From: The Pantophobic (trivik@stwing.upenn.edu)
Date: Sat Oct 05 2002 - 23:58:23 BST
> If I write a paper about Hamlet, my paper is not Hamlet.
yes
> If the physical world can in part be modelled with a vector space,
> that is irrelevant to the mathematical concept.
yes
> if I write a mathematical paper, there is nothing outside
> the paper that my paper is about.
no
this is getting into the philosophy of mathematics - there is a whole camp that
beleivs this to be so - the nothing more than a bunch of meaningless marks on a
piece of paper, vs those who beleive that there are actually mathematical
objects which are out there to be discovered. These 'objects' have an existanc
just like this chair does, however not a physical existance. So just as the
word 'chair' is not a chair, the charector '1' is not the number one, but
mearly refers to the number one. Anyhow, whatever you beleive about the subject
of mathematics for the moast part (actually not entierly true - it has greatly
changed some methods) it does not effect the manner in which mathematics is
done. e.g. cantor and godel both beleived there were mathematical objects out
there to discover.
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