Hume’s discussion of space in the Treatise addresses two main topics: divisibility and vacuum. It is widely recognized that his discussion of divisibility contains an answer to Bayle, whose Dictionary article “Zeno of Elea” presents arguments about divisibility as support for fideism. It is not so widely recognized that, elsewhere in the same article, Bayle presents arguments about vacuum as further support for fideism. This paper aims to show that Hume’s discussion of vacuum contains an answer to these vacuum-based fideistic (...) arguments. Key to this answer is a distinction between two ways in which vacuum was conceived in the early modern period: i) as a genuine thing that has spatial properties, and yet is immobile, indivisible, and penetrable ; ii) as a mere absence of spatial things. This paper also aims to provide a novel defense of Hume against the long-standing objection that he is inconsistent in denying that we can conceive of a vacuum, while allowing that we can conceive of “invisible and intangible distance.” As I interpret him, Hume consistently denies that we can conceive of a positive vacuum, while allowing that we can conceive of two or more objects’ being arranged so as to have privative vacuum between them. (shrink)

In Treatise 1.4.2, David Hume seeks to explain how we come to believe in the external existence of bodies. He offers a complicated psychological account, where the imagination operates on the raw data of the senses to produce the ‘vulgar’ belief in the continued existence of the very things we sense. On behalf of philosophers, he presents a perceptual relativity argument that purports to show that the vulgar belief is false. I argue that scholars have failed to appreciate Hume's peculiar (...) formulation of the perceptual relativity argument and its relation to his psychological account of the vulgar belief. On my interpretation, in order to account for all the premises that Hume explicitly offers, the argument is best interpreted as beginning with a reductio that opposes the effects of the senses and the imagination in the vulgar belief. Thus Hume can be interpreted as identifying an ‘antinomy’ in the habits of the vulgar mind that produce belief in bodies. (shrink)

In the Treatise, Book I, Part iv, Section 2, Hume seeks to explain what causes us to believe that objects continue to exist even when they are not perceived. He argues that we won't be able to prov...