Carlos Lobo

By going back to the starting point of Derrida’s debates with some of the main representatives of structuralism in France, I propose to highlight the ambiguities that cover the very notion of structure, and to take the measure of the exact role that the reference to phenomenology plays then and will continue to play thereafter. Among these ambiguities: the one that touches the mathematical notion of structure, central in the triumphant structuralist mathematical current in France at that time; and especially: the one called “groups of transformations,” the most important one to understand at the same time the audacities and the impasses of structuralism. The hard core of mathematization of modern physics, with Galileo’s principle of relativity, then developed in a masterly way in Einstein’s theory of relativity rest on this very structure. After tracing the broad outlines of these initial discussions, we engage in an analysis of how it is possible to understand the “epistemological contemporaneity” of relativity theory and Husserl’s transcendental aesthetics. Based on a thorough exploration of the analyses of the intersubjective constitution of space, time and the objective common world, we identify this central structure that Husserl calls “intersubjective group of transformation.” Equipped with this phenomenological structure, we trace this motif in Derrida’s work. Its insistence allows us to understand how the phenomenological premises of his critique of structuralism can help to understand his theoretical positions, especially in contrast to Jean-Luc Nancy.

This interdisciplinary volume collects contributions from experts in their respective fields with as common theme diagrams. Diagrams play a fundamental role in the mathematical visualization and philosophical analysis of forms in space. Some of the most interesting and profound recent developments in contemporary sciences, whether in topology, geometry, dynamic systems theory, quantum field theory or string theory, have been made possible by the introduction of new types of diagrams, which, in addition to their essential role in the discovery of new classes of spaces and phenomena, have contributed to enriching and clarifying the meaning of the operations, structures and properties that are at the heart of these spaces and phenomena. The volume gives a closer look at the scope and the nature of diagrams as constituents of mathematical and physical thought, their function in contemporary artistic work, and appraise, in particular, the actual importance of the diagrams of knots, of braids, of fields, of interaction, of strings in topology and geometry, in quantum physics and in cosmology, but also in theory of perception, in plastic arts and in philosophy. The editors carefully curated this volume to be an inspiration to students and researchers in philosophy, phenomenology, mathematics and the sciences, as well as artists, musicians and the general interested audience.

This interdisciplinary volume collects contributions from experts in their respective fields with as common theme diagrams. Diagrams play a fundamental role in the mathematical visualization and philosophical analysis of forms in space. Some of the most interesting and profound recent developments in contemporary sciences, whether in topology, geometry, dynamic systems theory, quantum field theory or string theory, have been made possible by the introduction of new types of diagrams, which, in addition to their essential role in the discovery of new classes of spaces and phenomena, have contributed to enriching and clarifying the meaning of the operations, structures and properties that are at the heart of these spaces and phenomena. The volume gives a closer look at the scope and the nature of diagrams as constituents of mathematical and physical thought, their function in contemporary artistic work, and appraise, in particular, the actual importance of the diagrams of knots, of braids, of fields, of interaction, of strings in topology and geometry, in quantum physics and in cosmology, but also in theory of perception, in plastic arts and in philosophy. The editors carefully curated this volume to be an inspiration to students and researchers in philosophy, phenomenology, mathematics and the sciences, as well as artists, musicians and the general interested audience.

