The author's aim in this biography is to shed light on the contrasts and polarity—yet relationship—between the rational and the irrational in Gödel's work and personality. On the one hand there is the genius logician whose technical work can be said practically to have attained the limits of what rational thought can produce; on the other hand, one is struck, claims the author, by the irrationality in Gödel's personality and psychic structure, such as his belief in the existence of spirits, (...) demons, angels, the devil, and other evil-wishing forces that he thought had haunted and deprived him of a peaceful existence.As is well known from other biographies, Gödel was of a frail physical health and psychic balance, having suffered from his student days on from bouts of depression and ‘nervous’ breakdowns—generally attributed to being overworked—that required at times short hospitalization in a sanatorium and culminating toward the end of his life in a marked deterioration in his mental health that resulted in his starving himself to death out of fear of being poisoned. These events are only mentioned here in passing.The author, who teaches philosophy at the University of Lille, is naturally interested in Gödel's philosophical views as well as in his metaphysical reflections, such as his thoughts about life after death and the survival of an immaterial soul. From the 1940s Gödel kept a philosophical diary that contains 670 handwritten notes, written in the now defunct Gabelsberger shorthand. Having feared controversies whenever his metaphysical/philosophical views went against the spirit of the times, Gödel was never led to a comprehensive publication of these views, preferring to put these notes in the private format of notebooks that are now preserved in his Nachlassat Princeton University. 1 The author had several opportunities to study the two of these notebooks …. (shrink)

The author's aim in this biography is to shed light on the contrasts and polarity—yet relationship—between the rational and the irrational in Gödel's work and personality. On the one hand there is the genius logician whose technical work can be said practically to have attained the limits of what rational thought can produce; on the other hand, one is struck, claims the author, by the irrationality in Gödel's personality and psychic structure, such as his belief in the existence of spirits, (...) demons, angels, the devil, and other evil-wishing forces that he thought had haunted and deprived him of a peaceful existence.As is well known from other biographies, Gödel was of a frail physical health and psychic balance, having suffered from his student days on from bouts of depression and ‘nervous’ breakdowns—generally attributed to being overworked—that required at times short hospitalization in a sanatorium and culminating toward the end of his life in a marked deterioration in his mental health that resulted in his starving himself to death out of fear of being poisoned. These events are only mentioned here in passing.The author, who teaches philosophy at the University of Lille, is naturally interested in Gödel's philosophical views as well as in his metaphysical reflections, such as his thoughts about life after death and the survival of an immaterial soul. From the 1940s Gödel kept a philosophical diary that contains 670 handwritten notes, written in the now defunct Gabelsberger shorthand. Having feared controversies whenever his metaphysical/philosophical views went against the spirit of the times, Gödel was never led to a comprehensive publication of these views, preferring to put these notes in the private format of notebooks that are now preserved in his Nachlassat Princeton University. 1 The author had several opportunities to study the two of these notebooks …. (shrink)

This paper is a discussion of Gödel's arguments for a Platonistic conception of mathematical objects. I review the arguments that Gödel offers in different papers, and compare them to unpublished material (from Gödel's Nachlass). My claim is that Gödel's later arguments simply intend to establish that mathematical knowledge cannot be accounted for by a reflexive analysis of our mental acts. In other words, there is at the basis of mathematics some data whose constitution cannot be explained by introspective analysis. This (...) does not mean that mathematics is independent of the human mind, but only that it is independent of our ?conscious acts and decisions?, to use Gödel's own words. Mathematical objects may then have been created by the human mind, but if so, the process of creation cannot be completely analysed and re-enacted. Such a thesis is weaker than some of the statements that Gödel made about his conceptual realism. However, there is evidence that Gödel seriously considered this weak thesis, or a position depending only on this weak thesis. He also criticized Husserl's Phenomenology from this point of view. (shrink)

This paper is concerned with Cavaillès’ account of “intuition” in mathematics. Cavaillès starts from Kant’s theory of constructions in intuition and then relies on various remarks by Hilbert to apply it to modern mathematics.

