In this paper is presented and discussed the notion of true finite by opposition to the notion of theoretical finite. Examples from mathematics and physics are given. Fermat’s infinite descent principle is challenged.

ABSTRACTIn this paper, I offer an account of propositional learning: namely, learning that p. I argue for what I call the “Three Transitions Thesis” or “TTT” according to which four states and three transitions between them characterize such learning. I later supplement the TTT to account for learning why p. In making my case, I discuss mathematical propositions such as Fermat's Last Theorem and the ABC Conjecture, and then generalize to other mathematical propositions and to non-mathematical propositions. I also (...) discuss some interesting applications of the TTT, and reply to some noteworthy objections. (shrink)

En partant du problème des partis, conçu comme un dialogue entre partenaires, nous ferons ressortir le tissage de sa structure avec des considérations religieuses et éthiques; puis nous reconsidérerons l’argument dit « du pari » en l’interprétant, mutatis mutandis, comme une préfiguration de la théorie des jeux plutôt que comme la résolution d’un problème de probabilité, ce qu’il est plus évidemment sous la plume de Fermat qui, à la limite, ne résout pas le même problème que Pascal, quoique les (...) deux épistoliers aient pu en avoir l’impression. (shrink)

The first half of the 17th century was a time of intellectual ferment when wars of natural philosophy were echoes of religious wars, as we illustrate by a case study of an apparently innocuous mathematical technique called adequality pioneered by the honorable judge Pierre de Fermat, its relation to indivisibles, as well as to other hocus-pocus. André Weil noted that simple applications of adequality involving polynomials can be treated purely algebraically but more general problems like the cycloid curve (...) cannot be so treated and involve additional tools–leading the mathematician Fermat potentially into troubled waters. Breger attacks Tannery for tampering with Fermat’s manuscript but it is Breger who tampers with Fermat’s procedure by moving all terms to the left-hand side so as to accord better with Breger’s own interpretation emphasizing the double root idea. We provide modern proxies for Fermat’s procedures in terms of relations of infinite proximity as well as the standard part function. (shrink)

This paper introduces a little-known episode in the history of physics, in which a mathematical proof by Pierre Fermat vindicated Galileo’s characterization of freefall. The first part of the paper reviews the historical context leading up to Fermat’s proof. The second part illustrates how a physical and a mathematical insight enabled Fermat’s result, and that a simple modification would satisfy any of Fermat’s critics. The result is an illustration of how a purely theoretical argument can (...) settle an apparently empirical debate. (shrink)

Bien des difficultés que nous éprouvons à comprendre les oeuvres philosophiques des Anciens proviennent souvent du fait que nous commmettons en les interprétant un double anachronisme: nous croyons que, comme beaucoup d'oeuvres modernes, elles sont destinées à communiquer des informations concernant un contenu conceptuel donné et que nous pouvons aussi en tirer directement des renseignements clairs sur la pensée et la psychologie de leur auteur. Mais en fait, elles sont très souvent des exercices spirituels que l'auteur pratique lui-même et fait (...) pratiquer à son lecteur. Elles sont destinées à former les âmes. Elles ont une valeur psychagogique. (shrink)

Pierre Bourdieu is arguably one of the twentieth century’s greatest socio-philosophical thinkers and his writings have much to offer anyone interested in the ways that people value, consume and produce architecture. Bourdieu spent much of his life attempting to understand cultural consumption and production through detailed empirical research that included studies of dwellings, art, museums, photography and aesthetics. This book introduces the architectural reader to Bourdieu’s key writings on culture and outlines the ways in which they offer powerful practical (...) tools and novel conceptual frameworks for understanding architectural value, taste, and practice. (shrink)

Synthesizing forty years' work by France's leading sociologist, this book exemplifies Bourdieu's unique ability to link sociological theory, historical information, and philosophical thought. It makes explicit the presuppositions of a state of 'scholasticism', a certain leisure liberated from the urgencies of the world. Philosophers have brought these presuppositions into the order of discourse, more to legitimate than analyze them, and this is the primary systematic, epistemological, ethical, and aesthetic error that Bourdieu subjects to methodological critique. Pascalian because he, too, was (...) concerned with symbolic power, he refused the temptation of foundationalist thinking, attended to 'ordinary people', and was determined to seek the reason for seemingly illogical behavior rather than simply condemning it. Bourdieu charts a negative philosophy, whose intellectual debt to such other 'heretical' philosophers as Wittgenstein, Austin, Dewey, and Peirce, renews traditional questioning of concepts of violence, power, time, history, the universal, and the purpose and direction of existence. (shrink)

The authors develop an analysis of education. They show how education carries an essentially arbitrary cultural scheme which is actually based on power. More widely, the reproduction of culture through education is shown to play a key part in the reproduction of the whole social system.

