Formal logic as apophantic analytics

Abstract

From our general explanations it is already understandable that, as historically the first part of a systematically executed logic, Aristotelian analytics arose, a first commencement of a logic of theoretical formations. Within the limits imposed by focusing on this theme, it was a “formal” logic in a particular sense; though, even as that, it did not attain the full purity and breadth prescribed by its essence. In a survey of the (always materially determinate) judgments of life and science, the most universal groupings of judgments according to types, the perfect likenesses of form among judgments pertaining even to heterogeneous provinces, immediately came to the fore. Aristotle was the first to bring out the idea of form which was to determine the fundamental sense of a “formal logic”, as we understand such a discipline today and as Leibniz already understood it in effecting his synthesis of formal logic (as apophantic) and formal analysis to make the unity of a mathesis universalis. Aristotle was the first, we may say, to execute in the apophantic sphere — the sphere of assertive statements (“judgments” in the sense expressed by the word in traditional logic) — that “formalization” or algebraization which makes its appearance in modern algebra with Vieta and distinguishes subsequent formal “analysis” from all material mathematical disciplines (geometry, mechanics, and the rest).