From: Scott R (jse885@spinn.net)
Date: Mon Oct 07 2002 - 21:37:37 BST
Pantophobic,
The Pantophobic wrote:
>>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.
>
I am aware of the "invented vs. discovered" debate, but feel that it is
a platypus arising from the need to see everything as a subject or an
object. If one forgets that, and asks what a mathematical entity is,
then my answer is: it is the thinking of the entity (actually, the idea
goes back at least to Coleridge). Whether it exists when no one is
thinking it doesn't matter. When I think it or you think it, it is the
same thinking. So it is definitely not "marks on a piece of paper".
Those marks are guides for the mathematician to keep his or her thinking
in order, and obviously can be changed without affecting the thought.
So, there is no subject thinking a mathematical object; there is just
the thinking, which is mathematical.
- Scott
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