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Seek_Equilibrium t1_jc8t769 wrote

Reply to comment by throwawayski2 in A philosophical dive into “Everything Everywhere All at Once” by Azmisov

How does this help define the frequency of an element within the infinite set?

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throwawayski2 t1_jcb56n3 wrote

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.

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Seek_Equilibrium t1_jcbheol wrote

> 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 phrase “from a given subset” is catching my attention. Are you talking about defining a probability measure on a finite subset of an infinite set? Because if so, that of course wouldn’t bear on the core issue being discussed of whether and how a unique probability distribution could be defined over an entire infinite set - but I am probably missing what you’re truly aiming at so maybe you can clarify.

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throwawayski2 t1_jccd2r6 wrote

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.

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