The Worth of A Priori Probability

In an interesting conversation the other day, we were discussing probabilities concerning nothingness. As Hans-Richard Grumm stated:

My point was that there isn't just a single state of "existence": there are states with 1, 2, 3 ... particles/fields/somethings with certain properties, interactions etc. and a full description would become arbitrarily long. In contrast, the state where no thing exists can be described in a very brief sentence. I feel honored by being a cause of your head-scratching :). IMHO, the famous question "Why is there something instead of nothing?" should be countered with "Why should there be nothing?",

Ryan M added:

Think of "nothing" like the empty set. There is exactly one empty set since if A is a set and B is a set, and A has no elements that B fails to have and B has no elements that A fails to have then A = B. If A has no elements and B has no elements then A is the empty set, B is the empty set, A has no elements that B fails to have and B has no elements that A fails to have, so A = B. Thus, if A = the empty set and B = the empty set then A = B, so there is exactly one empty set.

A state of nothing, that as a description of a world, would seem to be in the same situation as the empty set. If nothingness is a description of a world without anything at all then if A is nothingness and B is nothingness then A and B have exactly the same properties so A = B.

We could also look at existence-worlds like sets. Say nothingness is a world where no particles exist. Now say there exists a world with exactly a set of 2 particles, there exists a world with exactly 3 particles... there exists a world with exactly n particles, and so on. There are infinitely many existence-worlds in this scheme, whereas there is exactly one world where no particles exist at all, so there infinitely many worlds where particles exist vs exactly one world where no particles exist.

Here, we have the idea that nothingness, before we take account of any data, is one option amongst a potentially infinite set. In other words, nothingness is probabilistically infinitesimal in comparison to all other option (or another option).

Yes, granted. The point I was wanting to make, but failed to, was that this is perhaps meaningless since we cannot ascribe any weighting to these probabilities. What this means is that nothingness, as an option, might be only one option in billions, or infinite options, but might have a probability in and of itself of almost 1 (for the sake of argument). Therefore, even though it is a priori infinitesimally probable, a posteriori, it is almost certain.

The probability of me getting no pet, a priori, is 1 in [however many animals could be used as pets + no pet]. The reality is that this probability is meaningless for working out the actual probability of my pet choice. It turns out I really don't want a pet for a whole bunch of reasons, so the probability of having no pet is 1.

Point being that a priori probabilities arguably tell us nothing or have little to no use.

Unless you can convince me otherwise...