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In article <1992Dec30.184028.2949@guinness.idbsu.edu>
holmes@opal.idbsu.edu (Randall Holmes) writes:

>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.

MZ:
>>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.

MZ:
>>Correct.  Stratification is a purely syntactical trick.  Rage away,
>>Randall.

RH:
>For Quine, it was; for me, it is not.

So you have said on a number of occasions; alas, your claim remains
unsupported by anything more convincing than your personal
authoritativeness.  I see no help forthcoming from Forster's book,
either.

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?)

MZ:
>>A predicate is meaningful, if and only if it expresses a property.

(in whatever manner it happens to do so)

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.

MZ:
>>Well, that depends.  I suggested two interpretations of Grelling's
>>paradox.  A purely syntactical one is blocked by stratification;

RH:
>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.

Natural languages appear to have all the syntactical strength required
for generating such paradoxes; which is why I am favoring semanticsal
resolutions in all instances.  In any case, as Montague was known to
say, syntax is not interesting, except as a prolegomenon to semantics.

MZ:
>>								     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.

RH:
>Precisely!

Randall, you freely agree with something I said?  I am flabbergasted!

>>>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

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