Apuleius and the Square of Opposition

Abstract

Historians of logic are agreed that, although Aristotle stated the principal relations between the four types of categorical proposition, he did invent the heuristic diagram, traditionally known as the Square of Opposition, which maps those relations. But when it comes to the actual origin of the diagram, modern writers show some degree of uncertainty and even of confusion. The Kneales' are content to say that it is not to be found in Aristotle's text; a recent dictionary of philosophy2 appears to locate its origin in texts; many other writers merely apply the epithet 'traditional' to the figure, though often in contexts which would imply either a medieval or post-medieval origin. Bochefiski3 and Mark Sullivan4 correctly identify the first known occurrence of the diagram as being in the Latin handbook, conventionally titled HepL kpwqveias, from the Second Century A.D. and ascribed to Apuleius of Madaura. This rather neglected work, which will be referred to hereafter as P.H., has as its principal subjects the logic of categorical propositions and the theory of the assertoric syllogism, although its author also makes some adversions on Stoic logic. However, both Bochetiski and Sullivan reproduce, as the Apuleian Square of Opposition, a form of the diagram which contains non-Apuleian terminology and which runs beyond what is licensed by the Apuleian text although Sullivan admits both these points. The figures in BocheAiski and Sullivan are derived from that given by Thomas5 in his