^{page 263 note 1} See section x, ‘Of Miracles’, pp. 109 ffGoogle Scholar. All page references are to the Selby-Bigge, edition, revised by P. H. Nidditch (Oxford: Clarendon Press, 1975).Google Scholar

^{page 265 note 1} It may be remarked that (1)–(5) would still hold if one adopted the slightly different method of measuring the degree of rational assurance in h whereby A(h) = (m–n)/(m+n), where m ≥ n. This method gives the same maximal and minimal values for A(h) but differs over the value for intermediate cases. Thus, again using Hume's example, if m = 100 and n = 50, then by this method A(h) = (100–50)/(100+50) = 1/3. Nothing that Hume says indicates that he would have endorsed this method in preference to the one proposed by me in the text. (See further the next two footnotes.)

^{page 265 note 2} This would be the sort of approach one would expect according to modern probabilistic confirmation theory, where it is required that the degrees of confirmation assigned to hypotheses satisfy the axioms of the probability calculus; on this approach, Pr (h) = I – Pr (˜h). We have to realize, however, that Hume is not using the term ‘probability’ in quite this modem way. Observe that the requirement in question would be met if we were to set A(h) = m/(m+n) and A(˜h) = n/(m+n), since m/(m+n) = I-n/(m+n). However, this would obviously not capture Hume's idea that we must subtract the negative from the positive instances (where the latter predominate) to arrive at the degree of rational assurance.

^{page 266 note 1} Observe that it won't do simply to omit the divisor in the equation for A(h) set out above, saying instead that A(h) = m–n (where m ≥ n). For then we should have the no Is absurd implication that A(h) is the same for m = 100, n = 51 as for m = 50, n = I. Thus the mere absolute difference between positive and negative instances cannot sensibly be taken as the measure of the degree of rational assurance. The problem is that Hume does not tell us explicitly what further mathematical operation on the absolute difference is required to generate the degree of rational assurance. All he says is that the degree of evidence or assurance in h must be ‘proportioned to the superiority’ of positive over negative instances; but he cannot seriously be taken to mean by this that A(h) must be (in mathematical terminology) a monotonic increasing function of (m–n), for this would imply (for example) that A(h) is greater for m = 100, n = 50 than for m = 50, n = I, which is absurd. The ‘superiority’ he speaks of must, evidently, be construed as a relative rather than as an absolute one: but relative to what?

^{page 269 note 1} Even this assumption is in fact highly questionable, though I wi11 not trouble to question it here since my present object is to criticize Hume's bold claim to have a ‘proof’ against the occurrence of any miraculous event.

^{page 269 note 2} I should emphasize that I am implicitly excluding, for the purposes of the present discussion, statistical laws, such as those of quantum physics or of thermodynamics; it is very much more difficult to say what would constitute a ‘violation’ of such laws.

^{page 270 note 1} Obviously this remark only applies to those philosophers who have gone along with the conception of a miracle as involving a ‘violation of a law of nature’: but they constitute a very sizeable proportion of those who have written on miracles, and indeed represent what might be called the ‘mainstream view’ on the matter.

^{page 270 note 2} Of course, there might be more than one such conception.

^{page 273 note 1} See, e.g. my ‘ortal Terms and Natural Laws’, American Philosophical Quarterly, XVII (1980), 253–60Google Scholar and my ‘Laws, Dispositions and Sort al Logic’, American Philosophical Quarterly, XIX (1982), 41–50.Google Scholar

^{page 275 note 1} Inevitably I have had to gloss over a number of subtleties in describing my position in so short a space; for fuller details, see the articles cited earlier. I should also emphasize that much work yet remains to be done on the logic of nomological statements within the normative paradigm.

^{page 275 note 2} This indeed is why the law is naturally expressed by the sentence ‘Ravens are black’ rather than, say, by the sentence ‘All normal ravens are black’.

^{page 275 note 3} Here it is worth remarking how the normative account of laws fits in with my earlier comments on the logical form of statements of natural possibility. The normative account – as its title suggests – readily accommodates the parallels I suggested between natural laws on the one hand and moral and judicial laws on the other.

^{page 276 note 1} Including even explanation by reference to statistical laws.

^{page 276 note 2} This presupposes, what may well be correct, that explaining something as the intended outcome of an action is a different kind of explanation from explanation in terms of natural law.

^{page 278 note 1} Observe that Hume himself verges on allowing just this when he says that ‘I own, that … there may possibly be miracles, or violations of the usual course of nature’ (p. 127, my emphasis).Google Scholar ‘Usual’ here may plausibly be taken to mean something very much like ‘normal’.

^{page 278 note 2} Amongst the vast literature on the subject-matter of this paper, I have found the following items more illuminating than most, though I am by no means in full agreement with any of their authors: Swinburne, Richard, The Concept of Miracle (London: Macmillan, 1970);CrossRefGoogle ScholarFlew, Antony, Hum's Philosophy of Belief (London: Routledge and Kegan Paul, 1961, ch. VIII);Google ScholarMackie, J. L., The Miracle of Theism (Oxford: Clarendon Press, 1982, ch. 1).Google Scholar