We want to consider anew the question, which is recurrent along the history of philosophy, of the relationship between rationality and mathematics, by inquiring to which extent the structuration of rationality, which ensures the unity of its function under a variety of forms (and even according to an evolution of these forms), could be considered as homeomorphic with that of mathematical thought, taken in its movement and made concrete in its theories. This idea, which is as old as philosophy itself, (...) although it has not been dominant, has still been present to some degree in the thought of modern science, in Descartes as well as in Kant, Poincaré or Einstein (and a few other scientists and philosophers). It has been often harshly questioned, notably in the contemporaneous period, due to the failure of the logistic programme, as well as to the variety of “empirical” knowledges, and, in a general way, to the character of knowledges that show them as transitory, evolutive and mind-built. However, the analysis of scientific thought through its inventive and creative processes leads to characterize this thought as a type of rational form whose configurations can be detailed rather precisely. In this work we shall propose, first, a quick sketch of some philosophical requirements for such a research programme, among which the need for an harmonization, and even a conciliation, between the notions of rational (or rationality), of intuitive grasp and of creative thought. Then we shall examine some processes of creative scientific thought bearing on the knowledge and the understanding of the world, distinct from mathematics although keeping tight relations with them. Contemporary physical theories are privileged witnesses in this respect, for in them the rational thought of phenomena makes an intrinsic use of mathematical thought, which contributes to the structuration of the formers and to the expression of their concepts (which entails the physical contents of the latter). The General Theory of Relativity and the Quantum Theory are exemplar to this, as they directly reveal what can be called the “drag of physical thought par the mathematical form”, which makes possible to overcome the limitations of the physical knowledge previously adquired. This process is tightly related to the modalities and to the stucture of the rational thought underlying it. This is what we would like to show. DOI:10.5007/1808-1711.2011v15n2p303. (shrink)

The ArgumentThe purpose of this article is to read Heidegger's critique of modern science —especially in What Is a Thing? —as evolving from ontological issues that preoccupied Heidegger in the period after the publication of Being and Time. The main issues at stake are formal ontology and its connection with mathematics and modern mathematical physics, and the distinction between formal and regional ontology. The connection between these issues constitutes Heidegger's understanding of mathematics. An exposition of Heidegger's notion of the “mathematical” (...) can help us uncover his assumptions in his critique of modern science, and give us new possibilities for evaluating it. (shrink)

This article argues that only a developmental approach-one that views Derrida's 1967 work on Husserl, La Voix et la phénomène, in light of Derrida's three earlier encounters with Husserl's work and recognizes significant differences among them-is able to resolve the bitter controversy that has lately surrounded Derrida's Husserl interpretation. After first reviewing the impasse reached in these debates, the need for "a new hermeneutics of deconstruction" is set out, and, then, the reasons why strong development has been rejected internal to (...) Derrida's corpus are discussed. After this, in a discussion of interest with respect to Husserl's own late teachings, as well as Derrida's standpoint, this article focuses on Derrida's 1962 "Introduction to Husserl's Origin." Against the prevailing interpretation, an argument is made showing that Derrida is much closer to Husserl's own positions than has been suspected, most importantly, in section VII of the "Introduction" where the theme of writing is first introduced. Thanks to this, that significant development in Derrida's thought does take place between 1962 and 1967 is demonstrated-and the present piece concludes by providing a brief sketch of the development of deconstruction overall as it came about through Derrida's repeated encounters with Husserlian phenomenology in the years 1954–67. (shrink)

This paper critically examines the relation between problems and the formation and development of concepts in Bergson’s work, as well as in Bachelard, Canguilhem and Deleuze. Building on work by Elie During, I argue that it is not only Bergson but also Deleuze who shares with the French epistemological tradition an “anti-positivist” conception of concept formation, founded upon the posing and solving of novel problems as opposed to the acquisition and verification of empirical facts. Contrary to During, however, I argue (...) that it is not Bergson but Deleuze who furnishes us with an “anti-positivist” conception of problems that is adequate to this anti-positivist conception of concept formation. Deleuze’s anti-positivist view of problems holds, firstly, that genuine problems require the creation of novel terms in which to state and solve them. He shares this view with Bergson, Bachelard and Canguilhem. Secondly, however, Deleuze holds that a problem’s “truth” is not to be evaluated with reference to its eventual solutions, nor with reference to some privileged and contentful experience of reality, but is rather a matter of its purely intrinsic productivity. (shrink)

What philosophical motivations lay behind the emergence of the genealogical method in Foucault’s thought? Pace traditional interpretations, I argue that genealogy is best construed as a supplementary addition to the archaeological mode of investigation. It addresses an issue that arose within the problematic to which the archaeological method responds, but which that method was not designed to solve: the problem of “transcendental genesis” as this issue was defined within the unique parameters set forth by the French phenomenological tradition.

La presente nota crítica tiene como finalidad exponer y comentar las ideas fundamentales de la edición española del primer escrito de Jacques Derrida, El problema de la génesis en la filosofía de Husserl. Asimismo, hacemos algunas aclaraciones sobre el origen y significado de este escrito. Al concluir, añadimos algunas observaciones sobre la traducción y sobre el estudio final del editor y traductor Javier Bassas Vila sobre la filosofía del joven Derrida.

Dans cet article, je compare les vues de Lautman et Herbrand sur la théorie des nombres et la philosophie de l’arithmétique. Je montre que, bien que Lautman eût avoué avoir été marqué par l’influence de Herbrand, les postures fondationnelles des deux amis divergent considérablement. Alors que Lautman versait dans un réalisme platonicien, Herbrand est resté fidèle au finitisme hilbertien. Il est vrai que Lautman était philosophe et que Herbrand était avant tout arithméticien et logicien, mais il demeure que l’oeuvre de (...) Herbrand a une portée philosophique mieux accordée à la logique et aux mathématiques contemporaines.In this paper, I am contrasting Lautman’s and Herbrand’s views on number theory and philosophy of arithmetic. It is argued that despite the fact that Lautman had acknowledged Herbrand’s major influence on his own work, their foundational stances diverge profoundly. Lautman defended a variety of Platonism and Herbrand advocated a personal version of Hilbertian finitism. Of course, Lautman was a philosopher while Herbrand dealt mainly with number theory and logic. It remains though that Herbrand’s work is more in tune with contemporary logic and mathematics from a philosophical perspective. (shrink)