From: zeleny@scws7.harvard.edu (Michael Zeleny)
Newsgroups: sci.philosophy.meta,sci.logic
Subject: Re: Extensionalism (was re: Russell's Paradox)
Date: 7 Nov 92 06:12:05 GMT
Article-I.D.: husc3.1992Nov7.011207.17190
Organization: The Phallogocentric Cabal

In article <1992Nov6.225650.18651@guinness.idbsu.edu>
holmes@garnet.idbsu.edu (Randall Holmes) writes:

>I agree that a modal operator acting like "belief" for a sort of ideal
>reasoner (for whom deduction is free of charge) can be studied.  But
>it does not apply to belief properly so called.  For one thing,
>deduction is not free (it takes work).

Specialized use of language has been the rule of philosophical
discourse for 2.5 millenia.  Read some decision theory, where belief
is quite properly so called.

>The intrinsic nature of the True and the False plays no role in their
>use; any two objects can be used as the referents of sentences, the
>only requirement being that they be different.

By the same reasoning, any unique referent will do for a singular term
like `Randall Holmes'.  I think this is false, as distinguished from
being true.

>Truth is to a certain extent a matter of convention; it is a property
>of sentences, whose meanings are certainly a matter of convention in
>some sense.  But once the conventions are set up, the actual facts of
>reality impose themselves.

So far, this is quite unexceptionable.

>All of this is bound up with the issue of reference.  I don't think
>that the reference of our terms (or sentences) is actually accessible
>to us; from a standpoint from which it was accessible, I do not think
>that there is a unique account of it.  By this, I do not mean that we
>do not know the reference of _any_ of our terms; I mean that we are
>not acquainted with the relation "term t means object x" as an
>abstract object; we cannot refer to it or define it.

And yet, you have just referred to it, stopping but a little short of
making a definition.

>						      We know the
>reference of some of our terms, we cannot know the reference of some
>others exactly, and it is not necessary or useful for us to know too
>much about the reference of some of them, although we could establish
>it by fiat.  In the case of the True and the False, the only thing
>that an account of our reference to them usually requires is that the
>two objects be different; so there is an adequate account of our
>reference to the True and the False whereby the True is the Great
>Pyramid and the False is Napoleon; there is also an equally good
>account in which the roles of the two are exactly reversed.  

I shall remain content with allowing the intuitive merits of this
picture to speak for themselves.

>							      Of
>course, we may decide to explicitly identify the True with the number
>2 and the False with the number 1; in this case, we have more
>commitments as to which objects they are.  But in any event, once an
>account of reference is set up, it remains stable; the frames of
>reference cannot be mixed.  Even in the case indicated, my attitude
>(without the capabilities of the outside observer) toward the
>proposition "Napoleon = the False" would be that it was rather silly
>(by which I mean that I would not really _care_).  By the way, this is
>my understanding of "type"; it has to do with the presence or absence
>of criteria visible to me for determining whether the objects are the
>same.  In the case of Napoleon and the False, I do not need to know
>whether they are identical or different; there are adequate accounts
>of the reference of my terms in which Napoleon = the False and in
>which Napoleon # the False.  Thus, they are of different types.  But
>this does not mean that the question "Is Napoleon the False?" does not
>have an answer; it means that I don't care what the answer is,
>basically because the reference of "the False" is not "nailed down" at
>all; it just has to be different from the reference of "the True".

I see you have done your homework: these are Quine's views on
reference.  Would you mind explaining just what it is that makes you
*not* a Quinean pragmatist?

>	Similarly with various definitions of the natural numbers;
>both Church's and Frege's accounts of the natural numbers are
>"natural" in different contexts.  I cannot decide what the "real"
>reference of the numbers of ordinary speech is, though; it is not
>"determined" by the way we use them, although it is possible to give
>adequate accounts of the reference of ordinary speech in which the
>number words will refer to either kind of number (it is easier to do
>this for Frege's numbers).  3 might be the Great Pyramid in another
>account, though.

If, as is implied above, you think that the sole determining factor of
reference is use, then you *are* committed to being a pragmatist. 

>	The semantic paradoxes make it clear that a language cannot
>talk about the reference of its own terms with full competence.

Use a metalanguage then.

>Suppose it could; then we look at all substitution contexts "P(x)"
>(considered as quoted objects) and define the substitution context
>"the number 2 if the referent of the term produced by substituting x
>for "x" in x is nonexistent or something other than 2, otherwise the
>number 1".  Abbreviate this by "Q(x)" and consider the results of
>putting in "Q(x)" for x in "Q(x)".  We cannot have the ability to
>refer to our own reference relation freely [consider what this
>sentence says about itself -- Aieee!].

Read more Tarski.

>				        A language can give limited
>accounts of the reference of its terms (of "meaning") (I think this is
>what Church's system does, but I will have to look at that paper
>again) just as it can give limited accounts of "truth", but the
>paradoxes forbid an adequate account of the reference of the terms or
>sentences of a language from the inside.

I shall be looking forward to hearing more about your estimation of
Church's Logic of Sense and Denotation, which in my considered opinion
gives lie to your assertions of inscrutability of reference.  Keep in
mind that your objections will presumably be addressed by the ramified
version of Church's language, which is forthcoming in his latest
article, to be published in _Nous_.  The relative merits of Russellian
ramification and Tarskian object language versus metalanguage
distinction are discussed in Church's 1975 JSL article.

>	My argument for the reasonableness of NFU as a set theory
>depends on similar considerations.

				   ...and fails for the same reasons.

>-- 
>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
" -- I shall speak bluntly, because life is short."
Newsgroups: sci.philosophy.meta