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Article 4897 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.702037956@groucho.phil.ruu.nl>
Date: 31 Mar 92 10:32:36 GMT
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silber@orfeo.Eng.Sun.COM (Eric Silber) writes:

>In article <atten.701704311@groucho.phil.ruu.nl> atten@phil.ruu.nl (Mark van Atten) writes:
>>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')
>...
>>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?'

>Thanks for the Hao Wang references,
>I suppose my naive predilection is for, not 'materialism', but
>physicalism (mass-energy-ism).  All of OUR logic depends on the
>allowable physical combinations which our brains and ultimately 
>fundamental particles can enter into.  Now if in fact the
>physical hierarchy of this universe is made out of quarks etc that
>can combine in certain ways, this does not establish mathematics.
>Isn't the idea of 'map' or 'function' a fundamental concept which
>we use in our mathematics?  I don't see how maps, functions, or even
>elementary numbers and arithmetic have explicit objective existence
>just because the universe says that ''three''-quarks may combine to make
>a proton.  ( But perhaps I will get some new ideas from Wang et al.)

Thanks for your reply. However, I do not understand it completely. The reason
is that I am very much used to a philosophical approach to this problem, while
I do not no very much about quarks etc. I  have have just asked a friend of
mine also to reply. He is really heavy into physics, quarks and an almost
infinite number of universes. I am almost sure that he does not quite share
my philosophical views but I am sure he will say something interesting. (He is
Martijn Faassen, by the way-just in case, perhaps there will be more replies)

But there's more I can do for you. I will prepare an article on Goedel's views
on the objective existence of math. obj. versus the physics of our brain. I
will post it next Friday, i.e. April 3rd.

One last thing. I think you will find the ideas of Alan Turing very congenial.
Check out the interesting biography by Andrew Hodges, 'Alan Turing: the Enigma
of Intelligence'.


