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Article 1504 of comp.ai.philosophy:
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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: rec.arts.books,sci.philosophy.tech,comp.ai.philosophy
Subject: Re: Putnam again
Summary: a summary
Message-ID: <1991Nov22.154821.5774@husc3.harvard.edu>
Date: 22 Nov 91 20:48:16 GMT
Article-I.D.: husc3.1991Nov22.154821.5774
References: <5655@skye.ed.ac.uk>
Organization: Dada
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Nntp-Posting-Host: zariski.harvard.edu

In article <5655@skye.ed.ac.uk> 
jeff@aiai.UUCP (Jeff Dalton) writes:

>In article <1991Nov17.190935.5546@husc3.harvard.edu> 
zeleny@brauer.harvard.edu (Mikhail Zeleny) writes:

MZ:
>>                        It's well known that classical model-theoretic
>>semantics is incapable of fully characterizing reference; hence it is
>>incapable of sufficiently constraining any derived operational criteria
>>that purport to implement what you call the ``AI notion of success of
>>reference''.  (See e.g. an overview in Lakoff's ``Women, Fire, and
>>Dangerous Things'', chapter 15.)

JD:
>This is, of course, a ref to Putnam's argument.  I hope the Putnam
>thread has not died.  I sent something explaining my " Putnam has _an_
>answer to the "cats and cherries" argument", but that's the last I've
>seen.

My fault: I've been ill, and had to miss Putnam's seminar twice;
furthermore, having been involved in a shooting war with strong AI
fanatics, I haven't had time to participate in a reasoned discussion...
Excuses, excuses...

JD:
>I've received e-mail on that posting and apologize for not
>replying.  There's been trouble with the UK internet link,
>and I didn't want to add to the backlog (or have my message
>get lost).

Please duplicate to my e-mail address, and I'll do likewise.

JD:
>I raised two issues:
>
>1. If Putnam's argument is correct, how does he think we all end
>   up using more or less the same language, with the same references?
>   Or does he think we might be using widely differing reference
>   relations? 

I really can't speak for Putnam, as my use of his argument represents a
metaphysical realist d\'etournement, with whose conclusions he most
certainly would disagree.  Note that when he says that metaphysical realism
is incoherent, he means merely that it contradicts his intuition.  Since I
have my own intuition to contend with, I hope you would excuse me for not
paying heed to someone else's.

JD:
>2. If it were possible for people to use very different reference
>   relations without it being detectable, isn't it much more likely
>   that they'd use relations where the difference could be detected
>   in some cases but not in others.

I don't think that Putnam, or, for that matter, anyone else actively
involved in professional discussion of semantical issues, is actually
suggesting that such variation in reference occurs in practice; on the
other hand, how to explain such referential stability is an open question.
It appears that the Frege-Church theory is the only one among presently
known approaches to the problem of reference, that is capable of adequately
addressing the issue of stability of reference.  The problem is, how to
give a theory of mind that would explain our cognitive grasp of infinite
hierarchies of intensions.  I believe that I have an approach to this
problem, based on Spinoza's double aspect theory.

>Re 2 I received mail suggesting that people often do use different
>reference relations.  I think it is the case that people often 
>use different meanings for words, but this doesn't seem to happen
>for words like dog, cat, mat, etc.  The differences there are
>fairly minor, but why?  Why do we (almost?) never encounter someone
>who uses "cat" to refer to cherry?

Why indeed.

>-- jeff

I include a summary of my position on this issue.

In setting up model-theoretic semantics we are motivated by a desire to
explain the name relation; thus none can be assumed to hold a priori, but
must be substantiated on semantical grounds alone.  Now, Davidson's
model-theoretic semantics takes the set of sentences as the framework
against which we are modeling everything; the meaning of the said sentences
is taken as the set of their truth-conditions.  Whence, not surprisingly,
Putnam's result; question is, does it succeed beyond refuting his own
extensionalist preferences?  Given that the argument estabilishes that
truth-conditions are not sufficient to fix the meanings of predicates and
individual constants in the model, it seems that the most reasonable course
of action consists in adopting an intensional (i.e. Fregean) theory of
meaning; yet Putnam dismisses such theories as incoherent with nary an
argument.  Since his dismissal is often based on an appeal to Quine's
objections to intensional entities, such as propositions and concepts, it's
relevant that the latter can be reconstrued to apply equally well to the
extensional ones, like truth-values and material objects that our noun
phrases refer to.  Yet Putnam is unwilling to abandon the notion of truth
and reference,\footnote{See ``Representation and Reality'', pp. 60ff.} and
so hedges his skepticism on a crucial point.

