Abstract
The future is different from the past. What is past is fixed and set in stone. The future, on the other hand, is open insofar as it holds numerous possibilities. Branching-tree models of time account for this asymmetry by positing an ontological difference between the past and the future. Given a time t, a unique unified past lies behind t, whereas multiple alternative existing futures lie ahead of t. My goal in this paper is to show that there is an incompatibility between the way branching-tree models account for the open future and the possibility of time travel. That is, I argue that once time travel enters the picture, branching time fails to model the openness of the future by means of alternative future branches. I show how this holds independently of whether branching-time models are cashed out in A-theoretic or B-theoretic terms.
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Notes
Positing a branching structure of time is just one of the possible ways to account for the asymmetry between a fixed past and an open future. The discussion and development of branching-tree models goes back at least to the seminal work of Prior 1967. MacFarlane 2003, 2008 can be seen as one of the recent proponents of the idea that branching-tree models correctly account for the asymmetry between the past and the future. Belnap 1992 offers and defends a rigorous theory of branching-tree models in relativistic settings. There are ways other than branching-tree models to account for the asymmetry. For instance, Markosian 1995 holds that the openness of the future amounts to the failure of the principle of Bivalence for future contingents. Growing block theorists (e.g., Broad 1923) can argue that the past is fixed because past entities and events exists, whereas the future is open because there is no entity such that it is future. Or, the asymmetry could be explained via an asymmetry in counterfactual dependence between the past and the future (see Lewis 1979). Further proposals have been put forward. As mentioned above, Torre 2011 and Grandjean 2019 offer an overview and discussion of the different ways to account for the asymmetry.
For another kind of tension between branching-time models and the possibility of time travel, see Norton 2018 who argues that if backwards time travel to our location is possible, then our universe is not a branching universe.
Miller argues for a broader incompatibility in her article. That is, she takes (1) to be incompatible with any model of time that features both an objective present and an open future. To that goal, besides the shrinking tree, she offers arguments for the incompatibility between time travel and presentism — roughly, the view according to which only the present exists — and between time travel and the growing block view — roughly, the view that only the past and the present exist. In this article, I focus on branching-tree models, therefore I set aside the case from presentism and the one from the growing block view.
The two tenets are taken literally from Miller (2005: 225). There is actually a further one Miller considers, which has to do with the impossibility of traveling from a non-existent location to an existing one. However, this tenet is used by Miller in her arguments regarding presentism and the growing block view, whereas it plays no role in her argument with respect to the shrinking tree view. I therefore shall ignore it here.
See also Baron 2017 for a more recent discussion on this. Actually, there is a great deal more to say about the possibility of time travel resulting in alterations of the past. Some philosophers, for instance van Inwagen 2010, think that models of time that make use of a second dimension of time, i.e., hyper-time, can allow changes in the past due to time travel. See Wasserman (2017: Ch.3) for an overview of the debate. I will have more to say about this tenet in the next section.
More precisely, Martinez's point here is that what he calls ‘standard tree-pruning’ should not apply when backwards time travel takes place in the shrinking tree. According to standard tree pruning, if a time t is the objective present and we have branches stemming off t, then the universe evolves respecting the following two conditions: (i) only one of the branches stemming from t becomes actual up to the later branching node tx and all the other branches stemming from t cease to exist, (ii) the branches stemming off tx remain existing non-actual possibilities. In case of backward causation from a later time ty to tx, Martinez argues that the tree pruning does not have to respect standard tree-pruning. It might be the case that when time moves from t to tx, condition (ii) is not respected. That is, some branches stemming off tx might cease to exist before they normally would. The state of the universe depicted in Fig. 1 respects standard tree-pruning, but it is not acceptable, Martinez says, given the occurrence of backward causation from t5 to t1. My upcoming argument against Martinez does not assume standard tree-pruning, hence I can grant him that in case of backward causation standard tree pruning does not hold.
