1 Hume's only serious arguments for the necessity of contiguity and succession are found in A Treatise of Human Nature (hereafter “T”, with page references to the Selby-Bigge edition). My statement of Hume's claim follows closely his formulation in his Abstract of the Treatise (p. 12). An Enquiry Concerning Human Understanding (hereafter “EHU”, with paragraph references to the Selby-Bigge edition) only incorporates succession into the definition of “cause”; but we shall see that in Hume's philosophy “contiguity” and “succession” are similar in meaning.
2 Hume holds that there are non-spatial, non-quantitative, causally related objects. Passions, moral reflections, smells, sounds, etc. are examples. These objects are “nowhere” and so have “no particular place” (T, 235f).
3 Early in the Treatise Hume seems to relax his contiguity criterion when he says “each remove considerably weakens the relation” (T, 11). He is speaking here of connection in the imagination. He later disallows this relaxed criterion (T, 75).
4 For an orientation to the relevant scientific background of Hume's contiguity criterion, cf. Kuypers M. S., Studies in the Eighteenth Century Background of Hume's Empiricism (New York: Russell & Russell, 1966), Chapters I–IV; The Leibniz-Clarke Correspondence, ed. Alexander H. G. (Manchester: Manchester Univ. Press, 1956); and Koyré A., From the Closed World to the Infinite Universe (New York: Harper & Row, 1958).
5 Hume does defend a doctrine of “indivisible parts” of space and time, but these arguments are markedly weak. The temporal discontinuity thesis would now be almost universally rejected by philosophers. (Cf. his rather dogmatically asserted claims in T, 29–31 and EHU, §125.)
6 This analysis of causation and time is explored, but not necessarily endorsed, by Russell B., “On the Notion of Cause,” in Mysticism and Logic (New York: Doubleday, 1917), pp. 178–82; Ducasse C. J., Nature, Mind, and Death (LaSalle, Illinois: Open Court, 1951), pp. 133ff; and Kneale W., Probability and Induction (Oxford: Oxford University Press, 1949), pp. 62–64.
7 The argument, as I have stated it, seems to be held by: Taylor Richard, “Causation,” Monist, 47 (1963), p. 312; Riker William H., “Causes of Events,” The Journal of Philosophy, LV (March 1958), pp. 281–91; and B. Russell, op. cit. Unfortunately, Russell's analysis is complicated by the fact that he is operating with a definition of “cause and effect” which he rejects.
8 Whether or not under such circumstances the connection between a cause and its effect could properly be said to be a “logically necessary connection” is explored by Maxwell N. in “Can there be Necessary Connections between Successive Events?,” British Journal for the Philosophy of Science, 19 (1967), pp. 1–25.
9 Worse still, Hume seems guilty of the a priori causal legislation for which he censures rationalists as well as of the “enquiry beyond the senses” he everywhere denounces. He does occasionally mention our “profound ignorance” in such matters (EHU, §57, T, 638f). But this again strikes him as good grounds for deriding Cartesianism.
10 Berkeley, Principles of Human Knowledge, §110–117. In Siris, Berkeley also rejects postulation of an etherial medium for causal transmission as unproved and gratuitous. Cf. Works, ed. Luce and Jessop, Vol. V, pp. 108–18.
11 Taylor and Russell, op. cit.; Collingwood R. G., An Essay on Metaphysics (Oxford: Clarendon Press, 1940), pp. 314f.