[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
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