Saturday, June 27, 2015

FTA part 5: Aron introduces the normalizability problem (part of the Aron series)

Aron says:
If I grant a uniform distribution for the sake of argument, then the probability of G being "just right" is the ratio: (life permitting values/possible values).  As far as I know (and I'm no expert) there's nothing in modern physics that restricts the range of possible values.  Robin Collins, for example says, "The value of G, for instance, conceivably could have been any number between 0 and infinity" http://home.messiah.edu/%7Ercollins/Fine-tuning/FINETLAY.HTM).

So we can either say that the range of physically possible values is infinite, or we can say that we simply have no idea what the range is.  The second option kills the fine tuning argument, so you should prefer the first option.

Here is my problem: the axiom of normalizability requires that the probabilities of all the possibilities add up to 1.  If there are infinity possible values, and each is given the same super small non-zero probability, this adds up to infinity.  If, instead, we give each possibility a zero probability, it adds up to 0.  Either way, we can't normalize the probability space, so we can't meaningfully talk about probabilities in this context.  P(FT/~G) is not low; it just doesn't even make sense to ask for this number.  (This is the argument made by McGrew et al. here: http://philpapers.org/rec/MCGPAT.  The point was also independently made by Colyvan et al. here:
http://www.colyvan.com/papers/finetuning.pdf, and by Paul Davies in "The Mind of God.")

One solution to the normalizability problem is to drop the assumption of a uniform distribution.  A nonuniform distribution would allow us to normalize a space of infinite possibilities.  You took this approach and said something like this:  "I recognize that there are multiple possible distributions, and we don't know which distribution is correct.  But since the set of life favoring distributions is just a small set of the total number of possible distributions, the probability that the actual distribution favors life permitting values is still very low."

Notice that this approach does away with the assumption of a uniform distribution over the range of possible values, but then assumes a uniform distribution over the range of possible distributions.  While this proposal allows us to normalize the space of possible values, it simply recreates the normalizability problem, because now we are unable to normalize the space of possible distributions.  We are faced with an infinite number of possible distributions, and you seem to be asking that we lay a uniform distribution over this infinite range.  This is the normalizability problem all over again.
Another possible solution is to find a way to limit the range of possible values, but I don't think this works.  You seem to have done this by focusing on possible values for G between 0 and 2.  Why exactly did you restrict the range of possibilities this way?

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