Thematic issue of Annals of Mathematics and Philosophy M x Φ

Guest editors:

Gabriella Crocco (Aix-Marseille University)

Frédéric Jaëck (Aix-Marseille University)

**Deadline for submission: August 31, 2022 Notification date: November 15, 2022Final version: December 31, 2022**

Albert Lautman developed, in the course of his short career, a distinctive mathematical philosophy. It was engaged with the mathematics of his time, but also in a critical dialogue with a long philosophical tradition from Plato to his predecessors Léon Brunschvicg and Jean Cavaillès. After the Second World War, philosophers such as Jules Vuillemin, Gilles Gaston Granger and others continued this philosophical movement, in various forms, but all showing a genuine interest in the ideas developed in contemporary mathematical works.

If these authors, this line of thought and its guiding ideas – such as the will to never dissociate the philosophy of mathematics from philosophy, to never reduce the philosophy of mathematics to one of its components: ontology, logic, syntax… – are quite well studied in France and in Italy, they remain little known globally and are very seldom evoked outside of the few studies that are devoted to them.

It will be one of the objectives of this volume to develop and disseminate knowledge of this type of philosophical approach. Another is to encourage philosophers and mathematicians to take further on renewed bases, what Bachelard, speaking of Cavaillès and Lautman, described as a « heroic task of difficult thought ».

We encourage three types of submissions:

- Those that renew or extend our understanding of the philosophers cited above or others related to them. In particular, the distance we have from the mathematical work that was at the forefront at the time Lautman and his contemporaries were writing allows us to better understand in retrospect the context in which these philosophers developed their thought. The mathematical theories that inspired this philosophy cover a vast field, are often difficult and were to undergo important extensions and transformations. A a collaboration between philosophers and mathematicians could shed light on the role of mathematical ideas evoked in these texts.

- Contributions of a more specifically philosophical nature, that put the philosophers mentioned or the type of thought they represent in dialogue with other philosophers (not necessarily of mathematics). This dialogue can be established on historical grounds (their references to Plato, Kant or Husserl, for example) or on a more speculative basis (to take one example among others: what contribution can Lautman’s or Granger’s « structuralism » make to contemporary debates on the subject?) In any case, it is expected that this dialogue will have theoretical consequences for contemporary philosophy of mathematics, and that these aspects will be made explicit in the texts submitted.

- Contributions that explore the echo that philosophical proposals, even relatively old ones, can have in the current practice of mathematics. To take Lautman’s example (other philosophers would call for other questions): how do dialectical couples such as finite/infinite, continuous/discrete, etc. play a role, or are reconsidered, in the practice of mathematicians?

Submissions should follow the journal guidelines as detailed here.