Science And Math

[Lulu of the Lotus-Eaters]

Gonçalo Rodrigues <op73418 at mail.telepac.pt> wrote previously:
|mathematical field is roughly divided in the Platonist field, those who
|believe that mathematical objects exist somewhere out there in space
|...and the formalist field of those who believe mathematics is
|essentialy a game we play on paper with symbols with no "real" meaning
|attached to it besides the convenience in describing natural phenomena.

There is at least one philosophical position missing from Rodrigues'
enumeration.  The intuitionist approach to mathematics sees mathematical
reasoning as exposing the "rules of thought."  These rules are not
independently existing structures in the world (Platonism), but neither
is mathematics merely symbolic (Formalism).  Instead, there is a
substantial but procedural fact about the way mathematicians think about
their subject matter.

It is obvious from my other little note in the thread that I feel
sympathy with the Intuitionist idea about mathematics.  Of course, this
sympathy is somewhat forclosed by my attachment to the Axiom of Choice.
I'm not sure I'm able to quite go as far as Brouwer (even though I only
guiltily fail to).

Yours, Lulu...

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