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Article 2316 of comp.ai.philosophy:
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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech,sci.philosophy.meta
Subject: The Return of the Son of the Flame-Free Putnam Thread (was re: Virtual Person?)
Summary: what's wrong with this picture?
Keywords: intension vs. extension, the name relation, model theory
Message-ID: <1991Dec20.134023.6825@husc3.harvard.edu>
Date: 20 Dec 91 18:40:19 GMT
References: <1991Dec16.181202.526@cs.yale.edu> <1991Dec16.163345.6653@husc3.harvard.edu> <1991Dec18.200619.29195@cs.yale.edu>
Organization: Dept. of Math, Harvard Univ.
Lines: 151
Nntp-Posting-Host: zariski.harvard.edu

In article <1991Dec18.200619.29195@cs.yale.edu> 
mcdermott-drew@CS.YALE.EDU (Drew McDermott) writes:

>In article <1991Dec16.163345.6653@husc3.harvard.edu> 
>zeleny@brauer.harvard.edu (Mikhail Zeleny) writes:

MZ:
>  I see I'll have to drive the truth home.  A conclusive refutation of your
>  ludicrous semantic claims was made long before your birth in the work of
>  L\"owenheim, Skolem, G\"odel, Tarski, and Church.  I have argued along the
>  realist lines,responding to well-known model-theoretic results of Putnam,
>  for about two months.

DMD:
>I think Putnam has gotten off too easy so far.  Let me recap the
>theorem that I think is under discussion.  Suppose we have a theory
>with an interpretation "J" which assigns referents to symbols and
>predicates in the usual way.  So J("George Bush")= George Bush.  The
>interpretation comes with a universe U of individuals (I could be
>more formal here, but I'd rather not); George Bush is an example
>element of U.  Now take an arbitrary permutation T of U.  T(u)= some v
>in U for every u in U, T is one-to-one, etc.  We can produce a new
>interpretation J' of the same theory, such that J'(a)=T(J(a)).  We can
>extend this interpretation to predicates in the obvious way.  If J(P)
>is a relation R, let J'(P) be the relation R' such that R'(T(u),T(v))
>iff R(u,v).  For example, let T map George Bush into Barbara Bush, and
>Barbara Bush into the Eiffel Tower.  If J(Loves) contains the ordered
>pair <George Bush, Barbara Bush>, then let J'(Loves) contain <Barbara
>Bush, Eiffel Tower>.
>
>I hope it doesn't come as a big surprise that J' makes true exactly
>the same sentences that J does.  If George loves Barbara, then J makes
>the sentence "Loves(George Bush, Barbara Bush)" true, and J' does,
>too, and contrariwise if it makes the sentence false.  If we start
>with a set of axioms, then J' is a model of them if and only J is.  

This is essentially correct.

DMD:
>This is so obvious that most introductory model-theory books wouldn't
>even bother to make it an exercise.  Any mathematician would
>immediately switch to the more interesting question, Does the theory
>have two nonisomorphic models?  And soon enough we would get to the
>Skolem-L\"owenheim theorem, which is quite interesting.  So the only
>issue raised by Putnam's "theorem" is why he attached any importance
>to it.  The only answer I can come up with is that people like Putnam,
>Davidson, and (I suppose) Tarski really did suppose that formal
>semantics explains what it is that people know when they know the
>meanings of symbols.  That is, I think they believed that a person
>could have an "intended model" of a set of axioms; that someone could
>"grasp the intended referent" of a symbol.  Putnam's result is an
>acknowledgement that this whole picture makes no sense.  As far as
>purely formal semantics goes, you really can take your pick as to
>whether the symbol "George Bush" refers to the person George Bush (as
>in model J), or to Barbara (as in J'), or the Eiffel Tower, or the
>North Pole, provided that when you fool with the referents of the
>names, you're willing to fool with the referents of the predicates.  I
>see all this as more of a "mea culpa" by Putnam than a theorem.

The result is indeed mathematically trivial, but nevertheless important as
a consideration bearing on the adequacy of Davidson's approach to semantics
(don't mix Tarski in with the crowd; his sole concern was giving an account
of the semantic notion of truth).  Furthermore, the permutation trick can
be performed on any level of any purely extensional Montagovian intension,
i.e. any intension construed as a function (viewed as identical with its
own course of values) from indices (i.e. ordered pairs of possible world --
time coordinates) to extensions. [See the definitions in Dowty, Wall, and
Peters, "Introduction to Montague Semantics", pp. 131, 144--5.]  In other
words, Putnam's paradox destroys extensionality as we know it.  The only
extensional resolution I can see involves the adoption of a Churchian
transfinite intensional hierarchy of extensional languages, the first level
of which is comparable to the Carnap and Montague systems in their entirety.

DMD:
>Don't get me wrong.  I like formal semantics.  When doing knowledge
>representation, it is often helpful to ask the question, *Could* the
>real world be a model of this theory?  It's just crazy to suppose that
>you could ever get back the answer that the real world is the *only*
>model.  And formal semantics sheds little light on how a creature
>living in the same world with George Bush could come to manipulate
>symbols that refer to him.  Presumably explaining how that happens
>would require following causal chains that take us out of the realm of
>model theory.

The real question is of a wholly different nature: how can we explain the
empirically and introspectively observable fact that a creature living in
the same world with George Bush succeeds in manipulating symbols that refer
to him, given that it is manifestly incapable of following the causal
chains connecting the token `George Bush' with the current President of the
United States?

DMD:
>By the way, Zeleny's article on Putnam of November 22 is better than
>most Zelenyana.  (It lays ideas on the table rather than just ranking
>his opponents as lower than bacteria on the scale of philosophical
>wisdom.)

As you can see, when my opponents manifest any philosophical wisdom, 
I answer in kind.  

By the way, where's your argument? what's wrong with my picture? 

DMD:
>          His proposal (I'm probably not doing it justice) is to fix
>Putnam's problem by providing a meta-theory that stipulates that the
>first theory is to have only the intended model.  Since the new theory
>would have the same problem as the first, we have to provide another
>theory to constrain that one, and so on. 

Not quite.  No meta-languages are involved; Church-intensionality, in
effect, offers the possibility of stipulating arbitrarily strong concept
identity conditions by ascending to an appropriately remote level of the
concept hierarchy, all the while retaining the axioms of extensionality at
each particular level thereof.  Note that the same model-disambiguating
effect could be accomplished by taking the relation of extension (rather
than that of concept) as non-well-founded: just stipulate that the world is
bereft of logical individuals, everything in it being a non-empty set.
Either way, the Axiom of Foundation has to go, if not for concepts, then
for individuals.

DMD:
>                                          Turtles all the way up.

In fact, as in the original, the hierarchy extends downwards, as the
relation of metaphysical dependence is taken as the extensional object
being determined, however contingently with respect to existence (this
stipulation is needed in order to avoid Anselm's error in the Ontological
Proof) by its intensional concepts.  Indeed, my subject is cheloniology,
dedicated to the study of the turtle hierarchy, and its mathematical
structure.  For the folklorically impaired, here's the full story:

The sage announces that the world rests on a giant turtle.  ``What supports
the turtle?'' asks a child.  ``Another turtle,'' answers the sage.  ``And
that one?'' insists the child. ``Yet another turtle,'' says the sage. ``And
I suppose you are going to tell me that it is standing on a turtle as
well,'' says the child testily.  ``Yes,'' answers the sage patiently.
``It's turtles all the way down.''

>                                             -- Drew McDermott

`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'
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: Connais pas! Connais pas!                                 think    :
:                                                             so     :
: Mikhail Zeleny                                                     :
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