From: Patrick van den Berg (cirandar@yahoo.com)
Date: Sun Oct 06 2002 - 13:16:53 BST
Hi,
Something about the philosophy of mathematics! Interesting.
--- The Pantophobic <trivik@stwing.upenn.edu> 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.
That's an interesting analogy, that between the word 'chair' vs. the
(supposedly) real chair out there, and between '1' and the real number
one.
Do you think that the 'world of mathematics' is not fundamentally
different than 'the physical world'? I'd like your opinion on that.
If I'd try to formulate an answer to this question myself, I'd say I
bring in Nishida (a Pirsigian before Pirsig even existed): this man
tries to explain the world in terms of consciousness. That leads him to
certain conclusions, of which one of them is that perception and
thought are not distinct phenomena, but are essentially the same: they
only differ in matters of degree, not of principle. With this
conclusion, one has to say that the real chair and the real number one
are not essentially different from each other: the chair only has an
emphasis in perception, the number one an emphasis in thought.
> 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.
That seems a trivial notion, but I've come to think it's important. I
always thought that every physicist had an opinion about, for example,
what quantum mechanis MEANS: what it has to say about the world. But
most physicists seem not to think about that much, only work with the
theory in pragmatic ways. Maybe that isn't a bad attitude after all,
because deep thinking might lead only to complicated intellectual webs,
in which one gets easily stuck.
On the other hand, scientists like biological psycholigists, nowadays
seem forced to conclude from their EEG or fMRI-experiments that free
will doesn't exist, but nevertheless go to church every sunday where
they are told that people have a choice between 'good' and 'bad'. So
'deep thinking' might be wortwhile after all, in trying to create a
coherent, though also pragmatical worldview, and remove the
contradictions in certain beliefs.
Of course Pirsig has tried to formulate such a coherent worldview...
> e.g. cantor and godel both beleived there were mathematical
> objects out
> there to discover.
I didn't know that. Penrose however is one of them too.
Greetings, Patrick.
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