This project brings together two French and Bavarian research teams to study reverse mathematics and its contributions to the philosophy of mathematics from an interdisciplinary point of view which uses historical, mathematical, and philosophical methods.
Reverse mathematics is a research program in mathematical logic that determines the axiomatic principles that are necessary for proving different mathematical theorems. It does this by proving equivalences (“reversals”) between theorems of ordinary mathematics, for example those of analysis or algebra, and axiom systems of varying strength. It has substantial philosophical importance because of its role in determining which mathematical theorems can be proved within foundations of mathematics that impose strict limits on the allowable methods of proof. Reverse mathematics is a relatively new discipline, whose philosophical significance has not yet been adequately investigated.
The project will develop over two four-day seminars attended by both teams: one in Paris (25/02 - 03/03), and one in Munich (21/05 - 25/05). The seminar will study (1) the historical development of reverse mathematics, and its connections to the development of foundational programs such as finitism and predicativism; and (2) the philosophical role of reverse mathematics in contemporary foundational approaches to mathematics. The teams will each involve a combination of four researchers at different career stages: postdoctoral, doctoral, and Master's level. Prior to each meeting, a reading list of the relevant mathematical, philosophical, and historical literature will be assigned as preparation for the seminar.
Calendar of Meetings
Paris, February 25 - March 03, 2019 (IHPST, Paris)
- Meeting 1, 25 February. Overview and prehistory with respect to foundational programs.
- Meeting 2, 26 February. Set existence principles and the significance of reversals.
- Meeting 3, 27 February. Finitism and reverse mathematics.
- Meeting 4, 28 February. IHPST Workshop on proof theory.
- Meeting 5, 1 March. Simplicity and reverse mathematics.
Munich, May 21 - May 24, 2019 (MCMP, Munich)
- Meeting 1, 21 May. Ramsey's theorem for pairs. (Room C 033)
- Meeting 2, 22 May. Basis theorems and and reverse mathematics. (Room 133)
- Meeting 3, 23 May. Predicative provability and reverse mathematics. (Room 133)
- Meeting 4, 24 May. The idea of a "reversal". (Room 169)
The Munich meetings will take place at Oettingenstr. 67. For information, please contact Marianna.AntonuttiMarfori@lrz.uni-muenchen.de.
- Logic and Philosophy of Mathematics
This project is generously funded by the Förderprogramm zur Anbahnung bayerischer-französischer Kooperationen in der Forschung und Lehre / Programme de financement de projets de coopération franco-bavarois dans la recherche et dans l’enseignement.