[CvGmt News] Fwd: colloquium Girard
sorrentino at mat.uniroma3.it
Thu Sep 18 13:10:41 CEST 2014
*Jean-Yves Girard* (CNRS & Institut de Mathematiques de Luminy)
*8 october 16:00 room F (Colloquium di Matematica, Dipartimento di
Matematica e Fisica, Universita' Roma Tre, Largo San Leonardo Murialdo 1,
FOUNDATIONS IN THE POST-FOUNDATIONAL ERA
Most philosophers won’t hesitate to nominate 2+2=4 as the paragon of a
mathematical theorem : a complete misunderstanding.
We can either see 2+2=4 as a computation, i.e., an activity not involving
any sense, any reasoning : *analytic* in the kantian acception. Or we can
see 2+2=4 as the result of a reasoning — hence *synthetic — *however based
on experience : everything can be checked, there is no room for doubt. This
synthetic *a posteriori* is not typical of mathematics, which is naturally
synthetic *a priori. *This means that mathematics cannot be justified —
hence the failure of the foundational programs of a century ago.
If these programs didn’t succeed in alleviating our — however, unreasonable
— doubts, they however individuated, inside mathematics, a *synthetic a
posteriori *layer. This on a large scale, not limited to finite
computations. How is it possible to deal with infinity and still be based
on experience ? And what does this mean ?
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