Periodically, we take stock of SubStance and provide a brief statement regarding initiatives and priorities in the journal's interests. Three years ago, we announced that "Exploring hybrid writing with theoretical impact is at the center of our current preoccupations."1 Since that time, the journal has made significant changes. This issue marks our fourth issue of publishing with Johns Hopkins University Press in a transition that recognizes our new publisher as a leader among university presses.Our plan also expressed our intent to (...) move toward publishing digital work that exemplifies theoretical thinking in nonlinear, experimental forms. In 2018, we launched Digital SubStance, a platform for "hybrid work that... (shrink)

A key feature of Buchanan is emphasis put on the social impact of biomedical enhancement. This social turn enables Buchanan to reframe the question of the desirability of enhancers. The fundamental question is no longer an individual question but a social question: what would be the advantages and the drawbacks of X in our society? The individual question, in Buchanan’s analysis, is second to the social question. Now, if one accepts that an enhancer may have secondary effects, or drawbacks, the (...) social question requires a cost and benefit analysis. I will argue that there are two flaws in Buchanan’s position: 1) the way in which he envisions the social debate about biomedical enhancement, and a cost and benefit analysis, would only be adequate in a kind of utopia which no actual existing State seems to match; 2) The cost and benefit analysis needs to be complemented not by an individual ethics but by narratives accounting for the experience of the subject. The level on which takes place Buchanan’s discussion covers up an individual experience which needs to be articulated and taken into account. It is this kind of individual, or singular, narrative that I will look for in the work of the post-phenomenological philosopher Jean-Luc Nancy, thus attempting to bridge a gap between two different philosophical traditions and styles of writing. (shrink)

This paper is concerned with Cavaillès’ account of “intuition” in mathematics. Cavaillès starts from Kant’s theory of constructions in intuition and then relies on various remarks by Hilbert to apply it tomodern mathematics. In this context, “intuition” includes the drawing of geometrical figures, the use of algebraic or logical signs and the generation of numbers as, for example, described by Brouwer. Cavaillès argues that mathematical practice can indeed be described as “constructions in intuition” but that these constructions are not imbedded (...) in the space and in the time of our Sensibility, as Kant bclieved: They take place in other structures which are engendered in the history of mathematics. This leads Cavaillès to a critical discussion of both Hilbert’s and Brouwer’s foundational programs. (shrink)

L’épistémologie de Cavaillès est connue pour une critique abrupte des notions de conscience et de sujet. Cette critique ne vise pas à éliminer de la philosophie la notion de conscience mais seulement à la destituer de sa place de notion primitive. Dès lors, il s’agit de rendre compte de la conscience. Nous soutenons que la conscience est définie et constituée à partir de la réflexivité du devenir mathématique. Pour établir ce point, nous discutons de quelques textes. Nous sommes amené à (...) distinguer deux problématiques, celle des thèses de 1938, qui restent marquées par la philosophie de Brunschvicg, et celle des écrits posthumes. (shrink)

Cet article interroge la place du platonisme de Lautman dans la tradition épistémologique en France à partir de Brunschvicg. Nous soutenons que, malgré sa position originale, le platonisme de Lautman s’intègre en effet dans cette tradition et doit être compris dans ce contexte. La première partie rappelle certains éléments du relativisme critique de Brunschvicg. La seconde tente une reconstruction de la philosophie de Lautman. Nous concluons en montrant comment le rôle donné par Brunschvicg à « l’expérience » se traduit chez (...) Lautman dans une difficulté propre, concernant la « matière » dans laquelle se réalisent les « Idées ».This paper considers the position of Lautman’s Platonism in the French tradition of epistemology starting with Brunschvicg. We claim that Lautman’s Platonism does indeed belong to this tradition and can only be properly understood in this context. The first section discusses Brunschvicg’s “critical relativism”. The second section aims at reconstructing in this context Lautman’s philosophy. Finally, we show that Brunschvicg’s inheritance — or, more specifically, the role that Brunschvicg gives to “experience” — leads in Lautman’s texts to a particular problem, concerning the “material” in which “Ideas” are realized. (shrink)

Jean Cavaillès, héros de la Résistance fusillé par les nazis au début de l’année 1944, s’est efforcé, dans son travail théorique, de prendre la mesure des avancées et des controverses qui ont détérminé les mathématiques modernes. Son œuvre, dont Goerges Canguilhem soulignait le caractère énigmatique, a exercé une influence considérable dans la philosophie française d’après-guerre.Le présent ouvrage est un commentaire chronologique et linéaire des principaux écrits de Cavaillès. Il s’agit d’expliquer un appareil conceptuel, mathématique et philosophique, et de restituer dans (...) sa progression un réflexion originale. On suit Cavaillès à travers la théorie des ensembles de Cantor, les recherches sur le fondement des mathématiques et la critique des philosophies de la conscience, de Brunschvicg et de Husserl. Ce parcours conduit ç la thématisation, derrière la dialectique des concepts, d’une expérience mathématique. Il se dessine un rapport d’analogie entre l’épistémologie de Cavaillès en tant qu’elle thématise une expérience, et l’ontologie du dernier Merleau-Ponty. Par cette analogie, on voudrait donenr un nouvel éclairage sur l’œuvre des deux philosophes. (shrink)

