La réflexion Benthamienne sur les mathématiques

In 1814, Jeremy Bentham began to writeChrestomathia; this work is a presentation of what is useful to learn. However this text is, more generally, an entire organization of the knowledge of his time, through developing a «theory of fictions», which is a reflexion on concepts and a critics of nomenclatures. The following essay focuses on the fifty pages refering to mathematics in a work that considers the integrality of sciences at the beginning of the xix^th century and criticizes the FrenchEncyclopédie of Diderot and D’Alembert. A most singular idea expressed by the author, indirectly echoed by Gaston Bachelard through some books, is the conflict between concepts and their being designated by words. Signified, signifying entities and concepts are reciprocally adrift so that nobody, even the scholar, can keep control of these motions; what makes education unceasingly difficult.     

Paul Bernays et la rénovation des fondements philosophiques des mathématiques

The history of the foundations of mathematics in the XX^th century leads to a revision of the meaning of traditional philosophical notions such as «evidence», «experience» or «rationality». This paper focuses on the influence of Ferdinand Gonseth's «open philosophy» on Paul Bernays' philosophical interpretations of the technical results in the foundations. Familiar with the ideas of Jacob Friedrich Fries and Léonard Nelson, the logician Bernays turns at the middle of the century more and more towards Gonseth's ideas. Quite before Thomas Kuhn, Bernays considers the revisions under consideration not simply as a problem of truth and falsehood, but as a task requiring the introduction of a new conceptual system. Indeed, in opposition to Kuhn, according to Bernays, the necessary change is less the consequence from a change of paradigm and methodological incommensurability as a epistemological necessity.     

L’histoire des mathématiques de l’Antiquité

Historical research, during the last half-century, has improved our knowledge of the mathematics of Antiquity. Texts from Egypt and Mesopotamia have been better understood and their elucidation has left behind the crude alternative between empricism and rationalism. The landscape offered by Greek science grew richer and became more varied: it is no longer possible to reduce it to the sole geometrical theory. The main problems which were raised by its history have been deeply discussed. Things being so, more general questions arise, from an epistemological or philosophical point of view. Does the search into some far past of a single «birth» of mathematics make any sense? What link, if any, is there between the form of mathematics in such and such a civilization and its social structure? Can cultural anthropology help to elucidate the variety and unity of mathematics among various peoples? From what time and under what conditions is it possible for a single united historical progress of mathematics to begin?     

La vertu des images. Analogie, proportion et métaphore dans la genèse des sciences sociales au XVIIIe siècle

Moral newtonianism, in fashion by the middle of the XVIII^th century, is not only a metaphor. Based on the oneness of nature, it assumes a law of society equivalent to the law of distance innewtonian physics, perhaps offering the possibility of measurement. This method of inductive analogy (A/B=C/D) underlies Jean-Jacques Rousseau'sSocial contract: Rousseau uses classical metaphors of clockwork, modeling his notion of government on a watch and including mathematical proportions used by clockmakers to design the parts. Similarly, in hisTheory of moral sentiments, Adam Smith uses the old metaphor of the eye of the mind, modeling his social system on the recent notions of perspective: two persons, when they meet, will regulate their passions — of any type except interest — according to an imaginary distance between them, which varies according to the nature of the passion and its level. It is essential to restore these translations and the subsequent debates in order to understand the implications for sociology throughout the XIX^th century.     

Questions ethnographiques et mathématiques de la préhistoire

The study of the mathematics of prehistory cannot be founded on bare archeological data alone; it may be useful to set the archeological documents in context, with the help of comparative ethnography, according to which our own contemporaray or near-contemporary primitive societies can help us understand our prehistoric ancestors. Although once used spontaneously by several historians of mathematics, this approach has been rejected on principle by the recent school of ethnomathematicians. This paper sets out to show, by means of a certain number of examples, that the method can nonetheless yield rewards: on the one hand because it demolishes the fantastic theories so fondly constructed by certain mathematicians, and on the other because it opens up a vast field of research which has so far been vitually unexplored.     

La prière Ahuna Varya dans son exégèse zoroastrienne

Sans résumé     

La Dissuasion nucléaire française: Genèse et actualité

This article reviews three recent books on the history of the late nineteenth-century French anarchist movement—one by the French historian Vivien Bouhey and the other two by American scholars, Alexander McKinley and John Merriman. It replaces these works in the context of a renewed interest in the study of the anarchist movement, as an early example of transnational terrorist organisation, and as a relevant field of application for the historiographic concepts of network and transnationalism. In conclusion, it highlights the differences between French and US approaches to the study of anarchism, and evidences the limits of the ‘transnational turn’ in this particular historical field.     

La Fabrique de l’infini Phénoménologie du désordre et genèse sensible de l’idée d’infini chez Diderot

Against the classical point of view, for which the idea of the infinite is the expression of God’s in the human being, Diderot proposes a concept of the infinite that considers it as an immediate production of the body. Removing the infinite from its former divine origin, Diderot’s idea of the sentient body contests the classical concepts, particularly the one of order, which bound epistemology to theology. Thus, disorder acquires a new value, even in its pathological forms, which now can be considered as modes of an immanent and fundamentally creative process.     

Exégèse de l'ahuna vairya

Sans résumé