Mitchell_Porter comments on But Somebody Would Have Noticed - Less Wrong
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As it happens, I am currently in "somebody would have noticed" territory. About a week ago I abruptly switched to believing that Russell's paradox doesn't actually prove anything, and that good old naive set theory with a "set of all sets" can be made to work without contradictions. (It does seem to require a weird notion of equality for self-referring sets instead of the usual extensionality, but not much more.) Sorry to say, my math education hasn't yet helped me snap out of crackpot mode, so if anybody here could help me I'd much appreciate it.
So, is the set of all sets that aren't members of themselves, a member of itself, or not?
Insufficient data to answer your question :-) See my reply to Sniffnoy.