[FOM] About Paradox Theory

[Vaughan Pratt]

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