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Article 3556 of comp.ai.philosophy:
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>From: dlyndes@gothamcity.jsc.nasa.gov (David Lyndes)
Newsgroups: comp.ai.philosophy,sci.philosophy.meta
Subject: Re: Intelligence Testing
Message-ID: <1992Feb6.214010.14199@aio.jsc.nasa.gov>
Date: 6 Feb 1992 21:40:10 GMT
References: <12351@optima.cs.arizona.edu> <1992Feb5.204750.21898@midway.uchicago.edu>
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In article <1992Feb5.204750.21898@midway.uchicago.edu>
gross@befvax.uchicago.edu writes:

|> 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 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.

But the problem remains: namely

(1) platonism explains mathematical ontology and truth quite nicely but
    fails to explain its utility and epistemology, while

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

As I recall, W's theory went something like this:

(A) Logical terms do not denote.

    Consider the problem often called the Bradley Regress:
    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? ...

    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.

(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.

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