Re: pragmatic foundation

[Andre.Rodin@ens.fr]

I agree with WHAT Yuri Ivanovitch Manin says about foundations of mathematics
but DISagree when he calls these foundations "pragmatic". I might be mistaken
(in this case, I hope, Yuri Ivanovitch will correct me) but I don't think that
in the given context the word "pragmatic" is supposed to be understood with a
philosophical seriousness. In the given context "pragmatic" is rather
synonymous to "practical" as opposed to "theoretical" - and perhaps also to
"purely mathematical" as opposed to "philosophical". I fully share with Yuri
Ivanovitch his disappointment about what he calls the "normative foundations
that logicists or constructivists tried to impose". But I see a solution in a
new dialectical philosophy of foundations (tightly connected to mathematical
practice), NOT in developing foundations purely "pragmatically" without
theoretical and philosophical grounds. The history teaches us that
philosophical thinking is crucial for what Yuri Ivanovitch calls the
"rebuilding" of foundations, and I don't see any reason why this might cease to
be true today.
On the contrary, I think that the acceleration of mathematical progress
necessitates the acceleration of rebuilding of foundations - and this makes
philosophy more relevant to mathematical research than ever. "Logicists and
constructivists" don't have centuries to come to eternalise their findings by
establishing a new Scholastic tradition in philosophy - even if some of them
would wish it.

Andrei

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