Time travel and counterfactual asymmetry


We standardly evaluate counterfactuals and abilities in temporally asymmetric terms—by keeping the past fixed and holding the future open. Only future events depend counterfactually on what happens now. Past events do not. Conversely, past events are relevant to what abilities one has now in a way that future events are not. Lewis, Sider and others continue to evaluate counterfactuals and abilities in temporally asymmetric terms, even in cases of backwards time travel. I’ll argue that we need more temporally neutral methods. The past shouldn’t always be held fixed, because backwards time travel requires backwards counterfactual dependence. Future events should sometimes be held fixed, because they’re in the causal history of the past, and agents have evidence of them independently of their decisions now. We need temporally neutral methods to maintain connections between causation, counterfactuals and evidence, and if counterfactuals are used to explain the temporal asymmetry of causation.

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  1. 1.

    For possible scenarios, see Lewis (1976, p. 152), Smith (1997, p. 372ff.) and Sider (2002, pp. 131–133).

  2. 2.

    My arguments won’t depend on the details of how abilities and counterfactuals are related. One might think that counterfactuals and abilities are only related for a subclass of counterfactuals—those relevant to abilities (Sider p. 137 n. 9). Explicitly adopting this restriction won’t change the arguments to come. Nor will it affect the point here: that context-sensitivity is what defuses the grandfather paradox.

  3. 3.

    Vihvelin (1996) rejects the first reading for cases in which, she argues, the counterfactual antecedent can’t be brought about except by failure of the attempt (without introducing large miracles). Rennick (2015) rejects the first reading for cases in which the time traveller intentionally tries to bring about what they believe will not happen. I’m concerned with a broader class of cases. Moreover, my main concern at this stage is to defend the reasonableness of the ‘can’t’ reading, not to reject the possibility of the ‘can’.

  4. 4.

    The apparent “coincidences” can also be explained by the system’s dynamics (Arntzenius and Maudlin 2013).

  5. 5.

    Vihvelin (2011) and Rea (2015, p. 270 n. 7) also distinguish between arguments for future events limiting our freedom and fatalist arguments.

  6. 6.

    Kiourti (2008, pp. 349−350) also argues that future events are relevant to an agent’s abilities when they’re in the personal past. The arguments below are more general, and do not rely on demarcating the personal past. While Rea (2015) eschews talk of counterfactuals and abilities, he also uses causal features to argue that time travellers are not free. However, Rea relies on the premise that we should keep the whole causal past of an agent fixed when evaluating what the agent is free to do at t, where the causal past includes all events that stand in the ancestral of the causal relation to events at t concerning the agent (ibid., p. 271). As Rea acknowledges (ibid., pp. 269−270), his justification for this premise relies on assuming freedom is incompatible with determinism—an assumption that I, as well as Lewis and company, would reject. I’ll argue that some future events (in the causal past) should be held fixed, not that all events in the causal past (in Rea’s sense) should be held fixed—see Sect. 5.

  7. 7.

    Whether ¬B□→¬A is true depends on details of how counterfactuals are evaluated. The claim I make here is comparative: to the extent that holding past events fixed is required to rule out backtracking counterfactuals in the actual world, as in Lewis (1979) and on causal methods of evaluating counterfactuals, holding future events fixed is required to rule out backtracking in the above case.

  8. 8.

    Local approaches are also difficult to square with global methods of evaluating counterfactuals like Lewis’ (1979).

  9. 9.

    Lewis defines traces non-causally. However, he was wrong about the precise form and origin of the trace asymmetry (Elga 2001; Field 2003), and debate has continued over whether asymmetries of traces or ‘records’ can be explained in non-causal terms. See Reichenbach (1956), Horwich (1987, Ch. 5), Albert (2000, Ch. 6) and Loewer (2007) for attempts, and Earmam (1974) and Frisch (2010) for criticism. Earman (1974, p. 41), for example, argues that traces must be analysed in causal terms.

  10. 10.

    Even if cases of backwards time travel involve causal loops, accounts still need to give direction to the causal loop. The presence of causal loops does, however, create other trouble—see Sect. 5.

  11. 11.

    Lewis’ approach doesn’t actually imply that future events are held fixed. But this is due to a general problem his account has with cases of backwards time travel. Lewis’ method is global in character, seeking perfect match between largest possible spatiotemporal regions, and so has trouble capturing the local violations of causal order in cases of backwards time travel. For examples of this trouble, see Tooley (2002), Collins, Hall and Paul (2004, p. 11), and Wasserman (2015). For a related diagnosis and a causal solution, see Wasserman (2018, pp. 171–182).

  12. 12.

