The course aims to highlight the intertwining of philosophical and mathematical reflections that have marked the study of the foundations of mathematics and the development of contemporary logic during the second half of the nineteenth century and the first half of the twentieth century.
The course is organized in four parts. The first part is devoted to an exposition of the historical context and the philosophical issues related to the study of the foundations of mathematics. The second part consists of a presentation of classical first-order logic with identity, both from a model-theoretic and a proof-theoretic point of view. The third part is dedicated to set theory and the interpretation of basic mathematical concepts in terms of set-theoretical concepts alone. The fourth part proposes an analysis of Gödel's incompleteness theorems and their consequences for Hilbert's program.
The evaluation is oral and preceded by a period of preparation.
| Training | Study programme | Block | Credits | Mandatory |
|---|---|---|---|---|
| Master 60 en sciences mathématiques | Standard | 0 | 3 | |
| Master 120 en sciences mathématiques, à finalité spécialisée en Project Engineering | Standard | 0 | 3 | |
| Master 120 en sciences mathématiques, à finalité spécialisée en data science | Standard | 0 | 3 | |
| Master 120 en sciences mathématiques, à finalité didactique | Standard | 0 | 3 | |
| Master 120 en sciences mathématiques, à finalité approfondie | Standard | 0 | 3 | |
| Master 60 en sciences mathématiques | Standard | 1 | 3 | |
| Master 120 en sciences mathématiques, à finalité spécialisée en Project Engineering | Standard | 2 | 3 | |
| Master 120 en sciences mathématiques, à finalité spécialisée en data science | Standard | 2 | 3 | |
| Master 120 en sciences mathématiques, à finalité didactique | Standard | 2 | 3 | |
| Master 120 en sciences mathématiques, à finalité approfondie | Standard | 2 | 3 |