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). In the materially determinate statements taken as examples, Aristotle substituted algebraic letters for the words (terms) indicating the material: that which is spoken about in the statements, that which determines judgments as/judgments relating to divers material provinces or single matters. As concerning the sense, this implied that he substituted the moment “anything whatever” for each materially filled “core” in the judgments, while the remaining judgment-moments were held fast as moments of form, moments that persist without change when one changes the relatedness of the given judgment to matters — or interchanges judgments pertaining to different material spheres — at pleasure. With this taking of the materially filled cores as indeterminate optional affairs — lingually, as indeterminate terms, S, p, and the like — the exemplificative determinate judgment becomes converted into the universal and pure form-idea: the pure concept of any judgment whatever that has, as the case may be, the determinate judgment-form “S is p”, the form “If S is p, then Q is r, or the like.¹