[FOM] About Paradox Theory
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.
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