Chiara Martini
Summary of doctoral thesis: My thesis investigates and attempts to reconstruct Aristotle’s philosophy of geometry. The aim of this work is to tell a plausible story as to how, exactly, Aristotle thought mathematics could work without appealing to Platonic entities. This means investigating, on the one hand, how his account could make sense of mathematical truths and could fit with the mathematical practice of his time, and on the other hand, how it made sense of the application of mathematics to the physical world. The thesis is divided in two parts. The first part offers a close reading of Metaphysics M.3, and of its two main claims: that geometry is about sensible objects, but not qua sensible, and that geometers are allowed to posit as separate what is in fact not separate. I give a radically anti-Platonist account of geometrical truth, according to which geometry is true in virtue of sensible substances and their properties. However, I claim that Aristotle relies on a moderate form of fictionalism (which only concerns the mode of being of the entities in question) in order to account for geometrical practice. The second part of the thesis inquires whether Aristotle is justified in assuming that geometry is applicable to sensible reality. I focus in particular on the notion of intelligible matter, and on the role of change in geometry. I find that the applicability of geometry to sensible reality can be granted only by limiting its scope to localised configurations, both in space and in time.
Other research interests: Feminist Philosophy; Philosophy of Mathematics.
