Hume on Infinite Divisibility and Sensible Extensionless Indivisibles
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Footnotes
1. David Hume, Essays and Treatises on Several Subjects, Vol. II (1777), facsimile page for the "Advertisement," reprinted in Enquiries concerning Human Understanding and concerning the Principles of Morals, edited by L. A. Selby-Bigge, 3rd edition revised by P. H. Nidditch (Oxford: The Clarendon Press, 1975), 2.
2. Donald L. M. Baxter, "Hume on Infinite Divisibility," History of Philosophy Quarterly 5 (1988): 140.
3. C. D. Broad, "Hume's Doctrine of Space," Dawes Hicks Lecture on Philosophy, Proceedings of the British Academy 47 (1961): 171.
4. Ibid., 176. I do not share Broad's condemnation of Hume's theory, but I agree with his emphasis on the importance of phenomenal evidence in Hume's argument, as against most commentators who focus exclusively on the mathematical reductiones ad absurdum.
5. I shall not comment except in passing about Hume's theory of time, nor about his criticisms of the idea of a vacuum. Hume's parallel treatment of extension in space and duration and time is given in A Treatise of Human Nature, edited by Selby-Bigge, 2nd edition revised by Nidditch (Oxford: The Clarendon Press, 1978), 34-39; the vacuum in Treatise, 39-42, 53-65. See Broad, "Hume's Doctrine of Space," 171-76.
6. Treatise, 27. See also 42.
7. Ibid., 4.
8. Ibid., 33.
9. Ibid., 29.
10. Ibid., 19.
11. Ibid., 26.
12. Ibid., 27.
13. Baxter, "Hume on Infinite Divisibility," 135: "Going in for a closer look ruins this as a model of Hume's theory of the structure of space. You cannot go in to see if the grains are divisible; you cannot go in to see if they are touching or not."
14. Treatise, 27.
15. Ibid., 28.
16. See David Raynor, "'Minima Sensibilia' in Berkeley and Hume," Dialogue 19 (1980) 196-200. George Berkeley, An Essay towards a New Theory of Vision, The Works of George Berkeley, Bishop of Cloyne, edited by A. A. Luce and T. E. Jessup (London: Thomas Nelson & Sons, 1949-1958), § 54. John Locke, An Essay concerning Human Understanding, edited by A. C. Fraser (Oxford: Oxford University Press, 1894), Book II, Chapter XV, § 9. See my "Kant's Second Antinomy and Hume's Theory of Extensionless Indivisibles," Kant-Studien 84 (1993): 38-50.
17. Treatise, 28.
18. Broad "Hume's Doctrine of Space," 166. John Laird, Hume's Philosophy of Human Nature (London: E. P. Dutton, 1932), 68-69. Robert Fogelin, Hume's Skepticism in the "Treatise of Human Nature" (London: Routledge & Kegan Paul, 1985), 29. Fogelin, 27, offers a useful sketch of what he perceives as the principal "stages" of Hume's reasoning about infinite divisibility. This may not be intended as a reconstruction of any particular argument in Hume, but it ignores Hume's claims about the sense impression origin of the idea of extension, and mentions Hume's inkspot experiment only as an aside to what he regards as the more important finite divisibility limitations of imagination.
19. Treatise, 34. See 239-40: "And to cut short all disputes, the very idea of extension is copy'd from nothing but an impression, and consequently must perfectly agree to it." Hume makes precisely parallel remarks about the immediacy of the idea of duration in time; see ibid., 36: "Five notes play'd on a flute give us the impression and idea of time . . . . "
20. The classification of the idea of extension as complex follows from the distinction between simple and complex ideas; see Treatise, 2. The fact that the idea of extension is divisible into parts, ultimately into indivisibles, excludes it from the category of simple ideas. Hume nowhere explicitly refers to the idea of extension as "complex," but at 38 calls it "compound." See Ben Mijuskovic, "Hume on Space (and Time)," Journal of the History of Philosophy 15 (1977): 387. Norman Kemp Smith, The Philosophy of David Hume (New York: The Macmillan Company, 1964), 227.
21. Treatise, 5-6.
22. Antony Flew criticizes Hume's efforts to preserve the realist idea-reality distinction in David Hume: Philosopher of Moral Science (Oxford: Basil Blackwell, 1986), 29-37. Broad...
