wnoise 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.
How do you mean bisimulation in this case? This seems to be a reduction down to decidable predicates, e.g. a Turing machine for each set. Without a type theory, many obvious algorithms will fail to converge.