From: holmes@garnet.idbsu.edu (Randall Holmes)
Subject: Re: Extensionalism (was re: Russell's Paradox)
Organization: Boise State University
Date: Fri, 6 Nov 1992 22:56:50 GMT

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).

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.

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.

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.  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.  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".

	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.

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

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




-- 
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.meta