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Quantifiers are what is missing in probability theory but present in logic - while we could potentially write down mixtures of quantifiers and probabilistic sym
by cevi 5y ago
Quantifiers are what is missing in probability theory but present in logic - while we could potentially write down mixtures of quantifiers and probabilistic symbols, we don't have great ways to interpret them or to reason about them. That is the point he is trying to make.
- drdeca 5y agoI don’t see how that is, at least when quantifying over a countable set. A sigma-algebra is closed under countable unions and countable intersections, and that lets us produce events corresponding to quantification over a countable set. Like, we can talk about the probability that a particular sum of random variables converges, by handling quantifiers in this way. That seems like handling quantifiers and probability together well. Now, nesting “the probability of” type expressions, is maybe another story? But I’m not sure that that’s a problem with “extending logic”