gods.