Boole, critique d'Aristote : la logique de l'élimination du moyen terme

Abstract

There is an actuality of aristotelian syllogistic which still lays down rules of logical argumentation in the production of scientific knowledge today. The middle term (or mid-term) orientates here the structure and form of reasoning—this set of judgements—elaborated in such a way that the conclusion results necessarily from the premises. According to Aristotle, the discernment thus demands various procedures to be applied to reality. Yet, in doing so, Boole finds a methodological problem which has been widely neglected by logicians and some modern historians of science: Aristotle's problem concerning the mid-term which is cause, matter and form of the categorical syllogism at the same time. Nevertheless, both thinkers aim at the infallibility of reasoning by eliminating the mid-term in the search procedures for truth. Their positions differ both from a methodological point of view and in degree. For Aristotle rules out the mid-term from the conclusion of the syllogistic reasoning and according to the ultimate laws of the object. On the other hand, Boole rules out the mid-term of the symbolic reasoning on the basis of the ultimate laws of pure thought by denying it the status that Aristotle granted it. This article seeks to show, in the light of this "mid-term eclipse" for Aristotle that, according to Boole, the relevant solution to Aristotle's problem is "the general theory of signs" which establishes the mid-term elimination of the symbolic reasoning. It is a requirement of the knowing thought in that it constitutes its meta-methodological character. In so doing, the general theory of signs would thus made the actuality of aristotelicism more persistent if it is the case that Boole himself has not yet distanced himself from it.