When comparing explanations for any given event, most of us – often without realizing it – weigh probabilities. If you come home to find that your TV is missing, the best explanation might be that you’ve been burglarized. It may be true that aliens used a futuristic device to make your TV invisible, but knowing that (a) burglary is common and (b) aliens in general are completely unknown to us, then clearly the burglar hypothesis is the more probable (and thus superior) explanation.
This sort of probability weighing is not only important for every day life, but it is also important for statistical testing of scientific hypotheses (which use p-values or Bayes theorem), principles like Occam’s razor (i.e. more assumptions = less probable), and the old adage, “extraordinary claims require extraordinary evidence” (i.e. a claim which doesn’t fit our background knowledge requires evidence to increase its probability). Unfortunately, an infinite multiverse could mess this all up.
Very often I hear people trying to answer the fine-tuning argument for God by using various multiverse proposals, and usually these debaters tend to ignore (or not be aware of) further problems caused by this proposal. As alluded to in the opening of this post, one major problem is that infinity – the sort actualized in a infinite multiverse – doesn’t get along with probability.
As I explained in my post Ethics in the Multiverse, if there are an infinite number of universes, then this suggests that all possibilities, no matter how unlikely, are actualized an infinite number of times. So in my example about the missing TV, both the alien explanation and the burglar explanation are possible, but we chose the burglar explanation because it seems to be much more probable. But if we consider the infinite multiverse, then there are an infinite number of universes where burglars stole your TV and there are also an infinite number of universes where aliens made your TV invisible! So, as you can see, we run into a huge problem when we attempt to predict which explanation is more likely.
As physicist Brian Greene writes in The Hidden Reality, “Every possible outcome allowed by quantum calculations, however unlikely – a .1 percent quantum probability, a .0001 percent quantum probability, a .0000000001 percent quantum probability – would be realized in an infinitely many universes simply because any of these numbers times infinity equals infinity. Without a fundamental prescription for comparing infinite collections, we can’t possibly say that one collection of universes is lager than the rest and thus the most likely kind of universe for us to witness, we lose the capacity to make definite predictions” (p. 185).
But Greene’s concern goes much further than missing TVs. If we lose our ability to calculate probabilities, then all our evidence – even that which leads us to various multiverse proposals – is unreliable. Quite a paradox. Perhaps then it’s fortunate that Greene concludes the section with optimism. According to him, most physicists do suspect that this problem will be solved eventually.
But until then, it’s a problem worth considering when arguing about fine-tuning.