The aim of this article is to reinterpret the roles of infinite judgements in Hegel’s Science of Logic. If one tries to understand his account of this topic consistently, s/he will be faced with a huge problem: why did Hegel divide infinite judgements into two types, positive and negative? In the history of traditional logic, infinite judgements have usually been expressed in some negative forms that seem to represent something ridiculous and senseless. However, Hegel insists that there is also a positive type of infinite judgement in the form of tautological propositions.

In this paper, I approach this problem mainly by tracing the following two possible roots of Hegel’s idea of infinite judgements in a positive form. One is Hegel’s own younger idea about singular judgement in the Jena System (1804/5). Hegel thought that this type of judgement corresponds to infinite judgements in that both finally abolish the “subsumption” relationship between the terms in a judgement. The other possible root is an idea that came from Ploucquet, who had taught logic in Tübingen until just before Hegel started studying there. Ploucquet’s important idea is that logic should be treated as a kind of mathematical calculation on the basis of identifying the extensions of the subject and the predicate of a judgement. Hegel thought this idea also led to the equalization of the conceptual difference between the terms in a judgement.

In the light of these remarks, I put forth the hypothesis that Ploucquet’s idea led Hegel to rethink judgement types in the form of tautological propositions and to create a new perspective on them which was opposed to mathematical views of logic. In conclusion, I argue that a positive type of infinite judgement can also have a truly positive role in Hegel’s theory of judgments and that it should be understood to be positive in Hegel’s sense of “the negation of negation”.