Une épistémologie phénoménologique est nécessairement intéressée aux points de contact et de passage entre problèmes scientifiques et problèmes philosophiques. Il est instructif, dans cette perspective, de revenir sur un moment historiquement décisif, mais éminemment équivoque, encore porteur de prolongements et de retournements dont nous n’avons peut-être pas encore pris toute la mesure : l’énoncé du principe de Pauli. Le statut logique de cet énoncé est lui-même ambigu : règle technique, semi-empirique, postulat, principe ou théorème, etc. Pour le meilleur et le pire, ce principe se trouve accouplé dès l’origine au problème de l’individuation en physique. Nous proposons de revenir sur quelques traits philosophiquement saillants des interprétations que Weyl et de Broglie proposent dudit « principe d’exclusion Pauli » (ou PEP). L’un et l’autre y voient l’occasion d’un approfondissement du principe d’individuation prévalant jusqu’alors dans la physique classique : l’espace. Weyl associe le PEP au principe leibnizien des indiscernables et tente de modéliser l’espace en jeu au moyen de la théorie des groupes. Les changements de position de Pauli lui-même à ce propos ne sont pas moins instructifs. La position de De Broglie sur ce principe est un marqueur de sa trajectoire : de la théorie audacieuse, et, équivoque, de « l’onde-pilote », jusqu’à celle dite de la « double solution », en passant par la période de rétractation consécutive au congrès de Solvay de 1927. Ce qui persiste d’un bout à l’autre, c’est un partage entre espace « réel » empirique et espace de configuration mathématique imaginaire. Chez l’un et l’autre, cette interprétation est ainsi indissociable d’un nouveau partage du subjectif et de l’objectif et d’une réflexion critique sur le principe traditionnel d’individuation qu’est l’espace (ou le temps physique) au profit d’une articulation toujours plus subtile et complexe entre l’espace de la phénoménalisation (de l’observation) et les « espaces » de la modélisation mathématique, en particulier les espaces des états possibles décrits dans le formalisme de la statistique quantique.

This book investigates Hermann Weyl’s work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. Despite this freedom, Weyl “deduces”, with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This construction was then decisive for the development of gauge theories. Nevertheless, the question of the foundations of the metric of physical theories is only a piece of a wider epistemological problem. Contributing authors mark out the double trajectory that goes through Weyl’s texts, from natural science to philosophy and conversely, always through the mediation of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which he is inspired, and explore the mathematical tradition that permitted Weyl to elaborate and solve his mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors with whom Weyl discussed the nature of physical space. This volume features the work of top specialists and will appeal to postgraduates and scholars in philosophy, the history of science, mathematics, or physics.

Roshdi Rashed’s work illustrates perfectly what can be a conscious and cautious practice of reflection, with the purpose of setting history of science on renewed and deeper grounds.). This entails the methodical operations that he enumerates, such as enlargement towards undermined or ignored traditions, careful and reasoned decompartmentalization of disciplines, correlative changes of periodization. and appendices in The Notion of Western Science: “Science as a Western Phenomenon” and “Periodization in Classical Mathematics”.) Among mathematicians, Gian-Carlo RotaRota, Gian-Carlo is certainly both exceptional and, for this reason, exemplary. By choosing this perspective as a tribute, I hope that Roshdi Rashed will consider my comments not too unworthy. For any philosopher of science not insensitive to history of science, and for any historian not completely allergic to philosophical reflection, studying Rota’s contribution in the fields of logic and phenomenology reveals itself instructive and fruitful. Contrary to dominant trends amongst his colleagues, in his own way, RotaRota, Gian-Carlo showed a strong and continuous interest in logic, history of science and philosophy.

Les variations de Gilles Châtelet Sur une petite phrase de Riemann, montrent que loin de constituer une variante de la « philosophie baroque » telle que la définit Deleuze, son maniérisme épistémologique le rapproche étonnamment de l’attention aux « modes de données » et aux « modes de visée » caractéristique de la phénoménologie transcendantale. Comme Hermann Weyl, il voit à l’œuvre dans la phénoménologie husser-lienne un approfondissement de l’esthétique transcendantale kantienne, en la tenant pour une approche philosophique pertinente et ajustée à la science de son temps.Châtelet’s variation on a note by Riemann, shows that, far from constituting a variant of the “Baroque philosophy” such as Deleuze defines it, his epistemological mannerism pays attention to “modes of givenness” and “modes of constitution”, which is characteristic of transcendental phe-nomenology. This explains why he considers, like Hermann Weyl, phe-nomenology as a deepening of Kant’s transcendental aesthetics and as a philosophical approach, relevant and adapted to the science of his time. It is in this perspective that we should hear their joint statements that transcendental phenomenology is epistemologically contemporary to special and general relativity. Châtelets Variation auf einer kleinen Phrase von Rie-mann zeigt, daß sein erkenntnistheoretischer Manierismus, eine Variante der nach Definition „barocken Philosophie“ von Deleuze weit entfernt zu sein, im Gegenteil in der Nähe von transzendentale Phänomenologie und seine Aufmerksamkeit auf die „Gegebenheitsmodi“ und „Konstitution-sweise“ steht. Überdies betrachtet er, wie Hermann Weyl, die Phänomenol-ogie und die Vertiefung der transzendentalen Ästhetik als philosophischen Ansatz für die Wissenschaft seiner Zeit. Es ist in dieser Perspektive, dass wir ihre gemeinsamen Aussagen hören, dass die Kantische Ästhetik in Husserls vertieft wird, und dass die transzendentale Phänomenologie epistemologisch zeitgenössisch ist für speziell und allgemeine Relativität.This article is in French.

