Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kant’s logic negatively. What Kant called ‘general’ or ‘formal’ logic has been dismissed as a fairly arbitrary subsystem of first-order logic, and what he called ‘transcendental logic’ is considered to be not a logic at all: no syntax, no semantics, no definition of validity. Against this, we argue that Kant’s ‘transcendental logic’ is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first-order logic. The main technical application of the formalism developed here is a formal proof that Kant’s Table of Judgements in Section 9 of the Critique of Pure Reason, is indeed, as Kant claimed, complete for the kind of semantics he had in mind. This result implies that Kant’s ‘general’ logic is after all a distinguished subsystem of first-order logic, namely what is known as geometric logic.