For an exception, see Loss 2015 who argues that time travelers can change the past even if time is linear and one-dimensional. He proposes a sort of branching model where all the branches are ordered in a linear way. At any rate, I set aside this case here.
See Wasserman (2017: Sec. 3.3) for a summary of the debate on this specific issue. For the purposes of my argument, I do not need to take a stance on this.
One might think that there is a time which is the mereological sum of what I called t and t∗; t and t∗ would then be temporal parts of that time, which could change in virtue of having qualitative different temporal parts. Granting such possibility, the spirit of what I have been saying would then apply to this option too. In such case, one should say that the temporal parts of times composing a branching universe cannot change for the same reasons.
One might worry that when we move from the shrinking tree to the static tree, we no longer have a genuine account of the open future, independently of whether time travel takes place. For in the B-theoretic case the whole tree-structure is static and unchangeable, and nothing ever goes out of existence. If a future branch ahead of us contains a sea battle event and another one features peace instead, those two events are eternally and statically part of reality. One might then follow Lewis (1986: 207-8) and think that (static) branching is problematic insofar as “If two futures are equally mine, one with a sea fight tomorrow and one without, it is nonsense to wonder which way it will be — it will be both ways — and yet I do wonder.” Advocates of branching time have responses to this and other objections that have been raised against B-theoretic branching time. See Torre 2011 for an overview of the debate on this.
References
Baron, S. (2017). Back to the unchanging past. Pacific Philosophical Quarterly, 98(1), 129–147.
Belnap, N. (1992). Branching space-time. Synthese, 92(3), 385–434.
Broad, C. D. (1923). Scientific thought. New York: Harcourt, Brace and Co..
Grandjean, V. (2019). How is the asymmetry between the open future and the fixed past to be characterized? Synthese. https://doi.org/10.1007/s11229-019-02164-2.
Lewis, D. (1976). The paradoxes of time travel. American Philosophical Quarterly, 13, 145–152.
Lewis, D. (1979). Counterfactual dependence and time’s arrow. Noûs, 13(4), 455–476.
Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell publishers.
Loss, R. (2015). How to change the past in one-dimensional time. Pacific Philosophical Quarterly, 96(1), 1–11.
MacFarlane, J. (2003). Future contingents and relative truth. The Philosophical Quarterly, 53(212), 321–336.
MacFarlane, J. (2008). Truth in the garden of forking paths. In M. Kölbel & M. Garcı́a-Carpintero (Eds.), Relative truth (pp. 81–102). Oxford: Oxford University Press.
Markosian, N. (1995). The open past. Philosophical Studies, 79(1), 95–105.
Martinez, M. (2011). Travelling in branching time. Disputatio, 4(31), 271–287, 2011.
McCall, S. (1994). A model of the universe: space-time, probability, and decision (p. 1994). Oxford: Oxford University Press.
Miller, K. (2005). Time travel and the open future. Disputatio, 1(19), 223–232.
Norton, J. (2018). If time travel to our location is possible, we do not live in a branching universe. Analysis, 78(2), 260–266.
Prior, A. (1967). Past, present and future. Oxford: Clarendon Press.
Torre, S. (2011). The open future. Philosophy Compass, 6(5), 360–373.
van Inwagen, P. (2010). Changing the past. In D. W. Zimmerman (Ed.), Oxford studies in metaphysics (Vol. 5, pp. 3–28). Oxford: Oxford University Press.
Wasserman, R. (2017). The paradoxes of time travel. Oxford: Oxford University Press.
Acknowledgments
I thank an anonymous referee of this journal and the audience at the conference Modal Metaphysics Issues on the (Im)possible VI for helpful comments on earlier drafts of this paper.
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Andreoletti, G. Back to the (Branching) Future. Acta Anal 35, 181–194 (2020). https://doi.org/10.1007/s12136-019-00404-1
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DOI: https://doi.org/10.1007/s12136-019-00404-1