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Badiou’s suggestions for a better discussion of Platonism in mathematics

Miriam Franchella, Università degli Studi - Milano

In the age of the Internet it is hard for us to realize that scientific communication remains difficult. Especially difficult to remember is that there can be some kinds of research that are developed on different continents and whose results are not compared with one another. Nevertheless, mathematical Platonism remained an exception to this spreading of information for many years; there had been two traditions, one English-speaking and one French-speaking, each of them defining and discussing the subject in a different way, until the volume L’Objectivité Mathématique, edited by Panza and Salanskis, appeared in 1995, containing a collection of essays by French-speaking scholars that expressed their opinions on the English/American tradition. Among those scholars, we find Alain Badiou, and I intend here to stress the originality of his contribution and the active role that it can play in instilling new life into the English-American debate on the subject.

Mathematical Platonism in the twentieth century
First of all, let me briefly recall the story of the English/American tradition of mathematical Platonism, which, however, had its roots in Europe, with Paul Bernays’ 1935 article ‘Sur le Platonism dans les mathématiques’, where he presented the notion of mathematical Platonism as exemplifying confidence that mathematical entities exist independently of a human being thinking of them.
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