This paper examines Hegel’s accounts of the nature of judgements and inferences in the ‘subjective logic’ of the Science of Logic, and does so in light of the history of the tradition of formal logic to his time. It is argued that, contrary to the attitude often displayed by interpreters of Hegel’s logic, it is important to understand the positive role played by formal logic, ‘logic commonly so called’, in Hegel’s own conception of logic. It is argued that Hegel’s own (...) scientific presentation [Darstellung] of logic relies on a dialectic working through the tradition of formal logic from Aristotle to Leibniz. The positions within the dialectic are most easily brought into focus in terms of the distinction between Aristotelian and Stoic logic, but they can also be seen as internal to Aristotelian logic. The logical tradition can be regarded as presenting a type of reductio ad absurdum, and a science of logic must examine what it was about Aristotle’s original project that brought it to this fate. (shrink)