Space and the Self in Hume's Treatise (review)

Hume Studies Volume XXV, Numbers 1 and 2, April/November 1999, pp. 241-249 Book Reviews MARINA FRASCA-SPADA. Space and the Self in Hume's Treatise. Cambridge: Cambridge University Press, 1998. xiii + 220. ISBN 0-521-620-910, $59.95, cloth. Marina Frasca-Spada's Space and the Self in Hume's Treatise proposes a subjective idealist interpretation of Hume's account of space in part ii of Book I of the Treatise. The book is divided into four chapters. The first deals with Hume's position on infinite divisibility in I ii 1-2, the second with his position on the origin of the idea of space in I ii 3, the third with his account of geometrical knowledge in I ii 4, and the final chapter with his position on vacuum in I ii 5. The subject matter of I ii 6 on the idea of existence is dealt with over the course of the third chapter (146-149). Between the second and third chapters, the exposition is interrupted by what Frasca-Spada calls an "Intermezzo." This piece begins by promising to explain why Hume's theory of space is "central to the philosophical substance of the Treatise" (85), but turns to other topics before delivering on the promise. Its relation to the other parts of the book is unclear, and it would have been better included as a preface or appendix, or omitted altogether. The thesis of the first chapter is developed by way of commentary on a particularly problematic text: Hume's claim at Treatise 27 that while it is possible to have distinct ideas of the thousandth and ten-thousandth part of a grain of sand, it is not possible to have distinct images of these parts, and that the idea of a grain of sand is not separable into twenty, much less ten thousand , parts. Frasca-Spada resolves the apparent inconsistencies in this text by distinguishing between four different types of objects that figure in Hume's claims: Volume XXV, Numbers 1 and 2, April/November 1999 242 Book Reviews ideas of numbers and proportions, mental images of things and their parts, visual images of things and their parts, and the things themselves. As Frasca-Spada reads Hume, he means to say that we can form conceptions of arbitrarily small quantities by relating our ideas of numbers to one another. Since there is no limit to the smallness of the ideas of fractions that we can form, there is no lower bound to this process. But the mental images that we form to represent these arbitrarily small numbers do not get smaller as the numbers do. While we can think that there are ten ten-thousandth parts of a grain of sand in a one-thousandth part of a grain of sand, the mental image we form to accompany our thought of the ten-thousandth part is no different from the one we form to accompany our thought of the one-thousandth part. Both are points that have color but zero extension. Frasca-Spada points to an analogy with Hume's account of abstract ideas. With abstract ideas, a term gives rise to the thought of a particular individual that stands in for a whole group, and the mind has a tendency to very readily substitute any other member of the group for the representative idea. With very small objects, a mental image of a minimum stands in for any of a number of different numerical proportions and the mind uses the same image to stand for any of them. Frasca-Spada takes it that, for Hume, visual minima exist at a number of different levels. Any object will appear as a minimum if viewed from a sufficient distance. Upon approach or upon viewing the object with a telescope or microscope, the object appears as extended and it is its parts that appear as minima. Closer scrutiny expands these minima in turn. Having once moved down through a number of these "levels," the mind develops a tendency to carry on in the process and suppose that increasingly close scrutiny will continue endlessly expanding previously minimal visual images into further, only apparently minimal parts...