Comment author:cousin_it
04 May 2010 09:56:27PM
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1 point
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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.
Isn't "the set of all sets" (SAS) ill-defined? Suppose we consider it to be for some set A (maybe the set of all atoms) the infinite regression of power sets SAS = P(P(P(P....(A)))...)
In which case SAS = P(SAS) by Cantor-like arguments?
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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.
Isn't "the set of all sets" (SAS) ill-defined? Suppose we consider it to be for some set A (maybe the set of all atoms) the infinite regression of power sets SAS = P(P(P(P....(A)))...)
In which case SAS = P(SAS) by Cantor-like arguments?
And Russell's paradox goes away?