Category Theory for Aristotelian Diagrams: The Debate on Singular Propositions

Abstract

AbstractThe theoretical study of Aristotelian diagrams is at an all-time high since the conception of logical geometry. This framework studies Aristotelian diagrams in a systematic way, revealing many links with contemporary mathematics (esp. algebra). Most recently, this has led to the introduction of several notions of morphism between Aristotelian diagrams, which we are studying in the context of category theory. This is not merely a mathematical enterprise, but also carries major philosophical importance. As a proof of concept of this claim, we investigate the historically rich discussion on the status of singular propositions. It has been debated for centuries whether these should be viewed as a special kind of universal propositions or particular propositions, or as a third, completely separate kind. Interpreting each of these views as a morphism in one of our categories, we obtain a clean picture of the entire discussion in a single image. Additionally, we apply the machinery from category theory (in casu, the notion of equalizer) to make some interesting comparative observations regarding the three views on singular propositions.