From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!uwm.edu!ogicse!das.harvard.edu!husc-news.harvard.edu!zariski!zeleny Thu Dec 26 23:57:53 EST 1991
Article 2344 of comp.ai.philosophy:
Xref: newshub.ccs.yorku.ca comp.ai.philosophy:2344 sci.philosophy.tech:1559 sci.philosophy.meta:890
Path: newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!uwm.edu!ogicse!das.harvard.edu!husc-news.harvard.edu!zariski!zeleny
>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech,sci.philosophy.meta
Subject: Re: The Return of the Son of the Flame-Free Putnam Thread
Summary: an elaboration of earlier claims
Keywords: intension vs. extension, the name relation, model theory
Message-ID: <1991Dec21.015234.6837@husc3.harvard.edu>
Date: 21 Dec 91 06:52:32 GMT
Article-I.D.: husc3.1991Dec21.015234.6837
References: <1991Dec18.200619.29195@cs.yale.edu> <1991Dec20.134023.6825@husc3.harvard.edu> <1991Dec20.221220.26233@milton.u.washington.edu>
Organization: Dept. of Math, Harvard Univ.
Lines: 126
Nntp-Posting-Host: zariski.harvard.edu

In article <1991Dec20.221220.26233@milton.u.washington.edu> 
forbis@milton.u.washington.edu (Gary Forbis) writes:

>An explanation by way of a complaint and a very brief comment.

>In article <1991Dec20.134023.6825@husc3.harvard.edu> 
>zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:

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

MZ:
>>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.

GF:
>Don't get me wrong.  I know there are times talking is such shorthand helps
>cut the number of words used but when you do so make it very hard for untrained
>but (self-proclaimed) intelligent people like me to understand what you mean.
>Though I have followed this room from the start I haven't grasped all of
>the points made.  I do not have photographic memory so do not remember stuff
>which I have not grasped due to esoteric verbage.  If I latter grasp the 
>concepts I may refer to them and it gets annoying to be told this stuff was
>completely explained some months ago and does not bear repeating.

OK, I'll try to elaborate, but won't promise easy going.  Extensionality is
one of those things that are easy to talk about, but hard to define.  In
effect, when we say that a given theory is extensional, we are comparing it
to some other theory which makes finer distinctions between objects in its
universe of discourse.  For instance, we might regard propositions, as do
modal logicians, not only as true or false, but also as necessarily true,
contingently true, contingently false (i.e. possibly true, though actually
false), necessarily false, and so on.  On the other hand, classical
extensional logic recognizes only true and false propositions, not
differentiating between necessary ant contingent truths, and so on.  We say
that modal logic is intensional with respect to truth-functional logic,
simply because the former stipulates stronger identity conditions on the
fundamental relation of logical equivalence.  Likewise, set theory is said
to be extensional, because sets are individuated solely by their membership
conditions, rather than, as properties, by the specific nature of their
membership criteria: we say that the property of being an even prime is
non-identical with the property of being a positive square root of 4, even
though both properties characterize the same set.  An extensional language
is one that respects certain weak identity criteria: if based on a set
theory, it must stipulate the identity of two sets with the same members;
if based on a type theory, it must stipulate the identity of two functions
with the same course of values.

Mathematicians love extensionality, because it makes the things simpler.
Alas, Putnam's paradox destroys extensional semantics as we know it:
truth-functional identity conditions are simply insufficient for fixing the
name relation.  The only resolution preserving the axioms of extensionality
that I can see involves smuggling intensionality through the back door by
relating each object to an indeterminate number of intensional concepts
thereof via a fundamental partial morphism, called the reality relation
(the relation needs be partial, since we regard the reality of an object
falling under any given concept a wholly contingent matter); this is
tantamount to the adoption of a Churchian transfinite intensional hierarchy
of extensional languages, explained by me elsewhere, the first level of
which is comparable to the Carnap and Montague systems of intensional
semantics in their entirety (see Carnap's "Meaning and Necessity", and any
generic introduction to Montague semantics).
 
DMD:
>>>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.

MZ:
>>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?

GF:
>I'm not sure you can refer to "empirically and introspectively observable"
>facts at the same time.  Before you refer to empirical facts about George Bush
>you must assume a causal link.  Introspectively observable facts don't give
>you the right to assume such causal links.  I'm sure you could snow me by
>refering to some theorem by name.  It is up to you to decide if such is
>more important than communicating.  If communicating isn't important then
>please feel free to ignore this without response.

I see no reason to assume that introspection is fundamentally different
from sensory perception in the nature of causal links existing between the
respective objects and the subject thereof.  To put it differently, I see
my warrant for assuming that the number 2 exists to be fundamentally
similar to one for assuming that you exist.  This is a view dating back at
least to Plato, and however bizarre it might appear to some bystanders, I
would humbly request them to review some of the relevant literature, e.g.
by perusing "The Encyclopedia of Philosophy", before denouncing me as a
loony.  I may very well be a loony, but not simply because I believe in the
existence and causal powers of abstract objects like numbers.

>--gary forbis 

N.B.  It took me forty minutes to write the above (I don't touch-type).
Since you have repeatedly demonstrated good faith in conducting this
discussion, I am happy to do my part.  Unfortunately, my semester is about
to end, I have six or seven papers due, and my time is limited.  Please try
to forgive my telegraphic style in the future.

regards,
mz

`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'
: Qu'est-ce qui est bien?  Qu'est-ce qui est laid?         Harvard   :
: Qu'est-ce qui est grand, fort, faible...                 doesn't   :
: Connais pas! Connais pas!                                 think    :
:                                                             so     :
: Mikhail Zeleny                                                     :
: 872 Massachusetts Ave., Apt. 707                                   :
: Cambridge, Massachusetts 02139           (617) 661-8151            :
: email zeleny@zariski.harvard.edu or zeleny@HUMA1.BITNET            :
:                                                                    :
'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`


