Re: Interview with Manin ~~~> The Wand Chooses The Wizard

Interview with Manin ~~~> Pragmatic Norms
http://golem.ph.utexas.edu/category/2009/11/interview_with_manin.html

Thanks, Gary.  Give me a few days to metabolize that feast of inferential symboly.
In the mean time, my continuing interest in the issue led me to search Manin's text for
clues to the contrast that he or his translator drew between "normative" and "pragmatic".

Here's a sample of relevant passages:

<blockquote>
<p>Cantor's theory of the infinite had no basis in the older mathematics.
You can argue about this as you like, but this was a new mathematics,
a new way to think about mathematics, a new way to produce mathematics.
In the final analysis, despite the arguments, the contradictions,
Cantor's universe was accepted by Bourbaki without apology.  They
created "pragmatic foundations", adopted for many decades by all
working mathematicians, as opposed to "normative foundations"
that logicists or constructivists tried to impose upon us.</p>

<p>&hellip;</p>

<p>What Bourbaki did was to take a historical step, just as what Cantor himself
did.  But this step, while it played an enormous role, is very simple &mdash;
it was not creating the philosophical foundations of mathematics, but rather
developing a universal common mathematical language, which could be used for
discussion by probabilists, topologists, specialists in graph theory or in
functional analysis or in algebraic geometry, and by logicians as well.</p>

<p>&hellip;</p>

<p>When "pragmatic foundations" of mathematics are made explicit,
usually in several variants, the advocates of different versions
may start quarreling, but to the extent that it all exists in the
brains of the working generation of mathematicians, there is always
something they have in common.</p>
</blockquote>

 From reading that, I would guess that Manin means "pragmatic" in
the sense of culturally embedded practices &mdash; bringing to mind
[Wilder](http://www.gap-system.org/~history/Biographies/Wilder.html)'s
theme on "Mathematics as a Cultural System"

[1](http://www.gap-system.org/~history/Extras/Cultural_Basis_I.html),
[2](http://www.gap-system.org/~history/Extras/Cultural_Basis_II.html),
[3](http://www.gap-system.org/~history/Extras/Cultural_Basis_III.html)

&mdash; and, as far as "normative" goes, he seems to be using it more
in the sense of programmatic principles that are perhaps too prematurely
"prescriptive" than referring to norms with a solid grounding in practice
and oriented toward the ultimate _pragma_ of the given enterprise.

Jon Awbrey, 08 Nov 2009, 2:40 PM
http://golem.ph.utexas.edu/category/2009/11/interview_with_manin.html#c029004

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