The paper addresses two difficulties that arise in Treatise 1.2.5. First, Hume appears to be inconsistent when he denies that we have an idea of a vacuum or empty space yet allows for the idea of an “invisible and intangible distance.” My solution to this difficulty is to develop the overlooked possibility that Hume does not take the invisible and intangible distance to be a distance at all. Second, although Hume denies that we have an idea of a vacuum, some (...) texts in Treatise 1.2.5 are taken by interpreters to suggest that Hume nonetheless believes that there are vacuums in nature. I discuss the relevant texts and defend the view that Hume does not in fact countenance belief in vacuums. I conclude by outlining an interpretation of Hume’s intention in the Treatise that allows us to understand his discussion of ideas as having implications for the sciences. (shrink)

Hume's Treatise arguments concerning space, time, and geometry, especially ones involving his denial of infinite divisibility; have suffered harsh criticism. I show that in the section "Of the ideas of space and time," Hume gives important characterizations of his skeptical approach, in some respects Pyrrhonian, that will be developed in the rest of the Treatise. When that approach is better understood, the force of Hume's arguments can be appreciated, and the influential criticisms of them can be seen to miss the (...) mark. (shrink)

Since both berkeley and hume are committed to the view that a line is composed of finitely many fundamental parts, They must find responses to the standard geometrical proofs of infinite divisibility. They both repeat traditional arguments intended to show that infinite divisibility leads to absurdities, E.G., That all lines would be infinite in length, That all lines would have the same length, Etc. In each case, Their arguments rest upon a misunderstanding of the concept of a limit, And thus (...) are not successful. Berkeley, However, Adds a further ingenious argument to the effect that the standard geometrical proofs of infinite divisibility misread the unlimited representational capacity of geometrical diagrams as a substantive feature of the objects that these diagrams represent. The article concludes that berkeley is right on this matter, And that the traditional proofs of infinite divisibility do not show what they are intended to show. (shrink)

Hume had two principal arguments for denying that we can have an idea of a vacuum, an argument from the non-entity of unqualified points and an argument from the impossibility of forming abstract ideas of manners of disposition. He also made two serious concessions to the opposed view that we can indeed form ideas of vacua, namely, that bodies that have nothing sensible disposed between them may permit the interposition of other bodies without any apparent motion or occlusion and that (...) it is possible to conceive the contents of a room to be evacuated without being compelled to conceive the walls moving into contact. To reconcile these concessions with his arguments and show why we only “falsely imagine” that we can form the idea of a vacuum, Hume developed a psychological theory of the perception of “invisible and intangible distance” that has something in common with Berkeley’s account of the perception of outward distance. This paper argues that this theory is both untenable and inconsistent with fundamental Humean principles. It explains why Hume should have rejected the two arguments against the idea of a vacuum and why accepting ideas of vacua would have been more in line with the rest of his thought than attempting to deny that we have any such ideas. (shrink)

Scholars have almost universally agreed that Hume's account of space and time as manners of disposition of impressions is inconsistent with one of the most fundamental tenets of his empiricism: the thesis that all ideas are derived from simple impressions. This paper challenges that view and argues that Hume's position on the origin of our ideas of space and time is a profound, original, virtually unique, and even courageous approach to the problem of original space and time cognition, and a (...) theory that allows for hitherto unrecognized expansions to the resources available to his empiricism. (shrink)

This chapter contains section titled: Extension and Duration Hume's Reply to the Paradox of Composition Hume's Arguments for the Finite Divisibility of Perceptions (T 1.2.1) The Coherence of Hume's Account The Idea of Equality (T 1.2.4) The Infinite Divisibility of Objects (T 1.2.2) Manners of Disposition (T 1.2.3) The Simplicity of the Soul (T 1.4.5) The Idea of Vacuum (T 1.2.5) Hume's Account of Contiguity (T 1.1.5, 1.3.8, 2.3.7) Notes References Further reading.