A talk about formal logic and Hegel's critique of it.

We begin with Aristotle's syllogistic and its dominance throughout the medieval period; then discuss the transition to modern logic in the late 19th century, specifically Frege's development of predicate logic, which is now canonical. The transition was not just a technical improvement but a fundamental shift in how we understand the nature of logical categories -- a shift from a logic of internal relations to one of external relations, and the introduction of a sharp distinction between syntax and semantics.

The modern era is marked by the proliferation of different logics, some adopting incompatible logical principles. Modern logic hasn't realized Leibniz's dream of a universal calculus of reasoning, but instead has given us a forest of logics, each with its own domain of application and its own rules.So logical pluralism challenges the idea of a single, universal logic.

Drawing on Hegel, modern logical pluralism implies no special logic can claim foundational significance, fully justify its own normative force, or even be said to be truly logical. Our modern logic is technically sophisticated but perhaps we've become lost in the forest. Hegel's vision of a universal logic -- one that explains the conditions for the possibility of any form of reasoning -- points a way out.