Speaker:  JeanYves Girard

evento esterno  
Quando:  08/10/2014  16:00


Dove:  Dipartimento di Matematica e Fisica, Università Roma Tre,
Largo S. Leonardo Murialdo 1,
Aula F (blocco delle aule, primo piano)


Abstract
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 ? 