I am a tutor for the following undergraduate papers at the University of Oxford:

In Autumn 2020 (Michaelmas Term, weeks 1-4, Mondays 10am), I will give a mini lecture series for Oxford undergraduates. Due to the Covid-19 safety measures, the lectures will be held online: feel free to contact me if you wish to attend!

Continuity vs Atomism in Ancient Physics

Can matter be divided ad infinitum, or is it composed of indivisible chunks? What about time and motion: are they infinitely divisible, or are there time-atoms? And what is the relation between these physical magnitudes? These are fundamental questions that shape our metaphysical and scientific understanding of the world: they have been at the centre stage of the history of thought, and have always represented one of the most fertile ground of interaction between physics, mathematics, and philosophy. The polarity between theories of continuity and atomism runs through the history of these disciplines, and offers a privileged way into discussing their relationship and interconnections.

This mini lecture series will focus on the initial form that this debate has taken in Ancient Greek philosophy, and which shaped for millennia much of the discussion in Western physics and philosophy. In particular, we will focus on the Ancient Atomists and Aristotle. Thus, the course offers a detailed discussion of some key topics in Aristotle’s physics and metaphysics, as well as a panorama of the Atomists’ positions, from Democritus to Epicurus.

The goal of examining the ancient debate on this topic is not only historical: the course stresses the relevance of the ancient debate for contemporary philosophy of physics and mathematics. Aristotle’s account of continuity had a deep and long-lasting impact on the development of Western science and philosophy, while modern atomists explicitly connect their ideas to Democritus’ theories. Thus, looking at the ancient theories of matter, time and motion will shed light on some of the presuppositions that we inherit from the Greeks, as well as on the differences between the contemporary and the ancient debate. Greek mathematics and physics being radically different from the contemporary ones, the ancient debate provides a perfect case-study to examine the interrelations between mathematics, physics and metaphysics.

Lecture 1. Introduction and Mathematical Issues

The first lecture will lay down the background and context of the debate: both the Atomists’ and Aristotle’s theories can be seen as a reaction to the Eleatic challenge, in particular to Parmenides’ apparent denial of the possibility of change and plurality. The lecture will focus in particular on the mathematical problems associated with continuity, infinite divisibility, and atomism, paying particular attention to Zeno’s paradoxes of divisibility. We will also discuss the mathematical problems raised by atomism: if it is true that the atomists manage to escape the paradoxes of infinite divisibility, they risk ‘making geometry false’ by denying the existence of incommensurable magnitudes.

Lecture 2. The Ancient Atomists and the Void

The second lecture focuses on the Ancient Atomists, Leucippus and Democritus: we will see how postulating the existence of indivisible chunks of matter might solve some of the Eleatic paradoxes, and discuss in which way atoms can be said to be indivisible. We will pay particular attention to the Atomists’ introduction of the void, and its relation to the possibility of motion: for the atomists, void is a precondition for motion, while Aristotle maintains that it would make motion impossible. In particular, we will distinguish various ways in which void has been conceptualized throughout the centuries, from Democritus to Epicurus, and discuss how each of them is supposed to make atomic motion possible.

Lecture 3. Aristotle’s Continuist Kinematics

The third lecture will be dedicated to Aristotle’s theory of continuity, and his solution to Zeno’s paradoxes: this will bring to light the connection between the physical property of continuity and key metaphysical notions such as unity and eternity. We will discuss Aristotle’s account of the three main physical magnitudes (motion, megethos and time) as continuous, and spell out the details of his kinematic model. We will focus in particular on the Isomorphism Thesis (i.e. the claim that these three magnitudes must all have the same structure), which is one of the most long-lasting inheritances of Aristotle’s physics. We will discuss, among other things, the relations of dependence between the three magnitudes, and the status of the instant of change.

Lecture 4. Alternatives and Reactions to Aristotle

In the last lecture, we will discuss some alternatives and reactions to the dominant Aristotelian continuist account. We will see that most part of the ancient alternative kinematic models stick to the Isomorphism Thesis, and are thus led to postulate a ‘cinematographic’ account of motion and discrete space and time. In particular, we will discuss Diodorus Cronus’ idea that things cannot move, but they can be said to have moved, and the late Epicurean hypotheses of discontinuous space, time and motion. To conclude, we will briefly discuss how the Isomorphism Thesis permeates the history of Western science well into the modern era, and how it is put into discussion.