Francois Lepage

Le dernier ouvrage d'Yvon Gauthier, son quatrième, n'est certes pas d'une lecture des plus faciles. Le bon lecteur devrait à la fois être familier du formalisme de la mécanique quantique et des labyrinthes lacaniens, connaître la théorie des modéles êt etre revenu de Heidegger.Tout cela rend la tâche d'un critique de Gauthier ardue et périlleuse; aussi je prierai le lecteur de m'excuser à l'avance si, dans le foisonnement philosophique de l'ouvrage, j'ai dû restreindre mon attention à certains aspects particuliers.

SummaryIn this paper I will strive towards three main objectives. First of all, I will try to show that a very commonplace property of knowledge, that of yielding truth, can be used to characterize an ideal and radical notion of knowledge. It will be argued that this property generates a basic and autonomous concept of knowledge, i.e., a purely logical concept of knowledge that can be clearly separated from the psychological, intentional or epistemological aspects of knowledge. What results can thus be regarded as a kind of reduction of the concept of knowledge to that of truth. This reduction will be expressed by means of a criterion which a relation between an agent and a sentence must satisfy in order to be interpreted as exemplifying the relation of knowing.Secondly, 1 will offer an analysis of presuppositional knowledge which shows how the very strong and ideal notion of knowledge previously developed can be useful in interpreting the ordinary use of “knowing”.My third and last objective will be to use this criterion to characterize formally the semantic interpretation associated to a rational and competent agent, i.e. the space of his knowledge

Even though Church’s thesis is widely accepted among mathematicians, it is nonetheless controversial. In this paper, we argue against the position of [Cleland 1993], which defends that Church s thesis must be rejected because the limits of computation depend upon the physical structure of the world. We first give a brief overview of Church’s thesis and then we present Cleland s argument. We then propose a critical analysis of Cleland s argu­ment, which will involve some conceptual distinctions regarding the notion of computability, and finally we will show that the limits of computation are not physical but logical. In short, we argue that computation is limited by the fact that an effective procedure must be described in a finite way.

La théorie des types que Bertrand Russell proposa en 1908 ne se voulait pas une solution ad hoc au problème des contradictions, elle prétendait plutôt être la solution naturelle, celle que tout le monde reconnaîtra comme la solution attendue. En fait, il s'agit d'une théorie philosophique qui concrétise un projet grandiose: réduire les mathématiques à la logique. Le présent texte se propose d'examiner les thèses russelliennes et la dynamique de leur évolution de 1903 à 1907, c'est-à-dire des Principles à la naissance de la théorie des types.The theory of types that Bertrand Russell proposed in 1908 didn't present itself as an ad hoc solution to the problem of contradictions. Rather it pretended to be the natural solution, the one that everybody would recognize as the expected solution. In fact, it is a philosophical theory materializing an imposing project: to reduce mathematics to logic. This paper examines the russellian theses and their evolution from 1903 to 1907 i.e. from the Principles to the birth of the theory of types