I argue that the Hume of the Treatise maintains an account of knowledge according to which (i) every instance of knowledge must be an immediately present perception (i.e., an impression or an idea); (ii) an object of this perception must be a token of a knowable relation; (iii) this token knowable relation must have parts of the instance of knowledge as relata (i.e., the same perception that has it as an object); and any perception that satisfies (i)-(iii) is an instance (...) of knowledge. I then apply this account to the case of sense perception. I argue that Hume holds that relations of impressions can be intuited, are knowable, and are necessary. For Hume, these relations constitute sensory knowledge. While Hume is rightly labeled an empiricist for many reasons, a close inspection of his account of knowledge reveals yet another way in which he deserves the label. (shrink)

In the Treatise of Human Nature, David Hume mounts a spirited assault on the doctrine of the infinite divisibility of extension, and he defends in its place the contrary claim that extension is everywhere only finitely divisible. Despite this major departure from the more conventional conceptions of space embodied in traditional geometry, Hume does not endorse any radical reform of geometry. Instead Hume espouses a more conservative approach, claiming that geometry fails only “in this single point” – in its purported (...) proofs of infinite divisibility – while “all of its other arguments” remain intact. -/- In this paper, after laying out the prima facie case for Hume’s radical challenge to traditional geometry, I consider five strategies for blocking the arguments for infinite divisibility while conserving most of geometry. I show that each of these interpretive strategies suffers from serious substantive problems, and so none of them delivers an interpretation of Hume’s account that provides him with a way of blocking the geometric arguments for infinite divisibility while sustaining his geometric conservatism. (shrink)