Exposé de Stéphanie Ponsar dans le cadre du séminaire "Work in Progress". De 14h à 16h en salle Jean Ladrière. Pour plus d'informations, contacter Vincent Ardourel.
Résumé
Foundations of mathematics is a hot topic covering a wide variety of issues. These range from proposing theories of foundations to discussing the role of category theory as a competitor of set theory. Different conceptions of foundations of mathematics complexify these issues.
To better understand these issues, we propose to highlight a few key characteristics foundations of mathematics should have.
To this aim, we adopt a historical point of view. It will allow to identify the reasons why, at the end of the 19th century, mathematicians felt an urgent need for building foundations of their discipline.
To overcome the problems appearing in this crisis, mathematicians and philosophers decided to build foundations of their discipline. We give some characteristics of these foundations of mathematics in two steps. The first one consists in identifying the different problems mathematicians were confronted to within the crisis in mathematics. The different ways in which philosophers and mathematicians tried to provide these foundations are presented in the second part of the talk.