Cambrai, Bibl. munic. 940, ff. 1-59 [integralement reproduit]--Bibl. Vatic. Reg. Lat. 689 A, ff. 334-353.--Bibl. Vatic. Reg. Lat. 1653, ff, 1v-2v (feuilles de garde), ff. 3r, 29r-35r.--Pièces justificatives.

In Kant and the Demands of Self-Consciousness, Pierre Keller examines Kant's theory of self-consciousness and argues that it succeeds in explaining how both subjective and objective experience are possible. Previous interpretations of Kant's theory have held that he treats all self-consciousness as knowledge of objective states of affairs, and also that self-consciousness can be interpreted as knowledge of personal identity. By developing this striking new interpretation Keller is able to argue that transcendental self-consciousness underwrites a general theory of objectivity (...) and subjectivity at the same time. (shrink)

We study one way in which stable phenomena can exist in an NIP theory. We start by defining a notion of ‘pure instability’ that we call ‘distality’ in which no such phenomenon occurs. O-minimal theories and the p-adics for example are distal. Next, we try to understand what happens when distality fails. Given a type p over a sufficiently saturated model, we extract, in some sense, the stable part of p and define a notion of stable independence which is implied (...) by non-forking and has bounded weight. (shrink)

" Faire d'Aristote un Aufklârer serait méconnaître ce qu'il y a en lui de religiosité authentique, cette intuition de la transcendance et du chorismos, qui sont la raison profonde de sa prudence spéculative. Faire d'Aristote un tragique serait méconnaître cette confiance en l'homme, en sa recherche et en son action, qui tranche sur les lamentations du chœur de la tragédie et sur une certaine résignation socratique et, avant la lettre, stoïcienne. Mais Aristote exalte l'homme sans le diviniser ; il en (...) fait le centre de son éthique, mais il sait que l'éthique n'est pas ce qu'il y a de plus haut, que Dieu est au-delà des catégories éthiques, ou plutôt que l'éthique se constitue dans la distance qui sépare l'homme de Dieu. Livré à ses seules forces par un Dieu trop lointain, qui est suffisamment visible pour être désiré, mais se tient trop à distance pour être possédé, l'homme est en butte, dans la région du monde qu'il habite, à un hasard qu'il ne peut entièrement dominer. Ou plutôt la vie de l'homme se meut entre deux hasards : le Hasard fondamental de la naissance, qui fait que la bonne nature n'est pas également partagée ; le hasard résiduel de l'action, qui fait que les résultats ne sont jamais tout à fait prévisibles. Mais le hasard de la naissance est le hasard résiduel de l'action divine, et la grandeur de l'homme consiste, en prolongeant par la prudence l'action d'une Providence défaillante, à reculer le plus possible les limites de l'imprévisible et de l'inhumain. " Pierre Aubenque. (shrink)

Recognized as a masterpiece of Nietzsche scholarship, NIETZSCHE AND THE VICIOUS CIRCLE is available here for the first time in English. Author Pierre Klossowski suggests that Nietzsche's ideas and beliefs did not stem from his personal pathology, but rather were applied in a pathological manner. Thereby Nietzsche's beliefs resonated dynamically and intellectually with his alternating lucidity and delirium.

A presentation and discussion of Gottlob Frege's understanding of language, both natural and artificial, with close attention to his texts.

The French philosopher and intellectual historian Pierre Hadot (1922-2010) is known primarily for his conception of philosophy as spiritual exercise, which was an essential reference for the later Foucault. An aspect of his work that has received less attention is a set of methodological reflections on intellectual history and on the relationship between philosophy and history. Hadot was trained initially as a philosopher and was interested in existentialism as well as in the convergence between philosophy and poetry. Yet he (...) chose to become a historian of philosophy and produced extensive philological work on neo-Platonism and ancient philosophy in general. He found a philosophical rationale for this shift in his encounter with Wittgenstein's philosophy in the mid-1950s (Hadot was one of Wittgenstein's earliest French readers and interpreters). For Hadot, ancient philosophy must be understood as a series of language games, and each language game must be situated within the concrete conditions in which it happened. The reference to Wittgenstein therefore supports a strongly contextualist and historicist stance. It also supports its exact opposite: presentist appropriations of ancient texts are entirely legitimate, and they are the only way ancient philosophy can be existentially meaningful to us. Hadot addresses the contradiction by embracing it fully and claiming that his own practice aims at a coincidence of opposites (a concept borrowed from the Heraclitean tradition). For Hadot the fullest and truest way of doing philosophy is to be a philosopher and a historian at the same time. (shrink)

