Spring 2023: « La philosophie mathématique »

Mathematical and philosophical inspirations,
from Brunschvicg to Granger

Thematic volume of the Annals of Mathematics and Philosophy M×Φ

Guest editors: Gabriella Crocco and Frédéric Jaëck (Aix-Marseille University)

Deadline for submission: March 31, 2023

Submissions should follow the journal guidelines as detailed here and should be sent to: gabriella.crocco@univ-amu.fr and frederic.jaeck@univ-amu.fr

If you have any questions about submitting an article for inclusion in this special issue, please send an email to the editors.

About this thematic volume

The French epistemological tradition in the philosophy of mathematics is characterized by its attention to the history of mathematics and its practice as well as its relation to philosophy and its history. This special issue is open to the study of authors who have shaped this trend in the philosophy of mathematics during the 20th century.

Albert Lautman developed, in the course of his short career, a personal and committed mathematical philosophy. Committed to the mathematics of his time, but also engaged in a critical dialogue with a long philosophical tradition, or with his predecessors Léon Brunschvicg or Jean Cavaillès. After the war, philosophers such as Jules Vuillemin, Gilles Gaston Granger and a few others continued this philosophical movement, in various forms, but all showing a genuine interest in the ideas developed in mathematical works.

If these authors, this line of thought and its guiding ideas – such as the will to never dissociate the philosophy of mathematic 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 at the world level little known and very seldom evoked outside of the few studies that are devoted to them.

It will be one of the objectives of this volume to contribute to a better knowledge of this type of philosophical approach, but also to encourage philosophers and mathematicians to further develop on renewed bases, thanks to the recent progress of philosophy and mathematics, what has been the project of a certain mathematical philosophy, the one that Bachelard, speaking of Cavaillès and Lautman, considered to be a « heroic task of difficult thought ».

Types of submissions

We encourage three types of submissions:

The first are those that renew or extend our understanding of the philosophers cited above or 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 inspire philosophy cover a vast field, are often difficult and were to undergo important extensions and transformations. A cross-look or a collaboration between philosophers and mathematicians could in particular allow to shed light on the role of mathematical ideas evoked in different texts.

The second expected contributions are of a more specifically philosophical nature. They are those which 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 prospective 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.

Finally, and this is an important idea that the journal defends, it is important to understand 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?