Testing Definitions. Aristotelian Dialectic and Euclidean Mathematics

In my dissertation Euclid’s Philosophy, I argue that Euclid’s philosophical views pertaining to the ontology and epistemology of mathematical objects can be reconstructed from his mathematical practice in the Elements, and, in particular, from the ways in which he formulates his mathematical definitions. While Euclid does not expressly formulate a philosophical theory, he implicitly––yet systematically––introduces ontological distinctions and conceptual hierarchies.