Saturday, June 27, 2015

FTA part 7: Aron asks clarifying questions (part of the Aron series)

Aron wrote:
Thanks for the response!  I want to make sure I understand you, and that you understand me.  My objection was this: our universe is just one out of a pool of infinity conceivable universes.  P(FT/~G) is the probability of picking a universe like ours at random.  Probabilities only make sense if they add to one (ex/ for a die 1/6x6=1).  So for the FTA to work, we need to be able to assign each possible universe a probability that allows them to add up to 1.  But this is impossible because if each universe has a probability of 0, they all add up to 0.  And if each universe is given a small nonzero probability, they add up to infinity.  Since the probabilities can't add up to 1, it is meaningless to talk about probabilities here.   The objection is that our intuitions have led us to extend to concept of "probability" far beyond the context in which it is applicable.

The way you characterized the normalizability objection is like this: "everything's equally impossible or our current value is necessary."  I'm not sure this is what I was getting at.  Instead, it should say "each possible universe is either equally impossible, or they all have a small nonzero probability. They can't be impossible, because then the probabilities don't add up to 1, and they can't have a nonzero probability, because then the probabilities add up to infinity."

If I'm right that the concept of probability is simply not meaningful in this context, then this dissolves the mystery.  There would be no need for me to resort to a multiverse or necessity.

In sum, I'm not quite sure exactly what your objection was to the normalizability problem.

[See summary page of this discussion, with links to all the posts, here.]