‘If time travel were possible then travellers would be able to change the past and make contradictory states of affairs such as killing their own grandfathers before those grandfathers have become parents, thereby making their own existence impossible’
Since the early twentieth century, discussions on the nature of time have featured prominently in philosophical discussion. Time is that which clocks measure and we use our concept of time to place events in sequence one after the other, to compare how long an event lasts, and to tell when an event occurs. However, despite knowing the key features of time, many issues on the subject are still unresolved. Philosophical discussion on time often features exploration into the ontological differences of the present, past and future, with many philosophers and scientists believing that some form of time travel is actually possible. Theorists have investigated both the logical and physical possibility of time travel into the past or future, alongside debates regarding the key paradoxes associated with time travel[i]. The philosophy of time travel is often associated with the work of 20th century philosopher David Lewis who argues that an object time travels if the difference between its departure and arrival times in the surrounding world do not equal the duration of the journey undergone by the object[ii]. Within his 1976 paper ‘The Paradoxes of Time Travel’ Lewis outlines his arguments for the logical possibility of time travel by developing a one-dimensional account which relies on a four-dimensional manifold of events. Further, Lewis attempts to clarify his account of time travel by distinguishing between the external time and the personal time of the time traveller. Through close analysis of his paper, this project will present the reader with a deeper understanding of Lewis’s theory for the possibility of time travel. This will be followed by a critical examination of three key paradoxes of time travel in relation to his theory. Each paradox will then be refuted with a critical response from theorists within the field of the philosophy of time, each of which will then be illustrated through a case study of science fiction based film. The project will then turn to a discussion concerning each paradox and its refutation in relation to Lewis’s account, ultimately revealing that his arguments on time travel are successfully supported.
David Lewis: ‘Time travel, I maintain, is possible’
Many would agree that the strongest account of philosophy and time travel can be found in David Lewis’s 1976 paper ‘The Paradoxes of Time Travel’, his analysis within which has been described as ‘un-refuted in all its essentials’ and is dubbed as the philosophical work on the topic[iii]. Lewis argues unflinchingly for the logical possibility of time travel, opening his paper with the bold statement ‘Time travel, I maintain, is possible’[iv]. Lewis believes that the paradoxes which surround theories on time travel are not the same as impossibilities. Instead he refers to them as ‘oddities’ which he argues only prove that a world in which time travel was possible would be fundamentally different to the one in which we are accustom to and therefore it would be strange but not impossible. Lewis argues for a consistent and clear account of time travel and begins an explication of his account with a definition of what, exactly, time travel is. Lewis believes it involves a ‘discrepancy between time and time’ and expands by explaining that when a regular traveller departs and then arrives at his destination, the time which has elapsed between his departure and his arrival is the duration of his journey. However, if this traveller is a time traveller, the separation in time between departure and arrival does not equal the duration of his journey. For example, if he departs and travels for an hour, the time when he arrives may not be an hour later in time, it will be later than this if he has travelled toward the future or earlier if to the past and if he had travelled far in the direction of the past, then his arrival time might be even earlier than his departure time[v]. He does note however, that although he is arguing that the two events of arrival and departure can be separated by two unequal amounts of time, which would seem to suggest a theory of two-dimensional time travel, he in fact wishes to set that idea aside and place his focus on a one-dimensional theory of time travel.
Lewis moves on to discuss the time travellers world, which he also points out would be our world. He explains that it incorporates a four-dimensional manifold of events and that time is one dimension of the four. He believes that things endure through time, like streaks which are made up of temporal parts or stages, and are located at various times and places[vi]. By this it seems Lewis is explaining the movement of people or objects lasting and changing into different temporal stages, through the passage of time. He argues that change is the qualitative difference between these stages of the enduring thing, giving the example that if his paper was to change your mind about the possibility of time travel, there would be a difference of opinion between two different temporal parts of you (between the stage at which you had started reading and the subsequent stage when you finished reading)[vii]. Further, he goes on to argue that if ‘change is qualitative difference between temporal parts of something, then what doesn’t have temporal parts can’t change’[viii]. He uses numbers and events of any movement of time as examples of these things, explaining that since they cannot be subdivided into dissimilar temporal parts, they therefore cannot change. Lewis does make the distinction though, between two senses of the word change. He explains that there is that which is described as ‘Cambridge change’ which can happen even in numbers for example being to not being the rate of exchange or that momentary events can change from being a year ago to being a year and a day ago. He argues however that this change is not genuine change which can reverse the truth value, making a change in the actual thing itself[ix].