Résumé Cet article interroge la place du platonisme de Lautman dans la tradition épistémologique en France à partir de Brunschvicg. Nous soutenons que, malgré sa position originale, le platonisme de Lautman s’intègre en effet dans cette tradition et doit être compris dans ce contexte. La première partie rappelle certains éléments du relativisme critique de Brunschvicg. La seconde tente une reconstruction de la philosophie de Lautman. Nous concluons en montrant comment le rôle donné par Brunschvicg à « l’expérience » se traduit (...) chez Lautman dans une difficulté propre, concernant la « matière » dans laquelle se réalisent les « Idées ».This paper considers the position of Lautman’s Platonism in the French tradition of epistemology starting with Brunschvicg. We claim that Lautman’s Platonism does indeed belong to this tradition and can only be properly understood in this context. The first section discusses Brunschvicg’s “critical relativism”. The second section aims at reconstructing in this context Lautman’s philosophy. Finally, we show that Brunschvicg’s inheritance — or, more specifically, the role that Brunschvicg gives to “experience” — leads in Lautman’s texts to a particular problem, concerning the “material” in which “Ideas” are realized. (shrink)

The aim of this paper is to discuss the philosophical premises of Whitehead's definition of time in _The Concept of Nature and other works of the same period. Whitehead probably introduced this definition, which depends on what he calls the "method of extensive abstraction," in 1913, just after the publication of the _Principia Mathematica with Russell. He only published his results in 1919. However, Russell takes up the method, with slight modifications, after personal communication with Whitehead, as soon as 1914, (...) in _Our Knowledge of the External World. It is also carefully studied by G. Mead, in particular in _Philosophy of the Present, and by Merleau-Ponty, in his lectures at the Collège de France. (edited). (shrink)

If the greatest philosopher in the world finds himself upon a plank wider than actually necessary, but hanging over a precipice, his imagination will prevail, though his reason convince him of his safety. Many cannot bear the thought without a cold sweat. I will not state all its effects.This project explores phobia through twelve videos and many notes–absurd fears, where there is nothing to fear, really. Pascal's philosopher standing on the plank above the abyss knows there is nothing to fear. (...) He knows the plank is large enough. But it does not help. It is as if his vertigo were beyond the reach of his philosophy.When Descartes is attacked by thieves on a boat crossing the Elbe, he does not panic. He draws... (shrink)

Cet article est une discussion de l’ouvrage de A. Badiou, L’être et l’événement, autour de la question du rapport de l’état (et de l’Etat) à la situation. Nous commençons par rappeler la place que donne A. Badiou aux mathématiques dans son dispositif. Nous parcourons ensuite L’être et l’événement en prenant comme fil directeur cette question, du rapport de l’état à la situation. La dernière partie compare la position de A. Badiou à la tradition « épistémologique » en France et, en (...) particulier, aux textes de Jean Cavaillès, dont A. Badiou se réclame à plusieurs reprises. L’originalité de A. Badiou dans cette tradition est sans doute sa rupture avec la perspective historique mais le problème, que cette confrontation pose, est de savoir s’il est en effet possible de couper les théories mathématiques de leur histoire, comme A. Badiou doit le faire. (shrink)

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. (shrink)

— Nous interrogeons la fonction du concept d’organisme dans l’œuvre de Whitehead et l’élaboration de la cosmologie de Procès et réalité. Notre but est de déterminer à quels problèmes ce concept répond et de quelles hypothèses il découle. Whitehead justifie sa description des entités actuelles par le postulat cosmologique d’une homogénéité entre l’expérience humaine et les événements de la nature. Nous tentons, quant à nous, de montrer que le concept d’organisme dépend également, dès Le concept de nature, de l’hypothèse d’une (...) vie intérieure et qu’il relève finalement de ce que Cavaillès appelait une philosophie de la conscience.We investigate the function of the concept of organism in Whitehead’s philosophy. We wish to find out which problems this concept answers and from which hypothesis it follows. Whitehead justifies his description of actual entities by the cosmological postulate : the homogeneity of human experience and events in nature. We try to show that the concept of organism also depends on the hypothesis, already in The Concept of Nature, of an interiority and, therefore, belongs to what Cavaillès called a philosophy of consciousness. (shrink)

