Sometimes it is better to ask “why does this formal method EVER work in the messy real world” than “what’s the minimal extension needed to make the standard formal method work here”pic.twitter.com/CEKBI99nPm
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Sometimes it is better to ask “why does this formal method EVER work in the messy real world” than “what’s the minimal extension needed to make the standard formal method work here”pic.twitter.com/CEKBI99nPm
Yes, but also, your criticism of probability as generalizing only Aristotelian propositional logic is slightly out of date. With probabilistic programming, we can generalize arbitrary monadic/modal constructive type theories!
Probabilistic modeling of quantified statements -- sometimes. When they're constructively provable.
I see… there have been many cases of extending probability theory to cover some quantified statements (as I noted in my Cox post). Maybe this is cleaner or more general than others?
I would say that it's cleaner in the sense that its computational complexity is only a constant factor worse than an equivalent deterministic reasoning algorithm 1/2
, and somewhat more general in that, in exchange for sacrificing proofs by contradiction, constructive type theories can often handle logic of higher order than first. 2/2
As a further addendum that sorta gives the philosophical flavor of the thing... >Kopylov’s investigations established quite clearly that ... the propositions-as-types correspondence is as open-ended as our imaginations. https://pdfs.semanticscholar.org/d5e1/ab8a6cf164ca88c1c2a9d655c57a429de87a.pdf …
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