[FOM] truth and consistency

Charles Parsons parsons2 at fas.harvard.edu
Sun Jun 1 15:06:25 EDT 2003

At 11:42 AM -0700 6/1/03, Martin Davis wrote:
>Charles is right that I overstated the case, but in my defense I 
>should remark that the great bulk of ordinary mathematics uses only 
>a very limited part of ZFC, in fact a good deal less even than the 
>original Zermelo axioms. Tony Martin's proof of determinacy  for 
>Borel sets is notable for actually requiring omega levels of the 
>hierarchy. So classical mathematics can't really be invoked in favor 
>of the consistency of full ZF.

True enough. I was thinking not just of "ordinary" or "classical" 
mathematics but also Cantorian and subsequent set theory.



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