Splitting the Atom: An Interpretation and Defence of Hume’s Lead Argument against Infinite Divisibility in the Treatise

This thesis explains and defends Hume’s lead argument against the infinite divisibility of a finite extension (T 1.2.1). The structure of the thesis is as follows: First, I construct a comprehensive version of Hume’s lead argument, which I will divide into four parts, each with its own chapter. The first chapter provides a thorough textually-based defence of Hume’s first principle that “...the capacity of the mind is limited, and can never attain a full and adequate conception of infinity.” (T 1.2.1.2 SBN 26)
Chapter two explains Hume’s argument from the principle that the mind is limited to the conclusion that the only adequate idea the mind can use to form ideas of extended objects is an indivisible coloured or tangible point, i.e. Hume’s “least idea.” I will argue that Hume’s “least idea,” contrary to widespread opinion, is decidedly non-empiricist and follows from a priori and transcendental arguments. I will also reply to the criticisms that it is ridiculous to colour an extensionless point and that extensionless points cannot form an extension.
Chapter three unpacks Hume’s second principle that “...whatever is capable of being divided in infinitum, must consist of an infinite number of parts, and that ‘tis impossible to set any bounds to the number of parts, without setting bounds at the same time to division.” (T 1.2.1.2 SBN 26-7) Following Thomas Holden, I endeavour to show that Hume’s divisibility principle is not a mathematical, but a metaphysical principle, which depends upon the actual parts doctrine.
Chapter four interprets Hume’s adequacy principle, which states “WHEREVER ideas are adequate representations of objects, the relations, contradictions and agreements of the ideas are all applicable to the objects.” (T 1.2.2.1 SBN 29) Commentators generally interpret Hume as claiming that we can infer from our clear and adequate ideas of space the nature of space itself. However, I will argue that Hume simply means that when two ideas contradict, we infer that the objects of these two ideas do not both exist—a far more innocuous move. In this final chapter I will lay out Hume’s argument for why the idea of an infinitely divisible extended object is contradictory, despite our intuitive belief to the contrary. Under this reading, the case for Hume’s atomism and relational theory of extension becomes more potent, and is seen to be consistent with the philosophical elements found in his Treatise.