Les Conséquences Immédiates et Le Syllogisme

Abstract

In the standard theory of reduction of the traditional logic of terms, the valid moods of the first syllogistic figure have a privileged status: for while the validity of the (valid) moods of the remaining two (or three) syllogistic figures is demonstrated via first-figure moods and some sub-syllogistic or immediate inferences, the validity of the first-figure moods themselves depends on a principle, traditionally dubbed dictum de omni et nullo, which remains completely out of this reduction scheme. On this basis, Immanuel Kant argued, in an essay from his pre-Criticial period (Kant 1762), that the valid moods of the first figure were alone in being pure forms of reasoning, and that the other three figures brought forth a misleading sophistication of the syllogistic theory. French philosopher Jules Lachelier, however, argues in this essay that each one of the first three syllogistic figures legitimized by Aristotle is actually grounded on a distinct principle peculiar to itself, and accordingly each one of the valid moods in these figures constitutes (in a sense) a pure form of reasoning. But more importantly, Lachelier shows, on the grounds of his own conception of the categorical proposition, that the seemingly two-termed and single-premissed (i.e. immediate) inferences, some of which are called to aid in the standard reductions, are actually three-termed and two-premissed inferences, that is, sheer syllogisms in disguise, which are grounded on the same principles for the three syllogistic figures. Lachelier also uses the idea of the intensional ground of a syllogistic figure to justify the traditional denial of a distinct fourth figure.