🚀 go-pugleaf

In article <1992Dec29.114844.18880@husc3.harvard.edu> zeleny@husc10.harvard.edu (Michael Zeleny) writes:
>In article <1hpqgkINNmi6@cat.cis.Brown.EDU> 
>PL436000@brownvm.brown.edu (Jamie) writes:
>
>>>From: zeleny@husc10.harvard.edu (Michael Zeleny)
>>>PL436000@brownvm.brown.edu (Jamie) writes:
>
>J:
>>>>But, I don't understand how using unreified predicates instead of
>>>>objects helps avoid set theoretic paradoxes. Grelling's paradox
>>>>uses only a predicate, and (unless I'm very confused) does not
>>>>require reification.
>
>MZ:
>>>You are very confused.  If Grelling's paradox is regarded as purely
>>>syntactical, then it is unproblematic on a Quinian view that requires
>>>stratification (as spurious as such a requirement might be); if, on
>>>the other hand, it is regarded as semantical, then the contradiction
>>>depends on the assumption that the predicate "...is heterological"
>>>expresses a _bona fide_ property.
>
>J:
>>Well, if I was confused before, I am more confused now.
>
>You have my sympathies.
>
>J:
>>First of all, if a view (Quinean or otherwise) requires stratification
>>to deal with a purely syntactical predicate, then the issue of
>>reification is not the salient one. Stratification is a strategy
>>for eliminating the paradoxes whether the predicates are reified or not.
>
>Correct.  Stratification is a purely syntactical trick.  Rage away,
>Randall.

For Quine, it was; for me, it is not.

>
>J:
>>Second, I have no idea whether "is heterological" expresses a bona
>>fide property. I care only that whether it is a meaningful predicate.
>>(What would it express if not a bona fide property? A trope?)
>
>A predicate is meaningful, if and only if it expresses a property.
>
>J:
>>My point was that the Grelling paradox doesn't depend on any
>>quantification over properties, nor on a semantics that
>>assigns objects to predicates. It's solution is (must be)
>>independent of the question of reification.
>
>Well, that depends.  I suggested two interpretations of Grelling's
>paradox.  A purely syntactical one is blocked by stratification;

I think the analysis of the syntactical version of the paradox can be
exactly the same in NFU as in the usual set theory; I have proposed a
way to use stratification to avoid the paradox, but it isn't necessary
unless one is trying to pack a lot of strength into the language one
is using.

 on
>the other hand, the semantical one does not get off the ground, until
>and unless one comes up with a semantics that assigns a predicate
>object to the adjective `heterological'.  So there you are.

Precisely!

>
>>Jamie
>
>cordially,
>mikhail zeleny@husc.harvard.edu
>"Le cul des femmes est monotone comme l'esprit des hommes."



-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu