Diagrammatic and Modal Dimensions of the Syllogisms of Hegel and Peirce

While in his Science of Logic, Hegel employed neither diagrams nor formulae, his reinterpretation of Aristotle’s syllogistic logic in the “Subjective Logic” of Book III strongly suggests a diagrammatic dimension. Significantly, an early diagram depicting a “triangle of triangles” found among his papers after his death captures the organization of categories to be found in The Science of Logic. Features of this diagram help us understand Hegel’s logical project as an attempt to retrieve features of Plato’s thinking that are implicit within Aristotle’s syllogistic logic. It is argued that parallels between Hegel’s modification of Aristotle’s syllogistic figures and Peirce’s functional alignment of those syllogistic figures with his three inference forms—deduction, induction, and abduction—suggest modifications of the traditional “square of opposition” into a logical hexagon as found in recent discussions. However, Hegel had conceived of Aristotle’s syllogism as a distorted version of the “syllogism” thought by Plato to bind the parts of the cosmos into a unity as described in the dialogue Timaeus. In accord with this, it is argued that seen in the light of Hegel’s platonistic reconstruction of Aristotle’s logic, such logical hexagons should be understood as two-dimensional projections of a logical polyhedron.