This article examines the use of mathematical concepts in philosophy, focusing on topology, which may be viewed as a modern supplement to geometry. We show that Plato and Parmenides were already employing geometric ideas in their research, and discuss three examples of the application of topology to philosophical problems: the first concerns the analysis of the Cartesian distinction between res extensa and res cogitans, the second the ontology of possible worlds of Wittgenstein's Tractatus, and the third Leibniz's monadology. We also (...) consider the role of topology in mathematical explanations of the sort found in science, arguing that it can perform a role in philosophy that is of comparable importance. (shrink)

The letters that were found after years are the evidence of hard intellectual work that had been conducted under very infavourable conditions. They refer to the time when Wittgenstein was writing "Tractatus" while Frege was working on his articles "Thought" and "Negation". Correspondence between Frege and Wittgenstein prove the common will of communication and mutual understanding. Thus remains the question why those two close and well known to each other thinkers have not realized that willingness.

This paper addresses the problem of providing a satisfying explanation of the Tractarian notions of state of affairs, fact and situation, an issue first raised by Frege and Russell. In order to do so, I first present what I consider to be the three main existing interpretations of these notions: the classic, the standard and Peter Simons’. I then present and defend an interpretation which is closer to the text than the classic and standard interpretations; one which is similar to (...) Peter Simons’ but which differs from it concerning one important point with respect to the nature of situations. Accordingly, the above mentioned should be seen as three wholly distinct categories. States of affairs are to be understood as Russellian complexes, facts as the subsistence and non-subsistence of states of affairs and situations as possibilities of the subsistence and possibilities of the non-subsistence of states of affairs. (shrink)

Dans cet article, je soutiens que Wittgenstein n’a pas de position de principe comparable à l’adhésion de Russell à un sens robuste de la réalité ou à l’absence chez Meinong de préjugé en faveur de la réalité, mais qu’il est plutôt pragmatique sur la question de son engagement ontologique : il y a ce qu’il y a et c’est le langage sensé qui, en tant que miroir de la réalité, nous indique ce qu’il y a. Ceci dit, ce pragmatisme s’accommode (...) d’entités possibles et d’entités non concrètes dans la mesure où sa théorie de l’image l’engage à admettre des situations possibles et des faits négatifs. Contrairement à ce que soutiennent les partisans d’une lecture russellienne du Tractatus, il ne s’agit pas là d’une simple façon de parler, mais d’une thèse que Wittgenstein endosse et qui ne lui paraît nullement problématique.In this paper, I hold that Wittgenstein’s position on the issue of ontological commitment isn’t based on some fundamental principle such as Russell’s robust sense of reality or Meinong’s rejection of the prejudice in favour of reality, but is rather pragmatic : there is whatever there is and it is the meaningful language, qua miror of reality, which shows us what there is. This pragmatism goes together with a commitment to possible and non concrete entities, since his picture theory commits him to the existence of possible situations and negative facts. Contrarily to what friends of the Russellian lecture of the Tractatus believe, this commitment isn’t a mere façon de parler but is assumed by Wittgenstein and isn’t problematic. (shrink)