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I thought the principle of the excluded middle was the ultimate source of that paradox, not set theory itself?
by daxfohl 3y ago
I thought the principle of the excluded middle was the ultimate source of that paradox, not set theory itself?
- bmacho 3y agoNo, Russel's paradox and the Law of the Excluded Middle have not much to do with each other. (It is not easy to prove such a negative statement, but I googled them together, and found absolutely nothing.)
- nine_k 3y agoBoth the Russell's paradox and the Curry's paradox (yes, by Haskell Curry) are built on referencing a rule from itself, on breaking the contextual nesting. In a sense, it's like using `goto` to jump inside a loop, thus breaking the loop invariant. Practically all other paradoxes can be reduced to one of these two.