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Article 4887 of comp.ai.philosophy:
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>From: holmes@opal.idbsu.edu (Randall Holmes)
Newsgroups: comp.ai.philosophy
Subject: Re: The 'Big Bang' and the origin of 'mathematical  objects'
Message-ID: <1992Apr3.020657.13730@guinness.idbsu.edu>
Date: 3 Apr 92 02:06:57 GMT
References: <kth7fnINNflu@exodus.Eng.Sun.COM> <1992Apr2.181440.11808@guinness.idbsu.edu> <ktmtr2INNso8@exodus.Eng.Sun.COM>
Sender: M. Randall Holmes
Organization: Boise State University Math Dept.
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Nntp-Posting-Host: opal

In article <ktmtr2INNso8@exodus.Eng.Sun.COM> silber@orfeo.Eng.Sun.COM (Eric Silber) writes:
...stuff deleted...
Holmes
>>	Mathematical objects are not physical--the "Big Bang" is
>>irrelevant to their existence or non-existence.  They are also
>>eternal (they have no relationship to time) and therefore the question
>>of a physical beginning for such objects makes no sense.
>
Silber
>I think that as soon as you posit the existence of mathematical "OBJECTS"
>(separate from human ideas), then you have a responsibility to respond
>to ontological questions about them such as "how did they get here?".
>Cosmological theories seek to encompass the entire universe.  Now, if
>you assert that "real mathematical objects" are independent of the 
>universe, I think you are asserting a clearly paradoxical position.
>We are in touch with these "mathematical objects", yet they are not
>part of the universe?  But the universe is the TOTALITY of all and
>everything that IS.  So I refer you back to my original position,
>namely, that ultimately, in order to support "mathematical realism",
>mathematical realists will have to show how the existence of real
>mathematical objects is entailed by some cosmological theory.

The answer is that they exist--period.  Their existence is not
temporal.  The main point I want to make is that you are begging the
question: you are punning on two of the senses of the word
"universe"--the sum total of all physical objects (the physical
universe) and the sum total of everything that exists (the logical
universe).  It is fine for you to adopt as an axiom that these two
concepts are equivalent; you then can conclude immediately that
mathematical objects do not exist.  This is a very simple argument,
and the reply is to ask for evidence for your axiom.  Cosmology is the
subject of the origin of the physical universe--whatever non-physical
objects may exist are outside of its domain (to avert another
"pun"--non-physical does not coincide with "spiritual" or similar
terms).  "Real mathematical objects are independent of the _physical_
universe" is not a paradoxical assertion--to deny that they are in the
logical universe would be a paradox.  Again, if there are eternal
objects, it makes no sense to ask "where they come from".  It is fine
to challenge the existence of eternal objects, but you cannot do this
by trying to apply irrelevent criteria to them.  A possible challenge
to you is that cosmological theories are framed in mathematical terms
and thus clearly presuppose the existence of mathematical objects,
which are thus part of the necessary grounds (I won't say
"preconditions", because of the temporal sense of the word) of the
beginning of the physical universe (this is not an unassailable
argument)!
	I do not in fact maintain that "mathenatical objects" exist in
a domain dispoint from the physical universe; I suspect that the
physical universe is a (very small) subset of that domain.  (Again,
certainly a position which can be challenged!)
	I don't think this discussion is in the domain of philosophy
of AI.  Query to everyone out there--is the tendency of mathematicians
to be philosophical realists an issue of interest here?


				--M. Randall Holmes
				Math Dept, Boise State Univ.
				holmes@opal.idbsu.edu

The opinions expressed above are not the official opinions of any
person or institution.




-- 
	--alex			alex@opal.idbsu.edu