    Ismael (2003, p. 314) and Arntzenius (2006, p. 613) also note that violations of evidential asymmetry in time travel cases may spell trouble for asymmetric counterfactual and causal reasoning. But neither takes this to affect the time traveller’s abilities. Rennick (2015) argues that a time traveller’s freedom may be limited by her beliefs. The approach I take below provides a more general route to a similar conclusion.

  13. 13.

    Even so, one might hold future events fixed in virtue of the fact that they cause present events, or in virtue of the fact that they are evidenced by present events. As I discuss in the next section, these options suggests different approaches to evaluating counterfactuals.

  14. 14.

    Accounts differ on whether the asymmetry of records is strict. For example, while Albert begins by drawing attention to particular methods that apparently work towards the past (and not the future) (2000, p. 113), the asymmetry he ultimately derives (ibid., p. 122) doesn’t actually entail a strict asymmetry of local records. Loewer (2007, p. 303) defines records somewhat differently, and explicitly takes the asymmetry to be matter of degree—we only have more reliable records of the past (compared to the future). For criticisms of this program, see, again, Earman (1974) and Frisch (2010).

  15. 15.

    If Tim is unsure of the metaphysics of time, perhaps we’d not fault him for failing to believe his grandfather will survive—but he’d still be failing to follow his external evidence.

  16. 16.

    Won’t Tim have countervailing evidence in the form of evidence about what he can do? Certain of his ability to kill the man before him, shouldn’t he be certain it isn’t his grandfather after all? (My thanks to a reviewer for the case.) In particular scenarios, one’s alethic modal evidence about what one can do (and what that would imply) may outweigh one’s epistemic modal evidence about what does happen in the actual world. (See Ismael (2017, p. 117) for more on the distinction.) What I’m committed to is a priority of epistemic modality over alethic in new settings: in these settings, modal evidence takes priority over alethic evidence in cases of conflict. My reasons for this are themselves epistemic: in new settings, we learn about what would happen if we tried only by observing what does happen when we try. So Tim shouldn’t remain certain of his ability to kill young-gramps and take this to throw in doubt his evidence of young-gramps’ identity.

  17. 17.

    There are difficult issues to explore concerning what it is for Tim to ‘have’ evidence. For example, does Tim have evidence when he has an envelope that (unbeknownst to him) contains relevant information, but has, a) left it behind, unopened, or b) brought it with him, unopened, or c) brought it with him and read it? (My thanks to a reviewer for the case.) My responses are: a) no, b) probably not, c) yes. The answers (to my mind) turn on what we take the relevant epistemic standards of a world to be (noting that these may be different from standards of praise or blame). I suspect someone isn’t necessarily failing as an epistemic agent when they don’t open letters, but they are if they fail to take into account information contained in letters they’ve read. But one could argue for different standards, or take a non-normative approach.

  18. 18.

    Differences may also arise due to how fine-grained the relata are, or how probabilistic relations are treated.

  19. 19.

    There may also be events evidenced in the present that aren’t in the causal past, and events in the causal past that aren’t evidenced in the present. So holding evidenced events fixed is, again, not equivalent to holding the casual past fixed.

  20. 20.

    Horacek (2005, p. 424), however, argues that we should hold the past fixed when determining chances.

  21. 21.

    Arntzenius and Maudlin (2013) discuss independent problems concerning indeterminacy.

  22. 22.

    Rea (2015, pp. 273–274) also notes this concern with respect to what we are free to do. Rea prefers to keep the causal past fixed in a very wide sense. But his justification for doing so is an incompatibilist one.

  23. 23.

    What would happen were old-Coleridge not to teach the poem to his younger-self depends on details of the case. If Coleridge’s evidence of knowing the poem is had independently of his evidence of how he came to learn it, his knowing the poem is held fixed—he will come to learn the poem by some other means. Otherwise, his knowing it is not held fixed.


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My warm thanks to the following people for helpful comments, discussions and suggestions: David Albert, Kristie Miller, Achille Varzi, Carolina Sartorio, Alasdair Richmond, Jenann Ismael, Anjan Chakravartty, Matthew Brown, Kareem Khalifa, Yann Benétreau-Dupin, Edouard Machery, Jonathan Tallant, Christian Loew, Juliusz Doboszewski, and Giuliano Torrengo. This work was supported by a Postdoctoral Fellowship at the Center for Philosophy of Science, University of Pittsburgh, and a Research Fellowship on the AHRC project ‘Time: Between Metaphysics and Psychology’ at the University of Warwick (AH/P00217X/1).

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Fernandes, A. Time travel and counterfactual asymmetry. Synthese (2019). https://doi.org/10.1007/s11229-019-02186-w

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  • Time travel
  • Counterfactuals
  • Causation
  • Evidence
  • Temporal asymmetry
  • Backwards causation
  • Open future
  • David Lewis