1 Thanks are due to the Social Sciences and Humanities Research Council of Canada (grants 410 92 0674 and 410 1999 1125) for support of this work.

2 This is a very strong constraint, since it implies that any event we can have knowledge of is an event whose causes must be somehow beyond reach: There can be no means by which to ‘bring about’ (or prevent) such an event. This alone is enough to make backwards causation (in a single-time line universe) and prophecy unacceptable.

3 See, for instance, Suppes, P. A Probabalistic Theory of Causality. (Amsterdam: NorthHolland Publishing Company 1970)Google Scholar and Salmon, W. ‘Probabalistic Causality,’ Pacific Philosophical Quarterly 61 (1980) 50–74CrossRefGoogle Scholar.

4 Mellor declares that chances do not have completely precise numerical values, so this uniqueness requirement is less onerous than it might appear. Nevertheless, whatever sort of values they do have must meet it.

5 This is asserted in chapter 2 and argued — though unconvincingly — in chapter 17.

6 In fact they turn out, on Mellor's account, to be facta.

7 There is a serious mistake here: Mellor says that S does make it the case that R would be true if Q were (and similarly for R’ and ∽Q) — as he puts it, ‘If Q were the case, ∽R might be.’ is false, as is ‘If ∽Q were the case, ∽R’ might be.’ But this requires that R hold in the nearer Q worlds. And (30) implies that ch(P) = p holds in the nearer R and Q worlds. So ch(P)=p must also hold in the nearer Q worlds. As a result, the new definition is equivalent to the old.

8 See Tooley, M. Causation, (Oxford: Clarendon 1987)Google Scholar, Brown, J.R. Smoke and Mirrors, (London: Routledge 1994)CrossRefGoogle Scholar, and Armstrong, D. What is a Law of Nature? (Cambridge: Cambridge University Press 1983)Google Scholar.

9 Since ch(∽P) = 1- ch(P), it follows that ch(P) = 0 entails ∽P; against the objection that real-valued pointer results must have probability 0, and so any outcome for a real-valued measurement is ruled out, Mellor says that no pointer ever really produces a real-valued result; instead it produces a (vague?) range result (25 + /- .5, for example) which will have non-zero probability.

10 See McGee, V. ‘Learning the Impossible,’ 179-99 in Eells, E. and Skyrms, B. eds., Probability and Conditionals (Cambridge: Cambridge University Press 1994).Google Scholar

11 Cartwright, N. How the Laws of Physics Lie (Oxford: Clarendon 1983), 25CrossRefGoogle Scholar

12 Note that if this gap-filling cannot be carried through without violating the probability axioms, then Mellor's claim that chances are probabilities fails.

13 It's also worth remarking that some interpretations of quantum theory involve deterministic causation — but it is a (and this is equally unpalatable to Mellor — vide infra) non-local determinism.

14 It might be urged that something odd is happening here, since in the circumstances it's simply not possible for Bill not to smoke. But if we apply Lewis conditionals to our story, this only means we must consider a world at which the law or laws requiring this fail; following Lewis’ criteria, we must keep this failure to a minimum, and preserve fully the circumstances leading up to the point at which Bill fails to take up smoking. Thus in the nearest worlds at which Bill does not smoke, we will retain both his having C, and the laws and instances of laws leading from C to cancer. So the chance of Bill's having cancer should he not smoke will be 1 on Mellor's declared principles.

15 At that time and site — nothing rules out his failing to smoke somehow giving rise to some other cancer, although the deterministic view here would at least hold any cancer to which his smoking or non-smoking was causally irrelevant fixed.

16 See Brown, B. ‘A Defense of Backwards Causation,’ Canadian Journal of Philosophy 22.4 (1992)CrossRefGoogle Scholar for a discussion of bilking arguments and the assumptions they involve.

17 We might also ask, what is ‘incompatible’ about different laws imposing a reversed ordering of spacetime points? There is nothing wrong with one ordering being the reverse of another - the problem must be that these are meant to be causal orderings. But the possibility of temporally opposed causal orderings is precisely what is being considered here; Mellor is begging the question if he is simply rejecting such a possibility out of hand.

18 A similar example is due to Deborah Rosen, reported in P. Suppes, A Probabalistic Theory; Rosen's own response to this case is to make this very suggestion, calling for a more detailed specification of the circumstances relative to which the hook (in her example, a branch being struck) does increase the probability of the ball ending up in the hole.

19 See Salmon, W. ‘Probabalistic Causality,’ in Sosa, E. and Tooley, M. eds., Causation (Oxford: Oxford University Press 1993)Google Scholar.

20 Good, I.J. ‘A Causal Calculus I,’ British Journal for the Philosophy of Science 11.44 (1961) 318Google Scholar

21 Of course, someone might say that Moriarty's presence was clearly crucial to the second sort of causal story, in the sense that the probability of Watson's pushing the boulder is much higher with Moriarty there than it is with Moriarty absent, and so Moriarty's presence is part of the story leading to the push. But Moriarty's presence is arguably screened off from Holmes’ death by Watson's push: The probability of Holmes’ death given the push is equal to the probability of Holmes’ death given the push and Moriarty's presence. So Moriarty's presence is irrelevant to the link between the push and Holmes’ death.

22 Salmon, W. ‘Probabalistic Causality’, in Sosa, E. and Tooley, M. eds., Causation (Oxford: Oxford University Press 1993), 151Google Scholar

23 See for example Friedman, J. et al., ‘Cauchy Problem in Spacetimes with Closed Time-Like Curves,’ Physical Review D 42 (1990)Google Scholar, and Deutsch, D. ‘Quantum Mechanics Near Closed Time-Like Lines’ Physical Review D 44 (1991) 3197–219.Google Scholar

24 Maudlin, T. Quantum Non-Locality and Relativity (Oxford: Blackwell 1994)Google Scholar

25 Except, of course, by mere luck — but the violations of the Bell inequality are well established on strong statistical evidence, and similar correlations may eventually produce individual outcomes that rule out local realism.

26 Peacock, K. ‘On the Edge of a Paradigm Shift: Quantum Nonlocality and the Breakdown of Peaceful Coexistence,’ International Studies in the Philosophy of Science 12.2 (1998) 129–50CrossRefGoogle Scholar; see also Kennedy, J.B. ‘On the Empirical Foundations of the Quantum No-Signalling Proofs,’ Philosophy of Science 62, 543–60.CrossRefGoogle Scholar