In Lewis’s account for the possibility of time travel, he adopts a Parmenidean four-dimensional model that “time is one dimension of the four.” He argues that everything has temporal parts, and people have different person-stages that consist of moments in the dimension of time. In this sense, traveling in time seems possible, as it is similar to traveling in space and only involves movements in the four-dimensional model. However, Grey raises objections to this account for time travel, including the double-occupancy problem and the Grandfather Paradox. Furthermore, his critique on Lewis is in essence an attack on the nature of time in Lewis’s theory. I think his attack on the coherency of time travel is unsuccessful. Grey simply shows that Lewis’s deterministic account of time travel is incompatible with his incompatibilist concept of time, which, however, fails to reject the possibility of time travel.
Grey first argues that time travel (to the past) seems empirically or physically impossible, because the double-occupancy problem will necessarily arise. In Lewis’s four-dimensionalist framework, one can successful travel back in time. Since time is one-dimensional in his model, it seems that a time machine going backwards will inevitably collide with itself going forwards. Such a collision leads to an empirical paradox and discontinuity, for according to our empirical perception of identity, two distinct objects cannot occupy the same space.
Lewis may agree with Grey’s critique on the problem of discontinuity of time travel. Nonetheless, he can argue that physical impossibility of time travel does not rule out the logical coherence of his theory. Grey may further suggest that when time travel occurs, there will be one person occupying two different spaces at the same (external) time, which might undermine the personal identity. Lewis can respond that these are only different spatial-stages of one person. The two bodies preserve their personal identity by their psychological and causal continuities. Even though one may further ask how a time traveler can correctly find and know who is he back in time and may fail to recognize himself, this epistemological problem does not undermine the metaphysical preservation of personal identity.
Grey’s second attack is on the Grandfather Paradox in Lewis’s article. Lewis provides an example in which a young man Tim tries to travel back in time and kill his grandfather. He argues that Tim’s killing his grandfather is compossible with a set of facts but not with another. In this sense, it is logically coherent to say that he can and cannot kill this grandfather, though relative to different sets of facts. However, given a totality of facts that include the fact that Tim lives in the present, we know that he does not and cannot successfully kill his grandfather back in time. Grey is not satisfied by Lewis’s theory of compossiblity and claims “Tim can choose to shoot grandfather.” He argues that Lewis’s determinist claim undermines our free will. In his view, only when nothing is determinant, we can choose what we want to do. Moreover, his argument against time travel seems to challenge Lewis’s fatalism in the sense that there may be alternative worlds. If we consider Leibniz’s philosophy, we can see that it would therefore be possible for Tim to kill his grandfather in other possible worlds in the same moment even given the totality of facts. Even though Lewis mentions at the end of his essay that Tim might be able to kill his grandfather in other branches of time within the same world, he seems to reject the idea of alternative worlds in which Tim can kill his grandfather.
In general, Grey’s attack on Lewis’s explanation for time travel reveals the empirical paradoxes of time travel but fails to prove its logical inconsistency. Furthermore, Grey’s objection to time travel is in fact an objection to a compatibilist view of time. He argues that time travel in a four-dimensional model seems to undermine and even rule out our free will, since our freedom is incompatible with the deterministic nature of time. Nonetheless, the objection to a deterministic view does not undermine the possibility of time travel. Lewis’s defense for time travel therefore seems logically coherent, though in some aspects empirically impossible.