Abstract

Hume on Infinite Divisibility and Sensible Extensionless Indivisibles DALE JACQUETTE 'Twere certainly to be wish'd, that some expedient were fallen upon to reconcile philosophy and common sense, which with regard to the question of infinite divisibility have wag'd most cruel wars with each other. David Hume, A Treatise of Human Nature 1. THE DIVISIBILITY ARGUMENTS David Hume's refutation of the infinite divisibility of space and time, and his doctrine of the sensible extensionless indivisibles that constitute extension, are perhaps the least loved, and until recently, least examined aspects of his early philosophy. The fact that Hume reduced his lengthy discussion of the prob- lem from the Treatise to just two pages of the first Enquiry, together with his disavowal of the first work in the Enquiry's "Advertisement," have reinforced the tendency to ignore his arguments. ~ Opinions on the merits of Hume's analysis of space are widely divided. To give a sense of the disparity, Donald L. M. Baxter, in "Hume on Infinite Divisibility," maintains: "Far from begging the question, Hume has available a respectable argument against the infinite divisibility of finite spatial intervals."' C. D. Broad, on the contrary, in his Dawes Hicks Lecture on Philosophy to the British Academy, "Hume's Doctrine of Space," concludes: "I think, then, that Hume's whole account of spatial divisibility can David Hume, Essays and Treatises on...