Syllogistic Expansion in the Leibnizian Reduction Scheme

The standard inferential scheme of traditional assertoric syllogistic, based on the initial chapters of Aristotle’s Prior Analytics, employs single-premissed deductions, i.e., principles of immediate inference, in the reduction of imperfect valid moods to perfect moods. G. W. Leibniz (among others) has attempted to replace this scheme with his own version of syllogistic reduction (the core of which is, again, based on Aristotle’s observations on syllogistic transformation), in which the principles of immediate inference themselves are modelled as (and hence justified by means of) valid syllogisms. This paper examines the place of this modelling, i.e. syllogistic expansion, of immediate inferences in Leibniz’s scheme of syllogistic reduction (which he describes in his Nouveaux Essais and presents in one of his papers on syllogistic), and shows through this examination that the tenability of the whole scheme actually hinges on the interpretation to be given for the categorical propositional forms