Re: [asa] the Way Science Works/

The ultimate difference between science and mathematics is that the
former is necessarily connected to observation for testing, while the
latter (like logic) is not empirical. There are different major
geometries: absolute without the parallel postulate; three others with
different numbers of lines parallel to a given line ... The special
theory of relativity used Riemannian geometry, built on the claim that no
lines can be parallel. But Whitehead, who didn't like Riemannian
geometry, redid all that was recognized as relevant at the time in
Euclidean terms. He was a good enough geometer that I suspect that, had
he known in time of the other relevant matters, he could have redone more
in Euclidean terms.

In number theory, one can restrict the theory to cardinal integers, or go
on to rational, irrational and transcendental numbers. Additionally,
there are an infinite number of modular numbers. Taking off in a
different direction, there are Cantor's transfinite numbers, cardinal and
ordinal. They all fall under the restrictions of Goedel's theorems.

Logic is another nonempirical study. Aristotle's and mathematical logics
have different underlying assumptions, as do a host of modal logics. One
has to match the assumptions underlying the several logics and
mathematical calculi to the empirical requirements of a science to
produce sense. Sometimes this requires moving to statistical approaches,
another branch of mathematics. This also applies to logics, which assume
that p and ~p, or the related predicates, exhaust the universe of
discourse. But one cannot rationally classify adult human males neatly
into the bald and nonbald.

I understand that mathematics is so essential to empirical studies that
the common designation is STEM--Science Technology Engineering
Mathematics. But math is not empirical.
Dave (ASA)

On Thu, 26 Jul 2007 15:03:10 -0600 (MDT) gordon brown
<gbrown@Colorado.EDU> writes:
> Wendee,
>
> I don't follow your reasoning when you see mathematics as having
> more in
> common with history and philosophy than with science. Mathematics is
>
> establishing theorems. Typically theorems are just classified as
> conjectures before proofs are found for them. Can you clarify your
> thinking on this?
>
> Gordon Brown (ASA member)
>

To unsubscribe, send a message to majordomo@calvin.edu with
"unsubscribe asa" (no quotes) as the body of the message.
Received on Fri Jul 27 00:34:14 2007