William of Sherwood, Singular Propositions and the Hexagon of Opposition

Abstract

In Aristotelian logic, the predominant view has always been that there are only two kinds of quantities: universal and particular. For this reason, philosophers have struggled with singular propositions (e.g., “Socrates is running”). One modern approach to this problem, as first proposed in 1955 by Tadeusz Cze˙zowski, is to extend the traditional Square of Opposition to a Hexagon of Opposition. We note that the medieval author William of Sherwood developed a similar theory of singular propositions, much earlier than Cze˙zowski, and that it is not impossible that the Hexagon itself could have been present in Sherwood’s writings. 1