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Article 3573 of comp.ai.philosophy:
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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.meta
Subject: Re: Intelligence Testing
Message-ID: <1992Feb7.073841.8573@husc3.harvard.edu>
Date: 7 Feb 92 12:38:38 GMT
References: <12351@optima.cs.arizona.edu> <1992Feb5.204750.21898@midway.uchicago.edu> <1992Feb6.214010.14199@aio.jsc.nasa.gov>
Organization: Dept. of Math, Harvard Univ.
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In article <1992Feb6.214010.14199@aio.jsc.nasa.gov> 
dlyndes@deltahp.jsc.nasa.gov writes:

>In article <1992Feb5.204750.21898@midway.uchicago.edu>
>gross@befvax.uchicago.edu writes:

LG:
>|> The different philosophies of mathematics only arise when people start
>|> asking what mathematical statements mean.  The various theories are
>|> a result of their own theories of meaning.  
>|> 
>|> If we followed Wittgenstein's account of meaning about mathematics,
>|> we would avoid this whole discussion.
>|> 
>|> In a chess game, we ask whether a 'checkmate in 3 moves' exists.
>|> Somehow, there aren't any philosophical problems here.  We can talk
>|> about the existence of 'abstract objects' without being platonists
>|> or having any metaphysical views at all.

I find the last sentence wholly incoherent in its meaning; as for its
predecessors, it has been my understanding that the chess - mathematics
analogy has been put to sleep by Frege.  Alas, a good fallacy like that
just has to rear its ugly head in every generation.

DL:
>I do not see how Wittgenstein's theories would allow us to avoid
>the whole problem.  Giving a name to a problem does not solve it.  All
>Wittgenstein did was to give the problem a name ("Language Game") and
>declared the problem solved.

Quite so.

DL:
>But the problem remains: namely
>
>(1) platonism explains mathematical ontology and truth quite nicely but
>    fails to explain its utility and epistemology, while

This is hardly a problem, provided that one is serious about the causal
role of the Forms.  Epistemology and pragmatics haunt half-baked Platonists
only; the truly insane among us find that there's nothing wrong with
anamnesis, let alone the erotic epistemology of the later Plato.

DL:
>(2) Wittgenstein, pragmatism, formalism, constructivism, etc explain
>    the epistemology and (some better than others) utility but fail to
>    explain its truth and ontology.

This seems to be the received dogma, pace Benacerraf's "Mathematical
truth"; as I've said over and over, I find the first horn of the dilemma
much less threatening than it's usually made out to be.

DL:
>As I recall, W's theory went something like this:
>
>(A) Logical terms do not denote.
>
>    Consider the problem often called the Bradley Regress:

Where in Bradley is this to be found?  

DL:
>    Question: What makes a predication true?
>    Answer:   A relation (the copula) which holds between the subject and
>              predicate.
>    Question: Then what makes the copula relation hold, another relation?
>              And that relation another?  And another? ...

Sounds like a bad case of explanatory rationalist jitters, flavored with a
dash of use-mention confusion.  Of course, the copula expresses the
relation between the subject and the predicate, rather than "makes it
true"; as for the latter, it's rather more reminiscent of the "Third man"
regress in Plato's "Parmenides", which can be quite easily avoided, e.g. by
abandoning the subject-predicate conception in a Fregean manner.  Now,
given the extensional view of functions, you wouldn't be quite as concerned
about the question of what's the irreducible relation between a function
and its argument, would you?

DL:
>    Wittgenstein's solution was that relations do not denote at all.  People
>    EXPRESS relations by relate-ING the names of the related objects.  We
>    can express the relation *is bigger than* by placing the words
>    "is bigger than" between the names of the smaller and larger objects.

Sounds like a regurgitated "Sinn und Bedeutung" doctrine.

DL:
>(B) Language meaning is irreducably tied to action.
>
>    "EXPRESS" and "relate-ING" are actions.  Hence W's "do not ask the
>    meaning, ask the use."  But beyond some hand waving toward "language
>    games" and "forms of life", there is nothing there to indicate that
>    he has anything strong enough to account for mathematical truth
>    beyond mere utility.  Nor has he shown that reference to mathematical
>    "objects" can be adequately accounted for by a theory of action.  He
>    has only given some examples of how it would work for some simple
>    mathematics.

Quite so.

>So, please say more about how "If we followed Wittgenstein's account
>of meaning about mathematics, we would avoid this whole discussion."

I second that.

>-- 
>+-------------------------------------+---------------------------------------+
>| David K. Lyndes                     | "In 50 years, if we're nice to them,  |
>| Barrios Technology                  |  computers will keep us around as     |
>| email: dlyndes@deltahp.jsc.nasa.gov |  pets." --anon.                       |
>+-------------------------------------+---------------------------------------+
>| The opinions expressed are not necessarily those of my employer nor of God. |
>+-----------------------------------------------------------------------------+


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