Lewis then goes on to develop his case for a one-dimensional theory of time travel by distinguishing between the ‘personal time’ of a particular traveller and time itself which he calls ‘external time’[x]. Personal time is that which occupies a certain role in the pattern of events that comprise the time traveller’s life. All of the stages in a common person’s life which manifest certain regularities, Lewis states for example, the accumulation of memories or the digestion of food, do so with respect to external time. But for the time traveller, these regularities do not manifest with respect to external time, instead that which coordinates them and plays the role of time for them is their personal time. The time travellers journey may take an hour of his personal time, for example his own wristwatch would read an hour later at arrival than at departure, but in external time the arrival is more than an hour after departure if he had travelled to the future or less than an hour if he had travelled to the past[xi]. However, it could be argued here that personal time irrelevantly takes the place of the time we follow in the present in our regular daily activity, when not time travelling. Its components seem to echo those of regular time, as both play the role of guidance in the management of our lives. Personal time therefore, seems to be an unnecessary part of Lewis’s time travel theory, which then begs the question as to his reliance on it in reference to the rest of his account.
However, Lewis continuously uses his idea of personal time and explains that we may assign locations in the time traveller’s personal time, not only to each stage of the traveller, but also to the events that go on around him. Lewis gives the example, ‘Soon Caesar will die, long ago’, and explains that ‘soon’ would be a stage slightly later in the traveller’s personal time than his present stage, but ‘long ago’ in external time is simultaneous with Caesars death[xii]. Lewis likens the time traveller’s life to a mountain railway in an attempt to show that he is not dealing with two independent time dimensions when discussing personal time and external time. He states that on the mountain railway line ‘the place two miles due east of here may also be nine miles down the line, in the westbound direction’ as an analogy to explain that a travellers personal time is not a second dimension of time but is in fact correlative to external time, in the same way that the point two miles down the line eastbound is correlative to the point nine miles down the line in the westbound direction, instead of being separate lines. The locations of events in personal time depend on their locations in one-dimensional external time. Lewis argues that an event in the time traveller’s life may have more than one location in his personal time, for example if he were to double back slightly toward the past he may be able to talk to himself. This conversation would involve two of his stages which would be separated in his personal time, but simultaneous in external time. The location of the conversation in personal time should be the location of the stage of the traveller, but to share the locations of both stages, the conversation must be assigned two different locations in personal time[xiii]. He explains that for example if the time traveller was to talk to himself on the telephone, neither of the two stages of him involved in the conversation are the whole of him or even the whole of the part of him that is located at the external time of the conversation. The time traveller, however, unlike non time travellers, has two different complete stages located at the same time at different places. Lewis explains that what unites the stages of a time traveller is the ‘mental continuity and connectedness that unites anyone else’[xiv], in the way that regular peoples actions are linked by a mental continuity, the time travellers stages are linked in this way too. Mental decision making and continuity in anyone is mostly gradual rather than sudden and therefore Lewis argues that the probability of the time traveller randomly and suddenly making instantaneous journeys is unlikely. He believes that even time travel involves causal continuity, meaning that each stage in the traveller’s personal time is causally governed by mental continuity[xv].
Many would argue however that this idea that the traveller could double back toward the past and talk to himself weakens Lewis’s case for time travel. If people could return to the past, they could surely pass back with them, information about the future, thus providing knowledge about things that have not yet been discovered or understood and therefore changing the route via which the information would have originally been learned. Because this scenario contradicts what we know about where knowledge comes from, it would seem that past-directed time travel is not really possible. However, later in his paper, Lewis does address what is known as the Grandfather paradox, in which he provides argument as to why past facts actually cannot be changed by the time traveller.
