[FOM] About Paradox Theory
marcel.crabbe at uclouvain.be
marcel.crabbe at uclouvain.be
Mon Sep 19 04:11:05 EDT 2011
The argument doesn't even require equality; e.g. the axiom of singletons can be replaced by:
AyEzAx(F(xz) <--> F(xy) & F(yx))
Marcel Crabbé
Le 19 sept. 2011 à 02:22, hdeutsch at ilstu.edu a écrit :
>
> 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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