Martin Heidegger's overt alliance with the Nazis and the specific relation between this alliance and his philosophical thought--the degree to which his concepts are linked to a thoroughly disreputable set of political beliefs--have been the topic of a storm of recent debate. Written ten years before this debate, this study by France's leading sociologist and cultural theorist is both a precursor of that debate and an analysis of the institutional mechanisms involved in the production of philosophical discourse. Though Heidegger is (...) aware of and acknowledges the legitimacy of purely philosophical issues, Bourdieu points out that the complexity and abstraction of Heidegger's philosophical discourse stems from its situation in the cultural field, where two social and intellectual dimensions--political thought and academic thought--intersect. Bourdieu concludes by suggesting that Heidegger should not be considered as a Nazi ideologist, that there is no place in Heidegger's philosophical ideas for a racist conception of the human being. Rather, he sees Heidegger's thought as a structural equivalent in the field of philosophy of the "conservative revolution," of which Nazism is but one manifestation. (shrink)

Are there any advantages to thinking and speaking about ethical business in the language of citizenship? We will address this question in part by looking at the possible relevance of a vast literature on individual citizenship that has been produced by political philosophers over the last fifteen years. Some of the central elements of citizenship do not seem to apply straightforwardly to corporations. E.g., “citizenship” typically implies membership in a state and an identity akinto national identity; but this connotation of (...) citizenship is obviously problematic for multinational corporations. However, the language of citizenship does help to focus our attention on various legal and political virtues for corporations—topics that have been largely neglected by discussions under other rubrics, such as CSR or sustainability. We finish with an evaluation of the potential benefits and costs of conceptualizing and talking about ethical business practices in thelanguage of citizenship.“Citizen” and “Citizenship” are powerful words. They speak of respect, of rights, of dignity.... We find no perjorative uses. It is a weighty, monumental, humanist word.—Fraser and Gordon 1994: 90[The rhetorical appeal to citizenship often] seems to have no purpose other than to add normative weight to a policy, institution or practice that could just asaptly be described without reference to citizenship.—Weinstock 2002: 244. (shrink)

In this 1999 book Pierre Keller examines the distinctive contributions, and the respective limitations, of Husserl's and Heidegger's approach to fundamental elements of human experience. He shows how their accounts of time, meaning, and personal identity are embedded in important alternative conceptions of how experience may be significant for us, and discusses both how these conceptions are related to each other and how they fit into a wider philosophical context. His sophisticated and accessible account of the phenomenological philosophy of (...) Husserl and the existential phenomenology of Heidegger will be of wide interest to students and specialists in these areas, while analytic philosophers of mind will be interested by the detailed parallels which he draws with a number of concerns of the analytic philosophical tradition. (shrink)

The dissertation seeks to gain a comprehensive understanding of Frege's watershed work of logic, the 1879 Begriffsschrift . The treatise is the first since Aristotle's instauration of the discipline to have succeeded in completely recasting logic. Very generally stated, the dissertation aims at making explicit the conceptual origins of modern logic. To do that will require that each of the achievements of Concept-script be examined from one or more vantage points: either within the perspective of Frege's larger and guiding ambition, (...) that of providing a logical justification of arithmetic; or with respect to the horizon of modernity; or in relation to later developments in logical theory and the philosophy of language, developments stimulated, albeit not exclusively, by Frege's very work. The vantage point adopted in each case will depend on the nature of the topic and the extent to which it requires to be made explicit. One perspective will have preponderance, that of Frege's relationship to his early modern ancestors, a group that includes philosophers, scientists, and mathematicians. Since modernity is constituted in a nearly constant critical, if not polemical, relationship to the Ancients, they will also at times be drawn into the discussion. The elucidation of Frege's breakthrough work will be guided by the following thesis: Frege's attempt to justify arithmetic logically and the fine work of clarification he produced in actualizing this project; his discovery of function-theoretic logic and his fashioning of a concept-script ; and his critique of natural language and the attendant semantics developed over the course of that critique constitute an unfolding and an extension of the primacy of universal method over ontology that is the signature of modern inquiry. (shrink)