[FOM] About Paradox Theory

hdeutsch at ilstu.edu hdeutsch at ilstu.edu
Sun Sep 18 20:22:32 EDT 2011

I agree that the nonexistence of the class of grounded classes is not  
a theorem of FOL.  But I hesitate to agree that it requires  
specifically set theoretic premises.  The only required premise is  
AyEzAx[F(xz) <--> x = y] and as Vaughan Pratt mentioned, the argument  
does not even assume extensionality.  I must confess, though, I'm not  
sure what is at stake here.  Perhaps one should just say that the most  
significant application of the relevant reasoning is in set theory.

Harry Deutsch

Quoting Vaughan Pratt <pratt at cs.stanford.edu>:

> Think of "transitive closure" as a taboo term in the language of  
> FOL. Just because a term is taboo doesn't mean you can't work with  
> it.  This is true of various terms arising not just in logic but  
> personal relationships, divinity, etc.
> Vaughan Pratt
> On 9/17/2011 10:38 AM, David Auerbach wrote:
>> Might it be that it is full generalization of the paradox (to chains
>> of any length) that isn't first-orderizable, even though there's a
>> first-order version for each length? And that that's what T. Forster
>> meant?
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