[FOM] About Paradox Theory

Vaughan Pratt pratt at cs.stanford.edu
Thu Sep 15 21:45:27 EDT 2011

On 9/14/2011 1:03 PM, charlie wrote:
> 	I'm sure your project has merit, but I can never overcome "Russell's Paradox" because of the following theorem of  first-order logic.
> 	   ~EyAx[F(xy)<-->  ~F(xx)]
> 	       As a consequence, I tend to dismiss R's Paradox as having nothing to do with sets

This theorem holds in a Boolean topos, but I don't know how much further 
you can take it than that, those better grounded in category theory 
should be able to say.  The theorem is set-theoretic to the extent that 
the category Set is the canonical Boolean topos, so I don't think it's 
fair to say it has nothing to do with sets.

In less categorical language, the semantics with which you give this 
sentence meaning is set-theoretic.

Vaughan Pratt

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