About Logic - Choice vs. Excluded Middle: A Constructive Paradox
I didn't get much of this! See nlab on Diaconescu-Goodman–Myhill theorem and Wikipedia's Diaconescu's theorem . My comment : 11:05 FYI I found this very hard to follow. Actually it has so far been impossible for me to follow! I don't know the context of these statements like "a predicate of booleans is a function from bool (Boole?) to prop" I can guess that it means a well-formed formula with a parameter P, say, which when substituted with any well-formed boolean-valued expression produces a well-formed statement of a proposition, i.e. just another boolean-valued expression? But it could also be interpreted extensionally in set theory and the result would be completely different. So what is the sense in which these things are equivalent? The only way I can see to make this meaningful is to restrict to a language where you speak only of how these translations are made. To talk about sets and types as if they exist independently of this seems like mad...