[0-_-0]

> Though of course we can not infer that life is rare across any given set of universes if we determine we're alone in this one, because we don't know how other universes would be configured.

Not necessarily, you could assume a universal prior distribution over possible universes and count how many of those that have life have more than one.

https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_induc...

This might be a sort of a "last tool of science", a way to discover the laws of our universe without observing them.

[vidarh]

That presupposes knowledge of more than one universe to even start to enumerate the possible parameters deciding the set, and without a sufficiently complete sequence we would be unable to determine all of the possible parameters, or how they can change.

E.g. even given that we know, say, gravity exists, we do not know if or how its strength varies in a set of infinite universes. Based on a sample of one universe, it could be constant or vary in an infinite number of ways.

[0-_-0]

> That presupposes knowledge of more than one universe to even start to enumerate the possible parameters deciding the set

I think you entirely missed my point (because you didn't read the link!). You could use the universal prior, that is, you could enumerate all possible computer programs (e.g. Turing machine programs) starting from the shortest and find the shortest one that generates our universe. Now, 2^L where L is the length of such program is the prior probability of our universe.

So to determine e.g. the average value of the gravitational constant across all universes, you would measure the gravitational constant in all universes and calculate a weighted sum where you weight the value of the constant by the prior probability of the corresponding universe. The same for the occurrence of life, etc.