FOM: Platonism v. social constructivism
rhersh at math.unm.edu
Thu Dec 25 16:45:11 EST 1997
>Dear Prof. Tennant: First let me quote your astonishing dictum:
"...any social-institutional factors shaping the
> history of mathematics as thus far developed by human beings is
> IRRELEVANT to the truth of Platonism (or any other philosophy of
> mathematics opposed to social constructivism). The same goes for
> whatever social-institutional factors might have shaped the history of
> mathematics in any other extra-terrestrial civilization. "
I refrain from any extra-terrestrial arguments. According to the
first sentence, since history runs up to the present, all
social-institutional factors in present day mathematics
are IRRELEVANT to the truth of Platonism.
I agree with that, if I can rephrase it: to a
devout Platonist, no social-institutional (or social non-institutional)
factors in present or past mathematics can shake his/her Platonist
However, my project was not primarily to convert Platonists. Rather, I
sought to explain in what sense pure mathematics exists, without
resort to transcendental ideology. I concluded that it exists as
part of society and culture, historically evolved.
This proposal isn't new. It goes back to White and Durkheim. It does
not conflict with the common knowledge, that simple
measuring and counting deal with physical reality. Advanced mathematics
grows from simple measuring and counting, stimulated by social
needs and human curiosity, with many an assist from physical applications.
As you say truly, "Just because it's we who do the thinking doesn't
mean that what we are thinking about depends entirely on us."
If you try with an open mind to make a philosophical
analysis of mathematics, how can you begin without
looking at what is actually going on, and where it came from?
Well, if you're already in touch with a transcendent REALITY, the
natural yearning of the soul (or of Reason) to unite with that reality
makes actual life experience IRRELEVANT.
The trouble is that two thinkers, both in touch with transcendent
Reality, may give different reports of what it says. Thus, the proliferation
of schismatics. Another trouble is that any dicta about
real mathematical life that may come down from transcendent Reality may
not have much legitimacy for us low-level types who aren't in touch with
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