Lewis’s paper then turns to discuss reverse causation in backwards time travel. He notes that ‘Indeed travel into the past involves reverse causation’[xvi] because it involves personal identity, explaining that he who arrives at a certain point is the same person who departed, thus requiring causal continuity from earlier to later stages in personal time. The order of personal time and external time will disagree when it comes to backwards time travel to the past, as it involves a causation that runs from later to earlier stages in external time which is thus reversal causation. He argues that this can only occur though where there are local exceptions to the asymmetries of time. He believes that if there are local causal reversals there may also be causal loops which he describes as ‘closed causal chains in which some of the causal links are normal in direction and others are reversed’[xvii], by which he explains that each event on the loop would have a causal explanation from elsewhere on the loop. Lewis explains that the loop as a whole is inexplicable and that there is simply no answer as to how it came about. He states that ‘The parts of the loop are explicable, the whole of it is not’[xviii], which he then supports by arguing again that it is strange but not impossible. He gives further support by making reference to God or the infinite past of the universe and arguing that these are things which most believe to be uncaused and inexplicable but still possible and that therefore the same may go for inexplicable causal loops in time travel[xix].
However, if like Lewis argues, things happen causally, it is questionable how people in the present would understand a visit from a person of the future if they have not yet made any causal link or connection with that future. Lewis is concerned with a consistent time travel story, but surely random visits from our future self would seem inconsistent with our mental continuity. Further, he argues for a one-dimensional theory of time travel, but it is arguable how then there can be people living in a future, when we are still in the present. Overall however, Lewis’s account of time travel within his essay ‘The Paradoxes of Time Travel’ is consistent and meticulously thought through. It presents a thoroughly accessible account of what is often an overly complex philosophical topic, which is one of the main reasons for its success.
The Paradoxes of Time Travel
As shown by Lewis, philosophers and physicists take seriously their pursuit to prove that time travel is in fact possible. However, there are arguments which present paradoxical situations for theories of time travel, suggesting that the idea is illogical and impossible. In order to critically evaluate Lewis’s account of time travel, this project will examine three paradoxes of time travel against his theory in an attempt to test the strength and depth of his account. In order to investigate whether Lewis’s account can be successfully supported, each paradox will be refuted with a critical response from a philosophical theorist from the field of the philosophy of time. This response will then be illustrated through a science fiction based film.
The Grandfather Paradox
The first paradox I will consider is the ‘Grandfather Paradox’, as Lewis himself turns to address this standard concern in his analysis within ‘The Paradoxes of Time Travel’. The main argument within this paradox is that if time travel were possible then backward time travellers would be able to change the past and make contradictory states of affairs such as killing their own grandfathers before those grandfathers have become parents and thereby making their own existence impossible. However, as we have seen, Lewis denies this possibility, stating that ‘the events of a past moment could no more change than numbers could’, further he argues that if a time traveller were able to visit the past with the ability to change it, then there would no such thing as time travel[i]. Lewis argues that the grandfather paradox is not decisive against time travel because time travel need not entail an ability to create contradictions. He explains that the appearance of a paradox arises from conflating different senses in which an action can be possible[ii]. He states that ‘To say something can happen means that its happening is compossible with certain facts. Which facts? That is determined, but sometimes not determined well enough, by context’[iii]. Lewis asks the reader to imagine a young man called Tim, who violently hates his arms-dealer grandfather. His Grandfather died in 1957 when Tim was still a child. However, if Tim can travel back to 1920 and visit his grandfather’s vicinity in that year, can’t he then kill his grandfather? Lewis argues that the word ‘can’ is context dependent and that a sentence including the word ‘can’ may be true in some contexts and false in others. Tim’s success is compossible with some facts about the situation, for example, Tim has the necessary skills for a good shot and Grandfather is not wearing armour. However, other facts about the situation are not compossible with Tim killing Grandfather, for example, that Grandfather died in 1957. From this it seems guaranteed that Tim won’t kill Grandfather in 1920, however there may be any number of explanations for his failure and many of these will be rooted in local (1920) facts about Grandfather’s situation. It isn’t that Tim’s knowledge of Grandfather’s fate makes Grandfather bullet-proof. Thus, Lewis thinks, that if we disambiguate the relevant notion of possibility, the paradoxical impression should dissolve. Lewis’s time-travellers arrive and depart from the same, internally-consistent history and so if all consequences of backward time-travel are in the causal matrix before departure, no paradox occurs. For Lewis, time travel won’t let you destroy your grandfather- to-be as you know for a fact that he attains adulthood no matter what you do in the past[iv]. However, although Lewis argues that time travellers cannot change the past, as previously mentioned he does distinguish between two senses of change, thus meaning that he thinks we can change the past insofar as our mere presence as a time traveller is a change to the original situation. Lewis’s objections to the grandfather paradox are also supported by Robin Le Poidevin, who similarly argues that because Grandfather died in 1957 of natural causes, then he did not die in 1920 and if Tim were to have time travelled and attempted to kill Grandfather; he would have failed. He explains that anything may have happened to stop this, such as Tim may have fired a shot but missed. Whatever the case, Tim cannot kill his grandfather because time travelers “can’t change any past fact whatsoever” as the universe will not allow a contradiction to be created[v].
