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Article 3585 of comp.ai.philosophy:
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>From: zeleny@brauer.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.meta
Subject: Re: Intelligence Testing
Message-ID: <1992Feb7.161148.8591@husc3.harvard.edu>
Date: 7 Feb 92 21:11:44 GMT
References: <1992Feb5.204750.21898@midway.uchicago.edu> <1992Feb6.214010.14199@aio.jsc.nasa.gov> <1992Feb6.230645.27175@midway.uchicago.edu>
Organization: Dept. of Math, Harvard Univ.
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In article <1992Feb6.230645.27175@midway.uchicago.edu> 
gross@befvax.uchicago.edu writes:

>Wittgenstein is opposed to 'theories' of math, and doesn't give one.
>If you attribute to him a theory, it will be a theory he himself does
>not accept.  If you have a theory, no matter what it is, it's not
>Wittgenstein's view.

Rather convenient for him, isn't it?

>My point was that theories in the philosophy of math are attempts to
>give the meaning of mathematical statements, by saying what they are about.  
>	Math is about			symbols
>					mental entities
>					proofs
>					empirical objects
>					a realm of platonic objects.
>If we reject that we give the meaning of expression in terms of
>these other things, then we don't have any more theories.   Once meaning
>is separated from 'aboutness', we don't have these problems.

Correct me if I'm wrong, but I can't seem to find any indications of
"aboutness" in the writings of Frege, Hilbert, G\"odel, Brouwer, or Church.
Morover, even if the idiom is indeed used in the writings of reputable
philosophers of mathematics (you must forgive me if I don't include LW
among their ranks) , I'm sure you will agree that its use is fully
dispensable, for on the Quine-Church conception of ontological commitment
all we ever need to mention is the ranges of the existential quantifiers.

>If we accept a prioirty of mathematical reasoning over mathematical
>objects (which is what W means, in general, of meaning=use, i.e.
>that use determines the content of concepts, not that the content of
>concepts determines our knowledge of them), it make perfect sense
>to talk about math as objective, and to talk about mathematical objects,
>with out being a platonist.  We can say that 2+2=4 is about the 
>numbers 2, 2 and 4, and that its true, necessary, and objective
>without being platonist.  (Just like we can say that there are checkmates
>with just a rook and a king, without making metaphysical claims). 

Can we really?  If you want to defend this position, you must come up with
a proprietary version of ontological commitment criterion.  Exactly what
sort of existential claim would you take as possessed of metaphysical import?

>This relates questions of epistemlogy, ontology, and truth, and therefore
>there is no gap to bridge by a theory.

Convenient, but not convincing.

>Leon Gross
>I'm not an actor, but I play on on TV.


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: Mikhail Zeleny                                                     :
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