The aim of this paper is to analyse the reference to space and time in the foundation of mathematics. First, we describe the reference to time in Brouwer’s intuitionism and in Hilbert’s formalism in order to show that the reference to time leads to different restrictions on what can be considered a mathematical proof. We then study three attempts, by Frege, by Hilbert around 1900, by Gentzen, to eliminate the reference to time and ground mathematics on the intuition of space.RésuméLe (...) but de cet article est d’étudier la référence à l’espace et au temps dans le problème du fondement des mathématiques, au cours de la période 1880-1935. Après avoir évoqué la problématique kantienne, qui reste présente dans la controverse entre Brouwer et Hilbert, nous discutons de la référence au temps dans l’intuitionisme et dans le programme formaliste pour montrer comment, dans les deux cas mais de façon différente, la référence au temps introduit des restrictions sur ce qui peut être considéré comme une démonstration mathématique. Nous évoquons ensuite trois tentatives, Frege, le Hilbert d’avant le programme formaliste et Gentzen, pour éliminer la référence au temps et ne fonder les mathématiques que sur l’intuition de l’espace. (shrink)

Le but de cet article est de discuter d'une méthode philosophique, une façon de faire de la philosophie, fondée sur la fiction narrative. Il s'agit de réfléchir sur le recours à la fiction en philosophie ou d'en rendre l'usage explicite, systématique et de le fonder. L'hypothèse de départ est que la fiction narrative est le mode de donation du possible tel que l'exige l'analyse philosophique. Je commence par discuter de cette hypothèse avant de la confronter à la variation éidétique de (...) Husserl et de l'opposer à l'idée d'ordinaire telle que l'on peut la tirer des remarques du deuxième Wittgenstein. (shrink)

I could buy a Pepper, or better a Nao. I have seen him at Darty's last Sunday. A jolly little fellow, with a friendly face of white plastic and a perpetual smile. I shook his three fingered hand, and he said a few words, something like, "Welcome in, enjoy the evening." At home, it would be different. I could try and teach him things. I would let him wheel around the apartment, and make sure everything is alright. If I were (...) living in Japan, I could buy it as an individual. In France, I would have to pretend I am buying the robot for my university. I would have to pay for it myself, though. But I could: $9,500. I would have to sell the car. My partner might not be too happy. The children would be excited at first... (shrink)

Jean Cavaillès, héros de la Résistance fusillé par les nazis au début de l’année 1944, s’est efforcé, dans son travail théorique, de prendre la mesure des avancées et des controverses qui ont détérminé les mathématiques modernes. Son œuvre, dont Goerges Canguilhem soulignait le caractère énigmatique, a exercé une influence considérable dans la philosophie française d’après-guerre.Le présent ouvrage est un commentaire chronologique et linéaire des principaux écrits de Cavaillès. Il s’agit d’expliquer un appareil conceptuel, mathématique et philosophique, et de restituer dans (...) sa progression un réflexion originale. On suit Cavaillès à travers la théorie des ensembles de Cantor, les recherches sur le fondement des mathématiques et la critique des philosophies de la conscience, de Brunschvicg et de Husserl. Ce parcours conduit ç la thématisation, derrière la dialectique des concepts, d’une expérience mathématique. Il se dessine un rapport d’analogie entre l’épistémologie de Cavaillès en tant qu’elle thématise une expérience, et l’ontologie du dernier Merleau-Ponty. Par cette analogie, on voudrait donenr un nouvel éclairage sur l’œuvre des deux philosophes. (shrink)

