Editors: Gabriella Crocco, Frédéric Jaëck
This special issue in two volumes is devoted to a certain French tradition in the philosophy of mathematics, a tradition characterized by the tutelary presence of two major figures, Jean Cavaillès (1903–1944) and Albert Lautman (1908–1944), both of whom were shot by the Nazi occupiers for their involvement in the French resistance, and both of whom produced original, albeit unfinished, works in the course of their short lives.
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Introduction to the special issue (in two volumes) ‘La philosophie mathématique’: Mathematical and Philosophical Inspirations from Brunschvicg to Granger, devoted to a certain French tradition in the philosophy of mathematics.
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A translation of the famous 1939 exchange between Cavaillès and Lautman at the Société française de philosophie on the nature of mathematical thought.
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Are we right to attribute an a priori value to what we call French epistemology or the French tradition of epistemology? For a person educated in this country, it is difficult to answer in the negative. It's a bit like discrediting French wine, French cheese, or the French school of mathematics with its abnormal number of Fields Medals. Yet the various dignities just mentioned are obviously incomparable. On a more serious note, for me the notion of French epistemology overlaps three things and gives rise to at least two guilty feelings.
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Are we right to attribute an a priori value to what we call French epistemology or the French tradition of epistemology? For a person educated in this country, it is difficult to answer in the negative. It's a bit like discrediting French wine, French cheese, or the French school of mathematics with its abnormal number of Fields Medals. Yet the various dignities just mentioned are obviously incomparable. On a more serious note, for me the notion of French epistemology overlaps three things and gives rise to at least two guilty feelings.
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In this essay, I propose a new key to the interpretation of Cavaillès's "philosophical testament" Sur la Logique et la théorie de la science (1942/47), or at least to one of its main philosophical motives: to find a principled answer to the problem of coordination between pure mathematics and physical theory (and thus also to clarify, first of all, the status of mathematical physics). Cavaillès's manifesto, culminating in the idea of a "philosophy of the concept", not only articulates the core ideas of a new philosophy of mathematics around the dynamics of "paradigm" and "thematization"; it also contains a project of a new "doctrine of science" in general. The latter should explain the possibility of conceiving a worldly knowledge that incorporates the intrinsic dialectic of mathematical concepts, but at the same time supplements this internal conceptual development with something radically different: a reason-led action of experimenting and wagering on events in the world. I develop this view of Cavaillès against the background of the ideas of some of the leading thinkers on the coordination problem: Mach, Poincaré, Schlick, Reichenbach, Carnap, Brunschvicg, Gonseth, Suzanne Bachelard, Bas van Fraassen...
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In this essay, I propose a new key to the interpretation of Cavaillès's "philosophical testament", Sur la Logique et la théorie de la science (1942/47), or at least to one of its main philosophical motives: to find a principled answer to the problem of coordination between pure mathematics and physical theory (and thus also to clarify, first of all, the status of mathematical physics). Cavaillès's manifesto, which, as is well known, culminates in a "philosophy of the concept", does not merely articulate the core ideas of a new philosophy of mathematics around the dynamics of "paradigm" and "thematization"; it also contains the project of a new "doctrine of science" in general. This should explain the possibility of conceiving a worldly knowledge that incorporates the intrinsic dialectic of mathematical concepts, but at the same time supplements this internal conceptual development with something radically different: a reason-led action of experimenting and wagering on events in the world. I develop this view of Cavaillès in light of the ideas of some of the leading thinkers on the coordination problem: Mach, Poincaré, Schlick, Reichenbach, Carnap, Brunschvicg, Gonseth, Suzanne Bachelard, Bas van Fraassen.
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We offer a new perspective on Lautman's work, envisioning him as a "mathematical critic" rather than a so-called "philosopher of mathematics". We propose a distinction between Philosophy and Criticism, and, building on a study of Lautman's sources and mathematical studies, we situate the main bulk of his work in the realm of Mathematical Criticism.
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The aim of this article is to re-read Brunschvicg’s critical discussion of Russell’s philosophy. We attempt to highlight the philosophical reasons behind Brunschvicg’s distrust of logic, showing that in the final analysis his criticisms of Russell’s logicism relate to the difficulties Russell faces in thinking about the application of mathematics to the sciences of nature.
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Maximilien Winter was at the heart of French epistemology, shaping it by co-founding the Revue de métaphysique et de morale alongside Brunschvicg, Couturat, Halévy, and Léon. This study explores his unique philosophy through an examination of his extensive contributions to the Revue. Winter's philosophy directly opposed the dominant metaphysics, positivism, and logicism of his time. Instead, he advocated for a critical and historical epistemology of ideas and methods. For Winter, the role of philosophy was to clarify and organize the principles of science through a technical analysis of scientific texts and the development of ideas.
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This paper recovers the forgotten figure of Maximilien Winter, an early practitioner of mathematical philosophy in France whose work anticipated several later developments.
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By analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are imagined objects, some of which, at least approximately, exist in our internal world of activities or we can realize or represent them there; (ii) mathematical truths are not truths about the external world but specifications (formulations) of mathematical conceptions; (iii) mathematics is first and foremost our imagined tool by which, with certain assumptions about its applicability, we explore nature and synthesize our rational cognition of it.
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This is the second part of a tripartite paper discussing the research focus of the CIPSH Chair Diversity of Mathematical Research Cultures & Practices (DMRCP). We discuss a philosophical approach called "empirical philosophy of mathematics" and say why it should be done, who should do it, and how it should be done. This second part deals with the question "who?".
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A reflection on the relation between rationality and the meaning of the tools it uses, centered on the approaches of Gilles Châtelet and René Thom.
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A reflection on the relation between rationality and the meaning of the tools it uses, centered on the approaches of Gilles Châtelet and René Thom.
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