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Article 2250 of comp.ai.philosophy:
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>From: mcdermott-drew@CS.YALE.EDU (Drew McDermott)
Subject: Re: Virtual Person? (was re: Searle and the Chine
Message-ID: <1991Dec18.200619.29195@cs.yale.edu>
Summary: More ludicrous semantic claims
Keywords: personal identity
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References: <1991Dec15.023122.6582@husc3.harvard.edu> <1991Dec16.181202.526@cs.yale.edu> <1991Dec16.163345.6653@husc3.harvard.edu>
Date: Wed, 18 Dec 1991 20:06:19 GMT
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In article <1991Dec16.163345.6653@husc3.harvard.edu> zeleny@brauer.harvard.edu (Mikhail Zeleny) writes:

  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.

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 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.

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.

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.)  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.  Turtles all the way up.

                                             -- Drew McDermott


