On the Aristotelian Square of Opposition

A common misunderstanding is that there is something logically amiss with the classical square of opposition, and that the problem is related to Aristotle’s and medieval philosophers’ rejection of empty terms. But [Parsons 2004] convincingly shows that most of these philosophers did not in fact reject empty terms, and that, when properly understood, there are no logical problems with the classical square. Instead, the classical square, compared to its modern version, raises the issue of the existential import of words like all; a semantic issue. I argue that the modern square is more interesting than Parsons allows, because it presents, in contrast with the classical square, notions of negation that are ubiquitous in natural languages. This is an indirect logical argument against interpreting all with existential import. I also discuss some linguistic matters bearing on the latter issue. 1 The Classical Square When Aristotle invented the very idea of logic some two thousand four hundred years ago, he focused on the analysis of quantification. Operators like and and or were added later (by Stoic philosophers). Aristotle’s syllogisms can be seen as a formal rendering of certain inferential properties, hence of aspects of the meaning, of the expressions all, some, no, not all. The logical properties of these quantifiers were expressed in two ways: • the particular inference forms that Aristotle called syllogisms; • certain other logical relations that later were illustrated in the so-called square of opposition. A syllogism has the form: