A Study of the Peripatetic Mechanica

Change log
Harris, Arthur 

This study aims to understand the aims and methods of a less-studied work from the early Peripatos, the Mechanica. I argue that the Mechanica (Mech.) was an application of natural philosophy to the technical sphere of mechanics. The primary aim is to give causal explanations of various puzzling phenomena in this domain. While the author uses lettered diagrams and specialised, geometrical language to achieve this aim, the arguments should not be described as mathematical or demonstrative. Rather, Mech.’s explanations are fundamentally physical, causal and analogical.

In Chapter 1, I describe the structure of Mech., underscoring a degree of coherence across its 35 problems. I provide evidence for dating Mech. to the early Hellenistic period (late 4th – early 3rd c. BCE) and against the attribution to Aristotle. I also take issue with two standard arguments against that attribution: the claim that Mech.’s understanding of natural motion differs from Aristotle’s, and G.E.L. Owen’s claim that Mech. applies the notion of motion and speed at an instant. I then situate Mech. in its intellectual context through a survey of earlier Greek mechanics and mathematical investigations of motion. At the end of the chapter, Note A summarises Mech.’s structure, while Note B examines passages in Aristotle’s certainly authentic works sometimes thought to represent a theory of mechanics.

In Chapter 2, I argue that Mech.’s analysis of radial rotation as the combination of two rectilinear motions should be understood as claiming that two motions are present in a rotating radius, rather than as treating the component motions as useful fictions. To show this, I examine Aristotle’s approach to composed motions across several works. I argue that Aristotle’s accounts of change in Physics 3 and 5 imply a distinctive, realist view of component motions, according to which it is a fact that the rotating radius two simultaneous motions rather than a single motion along the same path. I then examine supporting evidence in passages concerning both celestial and sublunary motions.

In Chapter 3, I explore two further considerations that arise from Aristotle’s statements on types of locomotion and their compositions. First, I consider how we should understand Aristotle’s division of all motion into straight, circular and mixed. Then I explore the limits of the possible presence of distinct motions in a single object, through examining Aristotle’s claim that no contrary motions can be simultaneously present in a body.

In Chapter 4, I undertake a close reading of Mech. problem 1, showing that problem 1’s arguments draw on the resources of geometry to support a basically physical agenda and to deliver a causal explanation. In light of the arguments of Chapters 2-3, I argue that problem 1’s analysis targets radial rotation, which is distinguished from celestial circular motion by the simultaneous presence of two rectilinear motions in the rotating radius. I defend the explanatory potential of Mech.’s causal notion of constraint (ἔκκρουσις) and I explore an unresolved tension between the characterisation of the motions as radial and tangential (849a6-849a19, 852a8-13) and their different representation in a diagram (849a19-849b19).

Chapter 5 studies the explanatory strategies of the less-studied problems 4-22, with a focus on their use of lettered diagrams and specialised language. I argue that these problems fundamentally rely on analogies, a kind of reasoning distant from formal geometry, but that they use the specialised language and lettered diagrams of geometry to support these analogies. Since the arguments are analogical rather than deductive, Mech.’s method should not be identified with the demonstrative ideals of Aristotle’s Posterior Analytics.

Chapter 6 examines the paradox of Mech. problem 24, known as the Rota Aristotelis. This paradox challenges problem 1’s claims about rotation and thus threatens to overturn Mech.’s explanatory project. I show that the author’s aim is not to provide a geometrical explanation. Rather, he draws two distinct puzzles from the paradoxical phenomenon and answers each of them with a solution based on physical principles. This further substantiates my argument over the previous chapters that Mech. is not so much a mathematical work as an application of natural philosophy to the technical sphere of mechanics.

Chapter 7 argues that Physics 7.4’s startling claim that circular and rectilinear motions are incomparable may represent an earlier attempt to solve the Rota Aristotelis paradox. I criticise three alternative explanations of Phys. 7.4’s claim and show how Phys. 7.4’s argument would make sense as a response to the paradox.

In Chapter 8, I summarise the arguments of previous chapters.

Taub, Liba
Mechanics, Aristotle, History of Mathematics, Diagrams, Ancient Science
Doctor of Philosophy (PhD)
Awarding Institution
University of Cambridge
AHRC (2090854)