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Article 4758 of comp.ai.philosophy:
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>From: atten@phil.ruu.nl (Mark van Atten)
Newsgroups: comp.ai.philosophy
Subject: Re: mathematical realism
Message-ID: <atten.701704311@groucho.phil.ruu.nl>
Date: 27 Mar 92 13:51:51 GMT
References: <ksschhINNnst@exodus.Eng.Sun.COM>
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silber@orfeo.Eng.Sun.COM (Eric Silber) writes:


> Some theoreticians, Goedel for insatnce, say that 
> intuition about universal, platonic mathematical reality
> is the key to their discoveries.  This may well be true,
> but it still does not establish the truth of the 
> separate objective existence of mathematical objects.

 This is not true! I cannot offer a full reply (as I have no references at
hand), but I can give some hints at such a full reply.

1. It is hard to see how one can be 'objective' without there existing objects
of some sort. (This was pointed out by Hao Wang in his fab book 'Reflections
on Kurt Goedel')

2. This argument, if it would be true, is actually supporting mathematical
realism: even from the pragmatic standpoint, it is the right one. (I understand
 this is not quite your point, but it is useful to keep this in mind. This point is also due to Hao Wang (Is that correct English idiom?)

3. The question of the objective existence of mathematical objects is an exact
replica of the question of the objective existence of physical (material)
objects in physics. See the 1964 postscript to Goedel's  paper 'What is Cantor's continuum problem?'

4. I take your statement as meaning that mathematical is (or could be) a useful
heuristic, a useful way of thinking about mathematics (pretending), but not the true (right) way. However, the problem is that you must supply us with an alternative philosophy of mathematics, a non-realist one. But one of the reasons for
accepting realism is precisely that the alternatives ( all kinds of constructive ones, formalism, empirism (which Goedel regards as 'absurd', by the way)) are
so bad.  

I realize that these points are not very satisfactory as an answer. If this
 will grow to a large discussion, I will write a more detailed article. 
In the meantime, check out these books: 
  1. Reflections on Kurt Goedel, by Hao Wang
  2. From mathematics to philosophy, by Hao Wang
  3. Infinity and the mind, by Rudy Rucker
  4.  The emperor's new mind, by Roger Penrose
All of these books contain very useful material on the question of platonism 
in mathematics.

Reactions on e-mail (atten@groucho.phil.ruu.nl) are welcome, but perhaps
follow-up articles are better!

Yours,
Mark van Atten
Beneluxlaan 120
3527 HW Utrecht
The Netherlands.
e-mail: atten@groucho.phil.ruu.nl


