AlephNeil comments on Less Wrong Rationality and Mainstream Philosophy - Less Wrong

106 Post author: lukeprog 20 March 2011 08:28PM

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Comment author: AlephNeil 27 March 2011 04:01:03AM *  0 points [-]

Unfortunately, Quine's theory was found to be inconsistent.

Quine's set theory NF has not been shown to be inconsistent. Neither has it been proven consistent, even relative to large cardinals. This is actually a famous open problem (by the standards of set theory...)

However, NFU (New Foundations with Urelements) is consistent relative to ZF.

Comment author: Perplexed 27 March 2011 05:49:29AM *  1 point [-]

Unfortunately, Quine's theory was found to be inconsistent.

Quine's set theory NF has not been shown to be inconsistent.

Quoting Wikipedia

The set theory of the 1940 first edition of Quine's Mathematical Logic married NF to the proper classes of NBG set theory, and included an axiom schema of unrestricted comprehension for proper classes. In 1942, J. Barkley Rosser proved that Quine's set theory was subject to the Burali-Forti paradox. Rosser's proof does not go through for NF(U). In 1950, Hao Wang showed how to amend Quine's axioms so as to avoid this problem, and Quine included the resulting axiomatization in the 1951 second and final edition of Mathematical Logic.

So I was wrong - the fix came only one decade later.

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