Let us examine some of his arguments.  The downward Skolem-L\"owenheim
theorem guarantees that any first-order theory that has a model, has a
model with a countable domain.  If the theory in question is interpreted as
stipulating the existence of higher infinity, this result can be seen as
guaranteeing the existence of non-standard models.  Putnam's argument in
``Models and Reality'' is no more than an observation of the existence of
non-standard models from a given model, which generalizes to a skeptical
argument about realist theories of meaning only at the cost of assuming
that all such theories must be concerned with first-order languages, to
which the Skolem-L\"owenheim theorem applies.  His theorem in ``Reason,
Truth and History'', on the other hand, has to do with the fact that
model-theoretic semantics doesn't uniquely determine the reference
relation, in the sense that, given a non-trivial interpretation $I$ of a
language $L$, a second interpretation may be constructed, which disagrees
with the first one, but makes the same sentences true in every possible
world as $I$ does. If we go the Davidsonian model theoretic route of truth
conditions as maps from sentences of theories to truth-values, and models
as maps from predicates and individuals to extensions, Putnam's argument
is, in effect, that there are more models than syntactical theories and
thus theories, construed as sets of sentences, do not uniquely determine
their models; furthermore, by using a Carnap-style possible worlds
interpretation of predicates, Putnam demonstrates the insufficiency of the
modal intensional individual-haecceitist (in the sense of Kaplan, of
allowing trans-world identity relations for individuals) semantics to the
task of uniquely characterizing the linguistic relation of denoting.
Likewise, it seems that once haecceitism is admitted at any finite level of
intensional entities, by allowing trans-world identity conditions for such,
the Putnam permutation trick can be performed on them, together with their
successive extensions.

To sum, if all we have in model-theoretic semantics is the truth conditions
for some sentences, then the reference of all terms and all predicates
remains to be determined; Putnam claims that this can't be done, as from
the standpoint of the model itself, both the individuals and the predicates
are fungible: they may, generally speaking, be permuted without affecting
the truth-values of the theory's statements.

There appear to be several ways to escape this predicament.  One of them
involves using a non-well-founded type theory: evidently, if no individuals
are admitted in our framework, there remains nothing to be permuted.  On
the other hand, if the class of individuals and elementary predicates is so
restricted that their identity no longer matters, Putnam's objection
becomes irrelevant.  For instance, if elementary particles are taken as
individuals, we may very well remain unconcerned with the success of
reference to each particular one of them, concerning ourselves instead with
reference to highly structured macroscopic entities, which, by virtue of
their varying structure, may prove permutation-resistant.

Leaving the speculative realm, we may observe that, given a more finely
individuated account than truth or necessity conditions on the level of
finite intensions, Putnam's skepticism loses its force.  Hence I conclude
that an adequate semantical theory must be both intensional and strongly
anti-haecceitist, such as Church's Logic of Sense and Denotation,
characterized as follows.  Taking an extensional formalized language
(Church uses his version of simple type theory, but other choices can
surely be made), we define a transfinite hierarchy of successive levels of
such languages, successively connected by concept relations of appropriate
types and levels.  For a given language, the terms of the first ascendant
language are interpreted as denoting the concepts of the objects denoted by
the terms of the original.  Algebraically speaking, the concept relation is
defined as a partial morphism with respect to the fundamental relations or
operations of the language, in this case the application of a function to
its argument (Church uses the Sch\"onfinkel rediction of $n$-ary functions
to singulary functions on $(n-1)$-ary functions, and so on); in other
words, any concept of a function is a function on concepts of the argument.
Moreover, it turns out that the morphism also respects all derived
relations, such as the ones occurring in the boolean lattice induced by the
naturally defined logical consequence relation (of containment) within eash
propositional type.  The net result is that each intensional type may
contain a number of concepts, related by the concept relation to a single
extension; while each of the languages in question obeys the axioms of
extensionality, this device allows to sneak intensionality back in,
represented as a possibility of estabilishing stronger identity conditions
on each ascendant level.  In fact, Church is fond of saying that he views
intensionality as a relative phenomenon conditioned by stronger identity
criteria: propositions vs.  truth-values, individual concepts vs.
individuals, and so on.

It seems evident that, given a model theory developed on the basis of this
structure, one that would assign a transfinite intension to each
individual, function, and predicate constant of the object language,
Putnam's permutation theorem wouldn't go through.  A side effect of this
approach is that meanings are construed as essentially infinite objects, as
should we arbitrarily terminate the intensional assignments at some finite
level of the hierarchy, the permutation trick could be replicated there.
In other words, this approach validates mathematically Frege's principle
that intensions determine extensions.  Furthermore, it can be proved
algebraically that it validates another traditional principle, that
extensions vary inversely with intensions.

Consider Davidson's argument in ``Theories of Meaning and Learnable
Languages''.  Notably, his finite learnability criteria seem to be required
by any equivalent of a finite-state automaton with finite memory.  Now, the
semantical structure of the language described above is not finitely
learnable in the Davidson sense (although not for the reasons given by
Davidson himself), insofar as it presupposes the grasp of an infinite
hierarchy of senses for each of the terms (at least if we interpret it in
accordance with Frege's principle that intension determines the extension,
and that, for each level of intensions, our cognitive grasp of the
lower-level semantical entities can be seen as dependent on that of higher,
more finely differentiated intensional level), observing that in the
intensional hierarchy, each intensional object is an extension of its
ascendant concepts. This consideration can be seen as bearing on the
possibility of success in the AI research.  For even under the operational
criteria, such as those stipulated by the Turing test, the success of the
AI enterprise will depend on the theoretical adequacy of the theory of
reference implemented by it.  As noted above, classical model-theoretic
semantics is incapable of fully characterizing reference;\footnote{Also see
an overview in Lakoff's ``Women, Fire, and Dangerous Things'', chapter 15.}
hence it is incapable of sufficiently constraining any derived operational
criteria that purport to implement the AI notion of success of reference.
Now, the alternative to model-theoretic semantics that I am advocating
above (the Frege-Church semantics) doesn't seem to lend itself to an
implementation, or even a representation, in finite-state automata.  Thus,
if I am right, AI projects are doomed to failure.


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