RésuméGian-Carlo Rota est l’un des rares grands mathématiciens de la deuxième moitié du XX e siècle dont l’intérêt pour la logique formelle soit aussi ouvertement déclaré et ne se soit jamais démenti, depuis sa formation d’étudiant à Princeton jusqu’à ses derniers écrits. Plus exceptionnel encore, il fait partie des rares lecteurs assidus de Husserl à s’être aperçu que la phé-noménologie poursuivait un projet de réforme de la logique formelle. L’article propose d’attester l’existence d’un tel projet chez Husserl ; d’en examiner la réappropriation et les prolongements chez Rota.Gian-Carlo Rota is among the few great mathematicians of the second-half of the XXth century whose interest in formal logic is openly declared and has never flagged, since his training as a student in Princeton up to his last writings. Even more exceptional, he belongs to the rare diligent readers of Husserl, who noticed that phenomenology was pursuing a project of reform of formal logic. This paper propose to testify to the existence of such a project in Husserl; to examine how it is taken over and continued by Rota. Gian-Carlo Rota è uno dei pochi grandi matematici della seconda metà del ventesimo secolo, il cui interesse per la logica formale è, dalla sua formazione come studente a Princeton al suo ultimi scritti, apertamente dichiarato e mai negato. Cosa ancora più eccezionale, Rota è uno dei rari lettori assidui di Husserl ad aver percepito che la fenomenologia stava perseguendo un progetto di riforma della logica formale. L’articolo propone di attestare l’esistenza di un tale progetto in Husserl e di esaminare la sua riappropriazione e le sue estensioni proposte da Gian-Carlo Rota.This article is in French.

Departing from modal logic, Jean-Yves Girard, as a logician interested in philosophy, presented a distinction between essentialism and existentialism in logic. Carlos Lobo reflected about the Girard’s concept to reinterpret the Husserlian Platonism in regard of the status of logical modalities. We start rescuing the notion of modal logic in the Edmund Husserl’s works, especially Formal and Transcendental Logic and First Philosophy. Developing this reflexion, we propose a new contribution to this discussion, reinterpreting the platonic influence in the Husserlian notions of eidos and science, light of some readings of Lee Hardy and Johanna M. Tito. As a conclusion of this dialogue between Husserl and Girard, the method of eidetic variation is presented as a tool to review the idea of science, in a manner consistent with the phenomenological approach

Il est difficile de mesurer et de fixer la portée historique de la décontruction en tant qu’événement. C’est peut-être même impossible, si le « messianique », tel que l’entend Derrida, en constitue la dimension véritable, puisqu’elle excède alors tout horizon et donc toute anticipation. Il reste qu’elle se traduit, ici et maintenant, par certaines prises de positions théoriques et politiques dont on peut et doit repérer les effets et dont il incombe à une pratique responsable de la philosophie de déchiffrer les présupposés et les implications. Dans cette optique, il importe tout particulièrement de déterminer les modalités selon lesquelles la déconstruction, en tant qu’attitude et activité intellectuelle, reste endettée auprès de la critique, telle que Marx et Husserl ont prétendu la radicaliser.

Following Derrida’s late analysis of the multifarious concept of resistance, this article aims at detecting the motives that lead him to install from the start a tension between two methods of analysis of consciousness (phenomenological and psychoanalytical), that many would have considered, if not affectively unbearable, at least logically unsustainable. Yet this general logical and affective attitude remains describable, and in order to do so, the author proposesto delve into some underestimated and hence underexploited resources of transcendental phenomenology, particularly those related to the analysis of affectivesyntaxes of consciousness, which are part of the “realm of positionality”.