[FOM] About Paradox Theory

T.Forster at dpmms.cam.ac.uk T.Forster at dpmms.cam.ac.uk
Fri Sep 16 15:55:06 EDT 2011

Vaughan, Agreed, but how then *would* you characterise the difference 
between Russell's paradox and other indisputably set-theoretic paradoxes 
such as Mirimanoff? Charlie has pointed to *something*. what do you want to 
say about that something?

On Sep 16 2011, Vaughan Pratt wrote:

>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
>FOM mailing list
>FOM at cs.nyu.edu

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