The Limits of the Square: Hegel’s Opposition to Diagrams in Its Historical Context

Abstract

The square of opposition hardly appears in German texts on logic from the early to mid-nineteenth century. This cannot be due to a lack of awareness of the square, for although it only appears occasionally in works from this period, these rare appearances present highly elaborate variations of it or show its historical development. But this is, almost without exception, the case only in works about the history of logic (Biese, Prantl, Rabus, Ueberweg) or in school textbooks (Fischer, Gockel, Jäger, Troxler, Lindner, Waitz). This might seem like a lot of references, but in fact these works only represent a small minority of the numerous logics that were published in German during this period. The absence of the square should not be taken as a sign of critical attitudes towards the logical relations represented by it; the opposite is more likely. As part of the Aristotelian heritage of traditional logic, the content of the square may have been considered so obvious that there was no need for further illustration. Logic was believed to have been perfected or nearly perfected for 2000 years, after all. Diagrams that use circles, rather than the square, can be found more often. However, this was probably not because they showed new logical content but because the practice of showing old content using circles was quite new at this time. The lack of interest in diagrams among the more orthodox logicians was not counterbalanced by an increased use by the non-orthodox ones. For example, neither circles nor squares are to be found in the works of Hegel. But Hegel at least discusses, through the lens of his Science of Logic, the limits to the use of diagrams in the context of the relations traditionally represented by the square of opposition. This paper aims to clarify the arguments that draw an opposition between Hegel’s logic and diagrams like the square, in the light of his place within nineteenth-century German logic.