Now consider how the FAT argument might play out in the context of backwards time travel. According to Lewis (1976), in order for time travel to genuinely involve travel, there must be a ‘discrepancy between time and time’; that is, in order to travel back in time, the time traveler’s journey must take time. Suppose Tim travels back to a time before his birth in order to kill his grandfather. If Tim’s journey back to the time of his grandfather’s youth does not take time, then there is no sense in which Tim travels from the present to a time prior to his birth; rather, he simply exists at intervals that are not temporally contiguous. In order to deal with the discrepancy between different times required by genuine time travel, and in order to do so in a way that does not require two dimensions of time, Lewis introduces the devices of ‘personal’ and ‘external’ time. Personal time is the time measured by the time traveler’s wrist watch, while external time is time itself, the time that the time traveler is traveling back through.
So let’s assume that Tim travels back to a time during his grandfather’s youth. Can he succeed in his murderous plot? If so, then contradictions arise; but if not, then why not? Can the laws of logic alone stop him? Consider the following version of FAT, tailored to this context (where t* is the time of Tim’s birth, and t is a time before Tim’s birth):
6) It was true at t* that Tim does not kill his grandfather at t. (Assumption)
7) Necessarily, if it was true at t* that Tim does not kill his grandfather at t, then Tim does not kill his grandfather at t. (From 6 and the necessity of logical consequence)
8 ) Tim never had and never will have a choice about whether 6 is true. (From 6 and the fixity of the past)
9) Tim never had and never will have a choice about whether he kills his grandfather at t. (From 7 and 8 )
10) Therefore Tim is not free to kill his grandfather at t. (From 9)
I submit that neither of our earlier responses are going to work in this context. The relevant analogue of the eternalist’s response here would be to claim that premise 6 of FAT-TT is a timeless truth made true by Tim’s not killing grandfather at t, and therefore that premise 8 is false. But is the situation here really analogous to the earlier one? Compare premise 1 with its counterpart here, premise 6. The former is a truth that is not grounded in an event existing at t*, but one existing at t, and thus it is perfectly legitimate to say that Susan’s going to Anstruther at t makes 1 true (at all times). Can the same be said of premise 6? Is it’s truth grounded in the event of Tim not killing grandfather at t, or is it grounded in an event existing at t*; namely, in the event of his being born at t*? Given that the latter event is one that Tim never had and never will have a choice about, the answer one offers to this question is crucial for an adjudication of the matter at hand. Unfortunately, however, given the nature of closed causal loops, it is not at all clear how one should answer.
Lewis makes the following point in his discussion of the causal loops engendered by time travel. He says that though every event in the causal loop can be causally explained by events elsewhere on the loop, the loop itself may not have any such explanation. Similarly, we can explain Tim’s not killing grandfather at t in terms of (i.e. as being entailed by) his birth at t*, in which case the anti-fatalist response to FAT-TT is blocked; or we can explain his birth at t* in terms of (i.e. as being entailed by) his (freely) not killing grandfather at t, in which case Tim’s free agency is vindicated. In the latter case, it would appear that Tim does, in some sense, have a choice about his birth. But there seems to be no way of deciding which explanation is prior. This is why Lewis expresses doubt whether we can decide if personally past but externally future events (i.e. Tim’s birth) are straightforwardly past or straightforwardly future: all events in a closed causal loop are equally past and future. It is natural, here, to appeal to the causal order in attempting to defend Tim’s freedom; the thought being that as long as Tim’s deliberations at t are causally upstream from his birth at t*, then he is able to causally influence events that occur later than t. But the point is that his deliberations at t are also causally downstream from his birth at t*. And even by the lights of an eternalist, if an event e is earlier than t, then e is fixed at t, thus justifying premise 8.
As for the presentist’s response, it’s not clear that this kind of time travel is compatible with presentism (see Sider 2005). Even granting that it is, however, if the truth of 6 is grounded in the birth of Tim (an actual event), then the presentist response is not available, since that response depended upon there being no event corresponding to the past truth about the future.