In spite of their practical importance, the connections between technology and mathematics have not received much scholarly attention. This article begins by outlining how the technology–mathematics relationship has developed, from the use of simple aide-mémoires for counting and arithmetic, via the use of mathematics in weaving, building and other trades, and the introduction of calculus to solve technological problems, to the modern use of computers to solve both technological and mathematical problems. Three important philosophical issues emerge from this historical résumé: (...) how mathematical knowledge depends on technology, the definition of the hybrid concept of a computation, and the usefulness of mathematics in technology. Each of these issues is briefly discussed, and it is shown that in order to analyze them, we need to combine tools and ideas from both the philosophy of technology and the philosophy of mathematics. In conclusion, it is argued that much more of interest can be found in the historically and philosophically unexplored terrains of the technology–mathematics relationship. (shrink)

Is formal logic a failure? It may be, if we accept the context-independent limits imposed by Russell, Frege, and others. In response to difficulties arising from such limitations I present a Toulmin-esque social recontextualization of formal logic. The results of my project provide a positive view of formal logic as a success while simultaneously reaffirming the social and contextual concerns of argumentation theorists, critical thinking scholars, and rhetoricians.

Georg Wilhelm Friedrich Hegel (1770-1831) est probablement l’un des plus importants penseurs et philosophes de notre époque. On peut dire que les sciences humaines en général et la philosophie en particulier doivent prendre une position positive ou négative concernant la philosophie hégélienne avant de procéder à d’autres développements qui leur seraient propres. Plus précisément, ce collectif trouve sa racine dans une double urgence : les menaces des crises environnementale, politique et économique, les nouveaux enjeux qu’elles entraînent, d’une part, et l’absence (...) jusqu’à présent de réponses prometteuses, de l’autre. Il est temps de faire le point et de contribuer à fournir de nouvelles pistes de réflexion. Le présent ouvrage, bilingue, est le fruit de la collaboration d’éminents spécialistes internationaux qui ont répondu avec enthousiasme à notre invitation. Les 14 textes qui y sont réunis sont distribués selon trois thématiques et, tout en respectant la nature de la pensée hégélienne, leurs thèmes se chevauchent inévitablement. La première partie, « Aspects de la pensée de Hegel / Aspects of Hegel’s Thought », regroupe les textes qui discutent en profondeur d’un aspect de la pensée de Hegel, tout en analysant un enjeu qui se trouve dans ses propres œuvres. Les contributions de la deuxième partie, « Marx et Hegel / Marx and Hegel », examinent la relation entre ces deux philosophes. Comment faut-il comprendre les passages dans lesquels Marx accuse Hegel d’idéalisme, dont celui, largement cité, dans la préface du premier tome du Capital, n’est qu’un exemple? Dans la troisième partie, « Hegel à l’époque contemporaine / Hegel in Modern Times », les auteurs se penchent sur l’influence de la pensée de Hegel sur plusieurs penseurs. (shrink)

Many parts of the contemporary philosophical debate have been built on the radicalization of conclusions derived from the acceptance of a certain set of classical dichotomies. It also discusses how pragmatism and abduction are currently presented to solve the problems arising from these dichotomies. For this reason, the efforts of this article have been directed to analyze the impact of this fact on the philosophy of science and logic. The starting point is that accepting abduction implies, in many ways, accepting (...) the foundations of pragmatism. Also, that the analysis of such problems from pragmatism and the particular use of abduction dissolve the dichotomies and, with it, also modify the philosophical problems related to them. Therefore, I propose to understand abduction as the right conceptual device to review the problems and debates of the twentieth century’s epistemology from a pragmatic perspective. In doing so, the aim is to propose that the current use of abduction in contemporary debates may imply a change of the philosophical perspective. (shrink)

After the publication of Begriffsschrift, a conflict erupted between Frege and Schröder regarding their respective logical systems which emerged around the Leibnizian notions of lingua characterica and calculus ratiocinator. Both of them claimed their own logic to be a better realisation of Leibniz’s ideal language and considered the rival system a mere calculus ratiocinator. Inspired by this polemic, van Heijenoort (1967b) distinguished two conceptions of logic—logic as language and logic as calculus—and presented them as opposing views, but did not explain (...) Frege’s and Schröder’s conceptions of the fulfilment of Leibniz’s scientific ideal. -/- In this paper I explain the reasons for Frege’s and Schröder’s mutual accusations of having created a mere calculus ratiocinator. On the one hand, Schröder’s construction of the algebra of relatives fits with a project for the reduction of any mathematical concept to the notion of relative. From this stance I argue that he deemed the formal system of Begriffsschrift incapable of such a reduction. On the other hand, first I argue that Frege took Boolean logic to be an abstract logical theory inadequate for the rendering of specific content; then I claim that the language of Begriffsschrift did not constitute a complete lingua characterica by itself, more being seen by Frege as a tool that could be applied to scientific disciplines. Accordingly, I argue that Frege’s project of constructing a lingua characterica was not tied to his later logicist programme. (shrink)