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Article 3513 of comp.ai.philosophy:
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>From: gross@befvax.uchicago.edu
Newsgroups: comp.ai.philosophy,sci.philosophy.meta
Subject: Re: Intelligence Testing
Message-ID: <1992Feb5.204750.21898@midway.uchicago.edu>
Date: 5 Feb 92 20:47:50 GMT
References: <12351@optima.cs.arizona.edu>
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Organization: University of Chicago, Dept of Molecular Genetics
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In article <12351@optima.cs.arizona.edu>, gudeman@cs.arizona.edu (David Gudeman) writes:

>By assuming the existence of mathematical objects you become a
>Platonist, whether or not you say they are part of the real world.
>
Only if you think 'existence' has one meaning, regardless of the domain.

Mathemeticians can 'assume the existence of mathematical objects',  without
being philosophers of mathematics or being Platonists.

Asking whether there exists a prime number between 90 and 100 is different
then asking whether integers exist, which is different then asking whether
certain sets of numbers exists, which is different then asking whether
inaccessible cardinals exist.  

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.

Leon Gross                             	(Grad Student in Phil, U of Chicago)
I'm not an actor, but I play one on TV.


