Paul Redding, Conceptual Harmonies: The Origins and Relevance of Hegel’s Logic

Conceptual Harmonies is presented as the first half of a reconstruction of Hegel's logic aimed at grounding Hegel's metaphysics (p.xiv).The development of the grounding itself has been sacrificed for the time being in order to provide a novel access to the logic of Hegel's Science of Logic.Redding attempts to elucidate Hegel's account of the rationality of the syllogism, a major theme in Hegel's "Subjective Logic," through a historical contextualization of the idea of the "middle term."To this end, he takes an unprecedented journey, at least in Hegel scholarship, through Greek number theory and notions of ratio and proportion, their Neoplatonic elaborations and their echoes in modern geometric algebra and algebraic mathematical logic.More specifically, Redding sets out to trace the logical significance of the syllogism back to a Pythagorean conception of the middle term that Hegel had discovered in Plato.The starting point of his argument is Hegel's comparison in his Lectures on the History of Philosophy between Aristotle's formal logic of the understanding, in which a "geometric" middle term plays a prominent role, and the "most beautiful bond" of rationality spoken of by Plato in Timaeus 31c, in which a combination of Pythagorean means connects two "extremes":