1 I want to thank the SSHRC of Canada grant#410-89-06 and the Center for Philosophy of Science at the University of Pittsburgh for their support during the time this paper was being written. Thanks are also due to two anonymous referees for CJP, who pressed me to clarify many obscurities and pointed out several helpful references.

2 Lewis, D. ‘The Paradoxes of Time Travel,’ American Philosophical Quarterly 13 1976 145-52Google Scholar

3 Davies, P.C.W. Space and Time in the Modern Universe (Cambridge: Cambridge University Press 1977)CrossRefGoogle Scholar

4 Mellor, D. Real Time (Cambridge: Cambridge University Press 1981)Google Scholar. I use Mellor’s example rather than Dummett’s, who first discussed this sort of case in ‘Bringing About the Past/republished in Truth and Other Enigmas (Oxford: Clarendon Press 1976), because Dummett’s analysis concludes in favor of the possibility of backwards causation, though for reasons different from those I offer here. Versions of these paradoxes can be found throughout the literature on time travel (see for example Salmon, W. Space, Time, and Motion [Minneapolis: University of Minnesota Press 1977])Google Scholar. Salmon’s conclusion is that ‘at the very least, their (tachyon’s) existence would have severe repercussions for the concept of causality’ (122).

5 But see the discussion of locality at the end of section III below. This is where Mellor differs from Dummett, who regards this possibility as an escape for the defender of backwards causation.

6 See also Chapman, T. Time: A Philosophical Analysis (Dordrecht: D. Reidel 1982, 1-11CrossRefGoogle Scholar, for a presentation and defense of the sort of argument Mellor gives. Chapman relies heavily on the notion that ‘we know conclusively that there can be no evidence which would make it (backwards causation) the preferred explanation.’ However, he gives no discussion of cases in which our best theoretical account of the world involves backwards causation— for example, cases in which general relativity allows closed time like curves— and such cases are central to any serious exploration of the evidence we could have for backwards causation. Even if Chapman is right about cases in which our evidence for backwards causation is limited to correlations between various types of events otherwise unexplained, this cannot establish the wider conclusion he draws about the balance of evidence. Mellor has also claimed that the very idea of a closed loop of events, each of which increases the probability of the next, is incoherent, and that such a loop is essential to backwards causation. However, this argument involves assumptions about the nature of probability and causation which are open to dispute. Mellor’s argument is just not rich enough in its discussion of causation, probability, and loops to demonstrate the impossibility of backwards causation. See Riggs, P. ‘A Critique of Mellor’s Argument Against “Backwards” Causation,’ British journal for the Philosophy of Science 41 (1991) 75-86Google Scholar, for a fuller discussion of this argument.

7 For example, Gale, Richard in ‘Why a Cause Cannot Be Later Than Its Effect,’ Review of Metaphysics 19 (1965) 209-34Google Scholar, has argued that the appeal to agents and their capacities in consideration of backwards causation is methodologically indispensable: only appeal to the paradigmatic case of causation, intentional action, can ensure that what we are calling backwards causation is not just an unusual form of forwards causation, perhaps with abnormal boundary conditions. But there are other paradigms of causation, including the transfer of momentum between billiard balls in a collision. Although the direction of causation in such time-symmetric cases is usually a matter of the temporal order, where our theories allow for closed time-like curves, as general relativity apparently does, the temporal order itself will allow these standard examples of causation to occur in a way which produces temporally reversed causal connections and closed causal loops.

8 This is the minimal content that every form of libertarianism must share, if we assume only that libertarian agency is logically incompatible with physical determinism.

9 Journal of Philosophy 59 (1962); republished in Mathematics, Matter, and Method2nd ed. (Cambridge: Cambridge University Press 1979) 237–49

10 This account of states and orderings of states is the central theme of my ‘The Trouble with Time Travel’ (an unpublished ms) in which I offer a simplified account of what a physics allowing time travel would be like.

11 This notion is Lewis’s: a time traveler has two ways to locate events in time. She can locate them objectively according to their place in the overall time order, or personally, according to an analogy between her own causal relations to times and events and the causal relations typical for events and times in the past and future of non-time travelers. Thus the personal past of a time traveler can include events and times in her objective future, and her personal future can include events and times in her objective past. Either can give rise to paradoxical results, since when we speak of a person’s capacities we allow facts about the future to vary while holding fixed facts about the past, and we have two alternative construals of this, depending on whether we focus on the objective or personal time order. Worse still, times and events can have multiple locations in a time traveler’s personal time. Thus when we consider a time traveler’s capacities we must carefully decide what is to be held fixed and what is to be allowed to vary to avoid contradicting ourselves.

12 Those who hold that determinism does not rule out our being to do other than what we in fact do.

13 In Time Enough for love R. Heinlein apparently adopts this defense, declaring ‘you can’t change the past because you didn’t.’ I owe this reference to an anonymous referee for CJP.

14 Although the issue is largely avoided in ‘Dr. Who,’ and not always dealt with consistently, sometimes a version of this response is offered there.

15 That the first triad is inconsistent is somewhat controversial — David Deutsch has recently argued, in ‘Quantum Mechanics Near Closed Time-Like Lines,’ Physical Review D 44 (1991) 3197–219, that a pure quantum mechanical description rules out the sort of paradox we are considering here. However, such a resolution of the paradox is not available to any interpretation of quantum mechanics which includes collapse of the wave packet. And it is arguable, though perhaps only tendentiously, that the sort of capacities we ordinarily attribute to ourselves have a kind of determinacy of outcome that requires classical physics or at least collapse of the wave packet. So for now I will continue to claim that the triad is inconsistent.

16 Note that we also assume here that doing something different from what we actually do would necessarily involve a physical difference between the actual state of affairs after our action and the state of affairs that would obtain if we performed a different action.

17 See Stove, D. ‘Misconditionalisation,’ Australasian Journal of Philosophy 50 (1972) 173-83.CrossRefGoogle Scholar

18 B. Brown, ‘The Trouble with Time Travel.’ unpublished ms 1989.

19 I owe the terms ‘internal’ and ‘external’ to David Lewis, who suggested them to me in correspondence about ‘The Trouble with Time Travel.’

20 Friedman, J. etal., ‘Cauchy Problem in Space times with Closed Time-Like Curves,’ Physical Review D 42 (1990) 1915fCrossRefGoogle Scholar. But see Echeverria, Klinkhammer and Thorne, ‘Billiard Balls in Wormhole Spacetimes with Closed Time-like Curves: Classical Theory,’ Physical Review D 44 (1991) 1077-99CrossRefGoogle Scholar, where they argue that as a matter of fact none of the class of initial conditions examined suffered from this defect. Instead, they turn out to lead to multiple solutions: rather than undermine consistency, the troublesome boundary conditions merely give rise to a (badly behaved form of) indeterminism.

21 A more general account would consider the possibility of non-deterministic laws and internally but not externally possible sub-histories.

22 Horwich, P. Asymmetries in Time (Cambridge: MIT Press 1987)Google Scholar

23 ‘Closed Time-Like Curves Produced by Pairs of Moving Cosmic Strings: Exact Solutions,’ Physical Review Letters 66 (1991) 1126-9

24 However, Lewis may just be trying to reassure those who find the idea of time travel so absurd they would otherwise dismiss his case without a hearing. So perhaps this difference is more apparent than real.