No, it can also be defined on infinite subsets. That's why I mentioned Cantor sets, because these are measurable uncountable sets, such that choosing an element from it (given uniform choice from the bounded set on which it is defined) has probability 0 (which is different from our finite intuition, that it is impossible).

It is basically just a generalization of the concept of volume.

I didn't mention frequency if you read again. Frequency - at least in the probabilistic sense - requires a observational component, that is reasonable to assume when discussing possible worlds. But that has nothing to dobwith infinity but with the fact that you can't observe possible worlds.

But if you talk about proportions or the probability of choosing an element from a given subset (what I suppose you actually mean by frequency), then this is exactly the way you define these things in Mathematics when dealing with infinite sets.

>The lesson is just that you can’t define frequencies or proportions in infinite sets that lack natural orderings. The number line is the exception, not the rule.

You may need to explain a bit more, because as a mathematician that just seems plain wrong:

You can define sets of any proportion on any bounded set of R^n (an infinite set with no natural ordering for n > 1). That's a very basic thing in Measure Theory. For example you can just generalize the Cantor set to any dimension to get an infinite set of points that has no volume.

Edit: just some minor correction of my part