After just a single episode of Doctor Who, you’ll know that time travel does not come without its share of headaches. There are a great many paradoxes, most famously those that ask how changing the past in a way that eliminates you from existence could allow you to change the past in the first place. Intuitively for many, time travel is consequently an inconsistent notion. Here I defend David Lewis’ claim that backwards time travel (BTT) need not entail logical contradictions. I start by outlining his exposition of BTT, the resulting grandfather paradox and his compossibility solution. I then move to a critique of this answer from unexplained constraints on the traveller. I argue that it misconstructs Lewis’ argument and although puzzling fails to show that BTT entails contradiction. I conclude that prima facie Lewis did establish the logical possibility of BTT.
Picture: A police box on the Grassmarket in Edinburgh
As modal realist, Lewis believed that all logically permitted scenarios occur in a possible world. He argues that in some possible worlds, BTT is possible. In this post I shall focus on Gödelian universes that permit BTT through relativistic closed time-like curves as examples of such worlds that according to Lewis would be “most strange” (Lewis, 1976: 145; see also Gödel, 1949). Let us distinguish between two frames of reference: Time from the viewpoint of the traveler, a concept intimately connected to personhood, such that a person is the aggregate of stages that if assigned coordinates and played out will represent the personal time of that agent (Lewis, 1976: 148). This is opposed to the external time of the universe (for worries of objectivity, see Bourne, 2006). BTT occurs if there is a discrepancy between the two such that a positive interval in personal time is matched to a negative passage of external time (Lewis, 1976: 146). To avoid issues of personal identity in distinguishing travellers that meet themselves at a past stage, let me introduce also Lewis’ perdurantism, which states that these stages of a person are causally connected (Audi, 2009: 658). This notion of BTT necessarily involves backward causation for a perdurant traveller compatible with Lewis’ counterfactual analysis of causal dependence if there are local exceptions to the asymmetry of time (Lewis, 1973; in Lewis, 1976: 148).
The following scenario threatens the above picture: Tim is a BTTler that journeys to 1920. If BTT is possible, then he can find and kill his maternal grandfather, Arthur. However, he cannot kill Arthur since he would thereby remove a necessary condition for his own existence. Therefore BTT is logically impossible. Lewis points out an apparent equivocation in this argument between two senses of “can kill his grandfather” (Lewis, 1976: 149). He compares it to the sentence “can speak Finnish”. An ape’s physiology is not compossible with speaking Finnish, hence it cannot speak Finnish. My physiology is compossible, yet I cannot speak Finnish. By the same token, Tim can kill grandfather since his acts are compossible with facts about his physiology, yet he cannot considering a wider set of facts about 1920. “Either events of 1920 timelessly include Tim’s killing of grandfather, or else they timelessly don’t” (Lewis, 1976: 149; italic added). There is an important assumption about the structure of time embedded in the response of a single timeline in which 1920 only occurs once and through a BTTler cannot be “undone” (Horwich, 1975, 435). There is no old and new 1920 and Tim cannot kill because he cannot replace the past. Note that this does not entail that Tim cannot interact with the past to produce effects, however these are only counterfactually true (Lewis, 1976: 150) and “bring about certain events […] which constitute a certain period” instead of changing the past, which involves an “alteration in at least one event which is a member of that class of events” (Dwyer, 1977: 385).
