ALBERT LAUTMAN PDF

Notes 1. The quote is from [ 21 , p. The two theses referred to are [ 31 ] and [ 33 ]. Tannery for mathematics, and for other disciplines Rey, Meyerson, Ribot in Italy, apart from savant-philosophe Federigo Enriques, the only philosophe-savant figure in this area was Giovanni Vailati. For more on this, see [ 2 ] and [ 46 , xxxi]. Mathematician, historian and philosopher of mathematics, Gaston Milhaud — translated into French in P.

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Notes 1. The quote is from [ 21 , p. The two theses referred to are [ 31 ] and [ 33 ]. Tannery for mathematics, and for other disciplines Rey, Meyerson, Ribot in Italy, apart from savant-philosophe Federigo Enriques, the only philosophe-savant figure in this area was Giovanni Vailati.

For more on this, see [ 2 ] and [ 46 , xxxi]. Mathematician, historian and philosopher of mathematics, Gaston Milhaud — translated into French in P. About Milhaud, see [ 12 ]. He had close relations with Italian mathematician Federigo Enriques; for a first study about the relationship between the two, see [ 2 ]. Avoiding the calculations you have been able to bring out [mathematical] thought. And this is not the least merit. Every philosopher of science knows that this is an almost insurmountable difficulty With great sympathy, I hail in you a representative of the younger generation that is bringing philosophy back to the heroic tasks of difficult thinking.

That we could be at least a dozen! His major work, Raum, Zeit, Materie was translated into French in and later French philosophy of science cannot be fully understood if this constant critical confrontation with his thought is not kept in mind, another unique fact in the epistemological landscape of the twentieth century, as was the case with Riemann; on this see [ 47 ] and the various contributions in [ACRR].

It is no coincidence that Enriques was appreciated and followed on this ground by Bachelard and by Lautman himself. But the same could be said for other contemporary mathematicians like Lawvere, and Alain Connes and Jean-Yves Girard for the French area; on Grothendieck see [ 25 ].

We might add to this list, in the French area, first Winter and Bachelard and then mathematicians like Grothendieck and Alain Connes. With regard to this, it is sufficient to read the preface, written as late as by another Bourbakist, G. References 1.

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For an epistemology of mathematical contents: Albert Lautman

This book is born from the feeling that in the development of mathematics, a reality continues which mathematical philosophy has as a function to recognize and describe. The spectacle of the majority of the modern theories of mathematical philosophy is in this respect extremely disappointing. Generally, the analysis of mathematics reveals only very little things and very poor things, like the research of identity or the tautological character of propositions [1]. For Wittgenstein and Carnap, mathematics is nothing more than a language indifferent to the contents that it expresses. Only empirical proposals would refer to an objective reality, and mathematics would be only a system of formal transformations making it possible to connect the ones to the other the data of physics.

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