Albert Lautman

In Différence et répétition, Deleuze’s ontology is structured by his theory of dialectical Ideas or problems, which draws features from Plato, Kant, and classical calculus. Deleuze unifies these features through a theory of Ideas/problems developed by the mathematician and philosopher Albert Lautman. Lautman worked to explain the nature of the problems or dialectical Ideas mathematics engages and the solutions or mathematical theories endeavouring to understand them. Lautman drew upon Heidegger to do this. This article (1) clarifies Deleuze’s theory of dialectical Ideas/problems by analysing its debts to Lautman and Heidegger and (2) demonstrates a Heideggerian influence on Deleuze via Lautman.

This paper concerns the role of mathematical problems in the epistemology of Jean Cavaillès. Most occurrences of the term “problem” in his texts refer to mathematical problems, in the sense in which mathematicians themselves use the term: for an unsolved question which they hope to solve. Mathematical problems appear as breaking points in the succession of mathematical theories, both giving a continuity to the history of mathematics and illuminating the way in which the history of mathematics breaks up into successive theories with different kinds of operations and, in a sense, different kinds of a prioris. We briefly compare mathematical becoming to the succession of episteme in Foucault’s Les Mots et les choses. We then come back to the necessity that Cavaillès attributes to mathematical becoming, and which the position of mathematical problems illustrates, in order to discuss its various consequences in Cavaillès’ later works but also in Canguilhem’s discussion of Cavaillès’ role in the Resistance. Finally, we study other types of problems, in Cavaillès’ writings: philosophical problems and what we will call “questions” rather than “problems,” and which contrary to mathematical problems, as Cavaillès uses the term, cannot be solved but pervade the whole of the history of mathematics. We will put these “questions” in relation to Lautman’s Ideas.

Comment le thème des Prétendants, dressé par l'Odyssée dans une deuxième couche d'épopée, en traversant les trois couches de tragédie évoquées par Nietzsche dans "La naissance de la philosophie à l'époque de la tragédie grecque" va donner le logis de la philosophie dans la Ligne de Platon sur laquelle, aux prétendants sophistiques ou socratiques, vont être proposés comme objets X du désir et de la Dialectique les termes transcendentaux dont la première liste et la plus complète a été dressée avant la lettre par le disciple de Socrate destiné à devenir le maître d'Aristote.

This paper presents a short study of the relation between the concept of ‘model’ as explained in its logical sense by Alain Badiou in his 1969 work, The Concept of Model, and the model of politics as elaborated by Sylvain Lazarus in Anthropology of the Name, written in 1998. The study aims to show that, using Badiou’s concept of model, we can better understand the often-complex grammar that Lazarus adopted for his model of politics.

This paper presents a short study of the relation between the concept
of ‘model’ as explained in its logical sense by Alain Badiou in his 1969 work, The Concept of Model, and the model of politics as elaborated by Sylvain Lazarus in Anthropology of the Name, written in 1998. The study aims to show that, using Badiou’s concept of model, we can better understand the often-complex grammar that Lazarus adopted for his model of politics.

This paper investigates the influence of the mathematical problematic on the political function of Gilles Deleuze’s work (including his work with Guattari). Most prominent is an investigation into the Deleuzian problematic—signified by Deleuze as the (non)being or? being of being—which is traced through the work of French mathematics by way of Georges Bouligand, Salomon Maïmon and Albert Lautman. This mode of mathematical formalization is explored in relation to Kantian axiomatization (in terms of both extensive magnitudes and intensive magnitudes/distances, as well as the relationship between problems and ideas). This paper explores the way that Deleuze uses Lautman’s discussion of the mathematical real to bring mathematical concepts into other discourses (such as politics). The paper concludes by enacting this move, exploring the way that the concept of the problematic is used within the political register by putting it into conversation with the aleatory.

Continuity inscribes itself in the heart of almost every system—philosophical, physical, mathematical, vital, perceptual. It is not unusual for both the domain and the "conceptual machinery" crafted to survey that domain to draw explicitly and implicitly upon continuity. But few of these systems have concerned themselves with the provenance of continuity, or evinced much of an appreciation for its (often) destabilizing effects. There might be a reason for this: those who have tried to bring continuity into focus—either by unifying its various instantiations in a single concept or by grounding its different instantiations in a logical or experiential invariant—have foundered on rather caustic shoals. It is no accident that Leibniz identified the composition of the continuum as the principal labyrinth palling philosophical praxis.