RichardKennaway 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.
I am seeing substantial amounts of both sense and nonsense in this thread. I suggest that anyone who wants to talk about set theory first learn what it is.
The Wikipedia article is somewhat wordy (i.e. made of words, rather than mathematics), and Mathworld is unusably fragmented. The Stanford Encyclopedia is good, but for anyone seriously interested I would suggest a book such as Devlin's "The Joy of Sets".