— Nous interrogeons la fonction du concept d’organisme dans l’œuvre de Whitehead et l’élaboration de la cosmologie de Procès et réalité. Notre but est de déterminer à quels problèmes ce concept répond et de quelles hypothèses il découle. Whitehead justifie sa description des entités actuelles par le postulat cosmologique d’une homogénéité entre l’expérience humaine et les événements de la nature. Nous tentons, quant à nous, de montrer que le concept d’organisme dépend également, dès Le concept de nature, de l’hypothèse d’une (...) vie intérieure et qu’il relève finalement de ce que Cavaillès appelait une philosophie de la conscience.We investigate the function of the concept of organism in Whitehead’s philosophy. We wish to find out which problems this concept answers and from which hypothesis it follows. Whitehead justifies his description of actual entities by the cosmological postulate : the homogeneity of human experience and events in nature. We try to show that the concept of organism also depends on the hypothesis, already in The Concept of Nature, of an interiority and, therefore, belongs to what Cavaillès called a philosophy of consciousness. (shrink)

This article presents three extracts from the introductory course in mathematical logic that Gödel gave at the University of Notre Dame in 1939. The lectures include a few digressions, which give insight into Gödel's views on logic prior to his philosophical papers of the 1940s. The first extract is Gödel's first lecture. It gives the flavour of Gödel's leisurely style in this course. It also includes a curious definition of logic and a discussion of implication in logic and natural language. (...) The second extract is a discussion on undecidability and on Leibniz. The third extract concerns the paradoxes and Russell's theory of types. (shrink)

This issue should have been entitled, "The Man-Machine." It was the title that we had submitted to SubStance. At first, there was no question of dismantling the man-machine. The dismantling of the man-machine was an accident.This issue originates from a seminar organized at University of Paris 7, in the laboratory SPHERE, by Pierre Cassou-Noguès, Viktoria Tkaczyk, and Koen Vermeir. It ran for several years. The idea was to meet about once a month and invite scholars from various disciplines (...) around a common machine, or at least around machines with a common function. There were historians of science and technology, scholars in literature, art, media studies, gender studies, philosophers of science, and... (shrink)

Albert Lautman. Mathematics, Ideas and the Physical Real. Simon B. Duffy, trans. London and New York: Continuum, 2011. 978-1-4411-2344-2 (pbk); 978-1-44114656-4 (hbk); 978-1-44114433-1 (pdf e-bk); 978-1-44114654-0 (epub e-bk). Pp. xlii + 310.

This issue of SubStance is the first since 2010 not dedicated to a specific theme or author; it features ten eclectic essays submitted from different disciplines and countries by well-established as well as emerging scholars. We wish to take this opportunity to emphasize the importance of these varia, which illustrate the range of our speculative and critical interests, and to signal directions we anticipate the journal moving in the near future. Beyond its interest in French literature and theory, SubStance has (...) always promoted a dialogue between contemporary theory and a multifaceted outside, an outside where contemporary theory may be used to investigate literary, philosophical, and artistic traditions.. (shrink)

History and Philosophy of Logic, Volume 33, Issue 2, Page 193-195, May 2012.

My uncle is obsessed with thermometers. I have seen him, in the street, stop in front of a chemist to check whether there would not be a thermometer in the window. Then he would carefully read the temperature. In his house, every room has its own thermometer. There are thermometers hidden in various places in the garden, too. When he is visiting, he often leaves a thermometer somewhere in the house. He may pity his hosts, living without a thermometer at (...) hand. But, more likely, he just wants to make sure that he will be able to read the room temperature next time he comes. He is afraid to be too hot. He thinks that you are more likely to catch viruses when you are hot... (shrink)

L’auteur mène une analyse de la perception, au travers des notions d’invisible et d’intangible, et envisage la possibilité d’une phénoménologie imaginaire – si ce n’est de l’imaginaire. Les anges, l’homme invisible, le yéti, Dracula, et même aussi Dieu, ou bien les robots et les ordinateurs, sont en effet des êtres possibles, qui ont de fait une portée ontologique et peuvent par suite énoncer une propriété de l’existence. La thèse est donc simple : notre imaginaire, depuis le début du XIXe siècle, (...) est structuré par l’opposition entre deux figures, le vampire et la machine. (shrink)

L’ouvrage conjoint un double effort, que résume parfaitement le titre : Penser avec Whitehead. Au départ, l’ouvrage se présente comme un commentaire de l’œuvre de Whitehead. Isabelle Stengers cherche à éclairer les textes, souvent difficiles, de Whitehead et cela par ordre chronologique, pour en particulier analyser le passage de l’épistémologie à la cosmologie et les différentes strates de la cosmologie. Whitehead, qui a rédigé avec Russell les Principia Mathematica, commence son œuvre philo..