The Right Square

Abstract

It is shown that there is a way of interpreting the traditional Square of Opposition that overcomes the main historic problem that led to the present supremacy of modern predicate logic over Aristotelian Syllogistic: handing multiply quantificational, relational expressions like ‘All boys love some girls’. The interpretation has other advantages, is plausibly Aristotle’s own, original view, and was certainly known by several significant Aristotelian logicians in the late nineteenth century, and the early part of the twentieth century, when Syllogistic was falling from favour. That leads to a puzzle about why the proposed interpretation was not seen to overcome the problem of multiple generality at the time, and some points are made showing what might need to change before the interpretation is more widely accepted.