From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: Semantics of Set Theory
Organization: Boise State University
Date: Thu, 31 Dec 1992 19:47:03 GMT

In article <1992Dec31.112231.18915@husc3.harvard.edu> zeleny@husc10.harvard.edu (Michael Zeleny) writes:
>In article <1992Dec28.190416.1204@guinness.idbsu.edu> 
>holmes@opal.idbsu.edu (Randall Holmes) writes:

[...]

>
>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.

The point is simple and incontrovertible if I admit that my complete
working theory has a semantics in this sense; I don't.  Only theories
whose domains and all predicates and relations of which are sets have
semantics in this sense.  Any interpretation of NFU or ZFC which has
semantics in this sense is an unintended interpretation.  This is a
technical sense of "having semantics"; certainly terms of either
theory refer to objects in the world and sentences of either theory
make assertions about the world.

[...]

>
>>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.

What I mean is nothing more profound than that our reference relation
cannot be expressed in our own language (a standard result along the
lines of Tarski).  Certainly fragments of it can be so expressed; I
can say that "this hat" refers to this hat, but the meaning of
"refers" here must have some restriction.  I don't think this is
nonstandard; Quine makes similar points.  You really must not assume
that I am a follower of Quine.  I often agree with him; I have taken
relatively little directly from him.

>
>>-- 
>>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."


-- 
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
Newsgroups: sci.philosophy.tech