A critique of this view comes from Skow, who asserts that “can” in the sense of compossibility prima facie involves a constraint on an agent’s free will. His argument goes something like this: Tim performed X freely iff he could have not Xed. Let X be the restraint from killing Arthur. Could he have acted differently? Not unless it is compossible with the events of 1920. Therefore Tim is not free. Skow recognises that this is a weak argument by noting that even though I can swim, I cannot because there is no water nearby, making the “can“ context-sensitive. Hence Tim could have not Xed iff the context were different (2012: 9). This is what Lewis meant by the fatalist trickery making us mistake an irrelevant fact about the context for a relevant one (193: 150). However, Vihvelin goes on to argue that Lewis’ contextualism fails in light of a simple premise: If Tim were physically able to kill Arthur, then had he tried, he would have succeeded (1996: 318). In other words, “counterfactual failure entails inability” (Vranas, 2009: 530). Tim would fail under Lewis, therefore independent of context he lacks the ability to kill his grandfather. There are obvious counterexamples, such as the idea that whenever I consciously try to juggle, I do worse than otherwise (Vranas, 2010; in Skow, 2012: 12). Also, let us return to the way Lewis constructs his analysis of BTT through counterfactuals: Consider the permanent bachelor John, who is able to get married, but the closest possible world in which he attempts to do so, he remains a bachelor. Therefore the assertion that ability entails that conscious trying leads to success is false.
Still, the idea that Tim’s freedom is somehow impaired persists under Lewis’ analysis. Surely there is no “guardian of logic” stopping him (Sider, 2002: 132). Horwich agrees that no mysterious constrains are required (1975, 435). There is not necessarily a problem in asserting that I could attend an past event, even if I do not and there need not necessarily be assumptions about free will involved (ibid: 436). Let us instead move to a variant of Lewis’ paradox that does not require agents. Consider a probe that is fired into a closed time-like curve to emerge seconds earlier. The firing can be aborted iff the early returning probe emits a signal. Therefore, if the probe is fired, the signal is emitted and it does not fire. If it does not fire, no signal can interfere and it fires. This is a contradiction. For Earman, this thought example includes two premises in its construction beyond freedom. P1) the existence of closed time-like curves and P2) the physical possibility of constructing the aforementioned probe. Since the latter is both logically and physically intelligible and one of the two must go, we ought to abandon BTT (see Earman, 1995b). Horwich responds by stating that although this is empirically convincing in our world, the falsity of BTT is not logically entailed in all possible worlds, since there is no contradiction for a world in which P1 is true and P2 is false (1975, 439-442). Remember, the aim of Lewis’ paper was to defend the claim that there need not be logical contradictions in “strange” BTTling possible worlds, not ours.
Many do not find this very convincing. Gödel’s universes do not intrinsically forbid the construction of probes and it is hard to see why a possible world that contains P1 must not have P2. Horwich might respond in the following manner: 1) Closed time-like curves are governed by specific laws of physics that act as a constraint on possible causal chains including those of probes and 2) by those laws an event in a causal chain through a curve must be consistent with those in the immediate surroundings of the curve. Horwich calls these “consistency conditions” with little ontological baggage since they already apply to ordinary time (Horwich, 1975, 444). Surely though this begs the question. The opponent demands consistency and charges that with the existence of curves this may be broken, yet all Horwich’s argument amounts to is to affirm that consistency is a constraint. However, from the fact that Horwich cannot guarantee consistency in curves it does not follow that curves imply inconsistency, which I believe is his main point. All aside, a scenario like this is not what Lewis aimed at and clearly misunderstands the essence of his paper. To go a step beyond Horwick, I do not believe that it is necessary to divide worlds in which P1 and P2 are possible. There may be a Lewisian world in which both are, yet no probe is fired since it is not compossible with anything in that world simpliciter (for alternative grey state solutions, see Dowe, 2007).
If Gödel is correct and BTT is physically possible in some worlds, it stands to reason why we ought to worry about it being philosophically pleasing as Earman suggests (1995a: 281, 1995b: 170). Vranas compellingly points out that the reality of motion does not “trivialise Zeno’s paradoxes”. By the same token BTT may be puzzling and thought provoking even if physically possible (Vranas, 2009: 521), yet it being puzzling does not necessitate logical impossibility. The burden of proof is on the opposition of BTT to show why it entails contradiction and none of the afore mentioned arguments are immediately convincing. Therefore I assert that Lewis did succeed in establishing the logical possibility of BTT prima facie. The clearly needed more detailed analysis must however be left for another post.
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