From: zeleny@husc10.harvard.edu (Michael Zeleny)
Newsgroups: sci.philosophy.tech,sci.logic
Subject: Re: Semantics of Set Theory
Date: 31 Dec 92 16:22:29 GMT
Organization: The Phallogocentric Cabal

In article <1992Dec28.190416.1204@guinness.idbsu.edu> 
holmes@opal.idbsu.edu (Randall Holmes) writes:

>I've sent a longer reply directly to Zeleny; anyone who would like to
>see it may request it from me (at holmes@math.idbsu.edu ; you may have
>trouble if you just hit the r key).

I am working on a point-by-point reply, which should be ready in a
couple of days, and will likewise make it available on request.

>I do not agree with Zeleny that quantification involves ontological
>commitment to the domain over which one is quantifying as a completed
>totality.  It merely involves commitment to each of the objects in the
>domain.  I'll admit that I am committed to an ontology including all
>of the quantification ranges, since there is only one, the universe,
>which is in fact an object!  But this involves taking unfair advantage
>of my NF advocacy; even from a ZFC standpoint, it can be observed that
>quantification ranges are not necessarily objects; they can be
>non-reified predicates, and they can be "referred to" using
>syntactical means.

I reiterate that an adequate semantical theory has no choice but to
recognize the reified ranges of quantification of its object language
as _bona fide_ objects.  It is not taking unfair advantage of
Randall's NF advocacy to indicate that a Quinean (cf. "On What There
Is") or, for that matter, Churchian (cf. "Ontological Commitment")
semanticist, who recognizes the maxim stipulating that each theory
carries an ontological commitment to its ranges of quantification, is
_ipso facto_ obligated, when scrutinizing his semantical theory,
including this very maxim, to extend his ontological commitment to
*its* ranges of quantification, comprised of theories and their
ranges.  This point is so simple and incontrovertible, that no further
elaboration ought to be necessary, and I can't help wondering why
Randall is unwilling to accept it.

>Proper classes are a practically very useful means to partially evade
>the impossibility of reifying all predicates.  Only as long as they
>are eliminable in principle in favor of discussion of syntactical
>objects are they actually fulfilling this function; as soon as one
>quntifies over them or admits super-classes, one has surreptitiously
>made the universe of objects larger and kicked the problems upstairs.
>But they do not go away.  It is not possible to reify all predicates;
>the only way to talk about predicates in full generality is
>syntactical, ugly as it is.  Predicates do not _in general_ function
>as names of objects; that's the point of the paradoxes.

Clearly, each of us sees a different point in the paradoxes.  I
maintain that all *well-formed* and *meaningful* predicates function
as names of objects (propositional forms).  Furthermore, I wonder
whether Randall recognizes any merit in NBG, which allows proper
classes within its ontology.

>Reference in one's own language is inscrutable to oneself; I think
>that the success or failure of the reference of our terms depends
>ultimately on factors external to us, and I see no reason to believe
>that we should have unrestricted access to our own semantics.

I do not understand this appeal to inscrutability; surely it is not
justified by anything claimed by Quine ("Ontological Relativity"), --
each Quinean native is perfectly capable of articulating the
disquotational scheme
	"Gavagai" refers to gavagai.  
If Quine argues that inscrutability of reference is not limited to the
cases of radical translation between different languages, and that "we
can reproduce the inscrutability of reference at home", he does so in
the context of analyzing the case of "homophonic translation" of his
neighbor's idiolect.  Surely this is a far cry from blithely claiming
that "reference in one's own language is inscrutable to oneself", --
one is generally not required to homophonically translate his own
idiolect.  Randall, I entreat you to abstain from non-standard
philosophical use of technical terms.

>-- 
>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."
Newsgroups: sci.philosophy.tech