My main research interest lies in Ancient physics and philosophy of mathematics. My work on Aristotle is part of a broader research project on ancient philosophies of space: during my BPhil, I worked on Epicurus' notion of void, and I hope to soon be able to extend this line of inquiry to cover Stoic physics, too. I am particularly fascinated by non-standard accounts of space and place, and interested in the various ways in which mathematics can be used to model, understand and change the physical world. I believe that focusing on ancient theories of physics and mathematics is not merely of historical interest, and I try to connect my work in ancient philosophy to open issues in contemporary philosophy of mathematics.

Doctoral Thesis: Fiction and Reality in Aristotle's Philosophy of Geometry

My doctoral thesis sets to reconstruct Aristotle’s philosophy of geometry, focusing on its relation with his physical understanding of spatial notions and spatially extended magnitudes.

Aristotle never tries to express his physics in a mathematical form, but he takes it for granted that geometry can be applied to sensible substances and invoked in physical explanations. Is he justified in this assumption? Looking at Aristotle’s cosmology and theory of places, one might doubt it. The Aristotelian universe is finite, anisotropic and inhomogeneous; positions and places differ in nature and power. How can it accommodate Euclidean geometry, which requires an infinite, isomorphic and homogeneous space?

My investigation tackles this question by proceeding in two directions. On the one hand, I examine the notion of intelligible matter and evaluate whether it can be interpreted as spatial extension, in the light of Aristotle’s theory of place and position. On the other, I discuss Aristotle’s claim that geometers need to ‘separate in thought from motion’, and inquire whether it can account for the constructive character of Greek mathematics, and whether the results of these constructive procedures can be applied to physical substances whose nature is an ‘inner principle of motion and rest’.

I conclude that Aristotle’s philosophy of geometry can account for both issues, for he takes the applicability of geometry as a strictly localised phenomenon, from a spatial as well as a temporal point of view. Geometry is not supposed to describe the spatial structure of the universe nor the motion and temporal development of physical bodies, but it does grasp the structural relations among physical objects in a specific and limited system, and at a certain instant. 


Work in Progress