Subject: Re: [HM] What is good math history?
From: Milo Gardner (milo.gardner@24stex.com)
Date: Mon Jan 10 2000 - 21:59:25 EST
Dear HMer's:
I would like to comment on two posts. The first is Don Cook's support of
constructive algebra. The second is Julio's anonymous reviewer suggestion.
Beginning with Cook's suggestion that it is generally okay to exclude the
'excluded middle', may I say such an analytical position seems correct
only within bivalent systems. It is true that the majority of Western
languages only consider bivalent syntax; however, world-wide there are the
Aymara from Bolivia, 1,000,000 strong, for example, that speak a trivalent
tongue that would never consider excluding the 'excluded middle'.
At its core, mathematics and especially algebra should be intended to
match the skills needed in everyday society. I live in California, and our
Governor Gray Davis just announced an 7th/8th grade algebra academy. How
many out there would proposed that only constructive algebra be taught as
pre-algebra or algebra courses within Gov. Davis' academy?
My position is that Goedel was correct. All binary systems of arithmetic,
and their algebraic equivalents, logically do break down, at some point.
My vote would be to present constructive algebra only in marginal ways in
California schools. Our youths' minds should be opened up to 'excluded
middle' situations in life, as well as to non-Western forms of thinking.
Given that Europeans are now a minority in California schools, what other
policy can be politically and logically accepted?
Concerning Julio's anonymous review point, I agree with the implication
that openness is critical on some level. There are several forms of biases
that are found in reviewing ancient mathematics. Constructivism is one of
those biases. An acid test for a reviewer is to read the manuscripts with
an eye only to the ancient context of the mathematics involved. Modern
issues of all types MUST be excluded, or duly noted when found in a paper
submitted for publication.
Regards to all,
Milo Gardner
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