The arguments given against the Grandfather paradox by Lewis and Le Poidevin can be seen illustrated in the plot of the 1985 science fiction film ‘Back to the Future’. Set in 1985, mad scientist Doc Brown discovers time travel and transports himself and his friend Marty McFly back to the year 1955 (the year Marty’s parents met). Marty accidently prevents his parents from meeting, putting his own existence at stake, and is then forced to set off in pursuit of putting things back to the way they were supposed to happen. Marty’s parents originally meet because Marty’s grandfather (his mother’s father) hits his father-to-be with a car, which leads to the introduction of his mother and father. However, when Marty travels back in time, he sees his dad about to be hit by a car and pushes him out of the way, meaning that instead it is he who is hit by the car and then introduced to his mother, leading to his mother falling for him. The film is based around an idea of the grandfather paradox, with reference to it being made throughout. Marty’s mother makes reference to the paradox in a scene just before Marty travels back in time, she states ‘If Grandpa hadn’t hit him then none of you would’ve been born’[vi], which reiterates the idea put forward by Lewis and Le Poidevin, that the past cannot be changed. One of the final scenes in the film shows Marty in his last attempt to get his mother and father to fall in love and as it seems that he is failing, he himself, begins to slowly fade away, which shows that if he had changed the past then he would not exist in the first place. Finally, his parents find one another and fall in love, and as they do so, Marty begins to reappear, because things are as they should always have been. The film complies with Lewis and Le Poidevin’s argument that we cannot change any past facts whatsoever firstly because we already know for a fact how things have happened and turned out and secondly because the universe would not allow for contradiction to occur, such as the ability to change past facts. The film shows, similarly to the situation of Tim and his grandfather, that although Marty’s mistake is compossible with some facts about the situation (for example that his mother seems to be falling in love with him instead of his father), other facts about the situation are not compossible with Marty’s mother falling in love with him and not meeting his father (the fact that she gives birth to Marty in the future). Following the latter set of facts, it would seem guaranteed that Marty’s mother will fall in love with his father, due to the fact that Marty exists. The film shows that no matter what happens, the situation in which Marty’s mother fails to meet his father, is avoided, as this is not how it originally happened in 1955.
The Nowhere Argument
The second paradox to be examined is rooted in a presentist view of time and is known as the ‘The Nowhere Argument’. According to presentism, only the present exists and consequently only present objects exist. The presentist would argue that things in the past have existed and that future objects will exist, but because they do not presently exist, we cannot truly claim that they do exist[vii]. The nowhere argument therefore follows a belief in presentism and thus argues that because the existence of the past or future cannot be proven, one cannot travel either to the past or future because they do not exist, ultimately leading to the belief that time travel is impossible as we would be trying to travel somewhere that does not exist.
Presentism, however, is regularly rejected on the basis that we readily accept and discuss the past and future using present tense. For example, we make statements such as, “Nixon is the only president of the 20th century to resign”, and we have no trouble in saying or believing them, even though Nixon no longer exists. We even use the past tense regularly which would seem to present problems for the presentist, as for them the statement would be false, yet we still use such statements without hesitation or second thought[viii]. Another problem with the nowhere argument is presented by Simon Keller and Michael Nelson who believe that the argument holds contradictions. They point out that if it were the case that only the present moments and objects exist, then the theory would actually rule out the passage of time altogether, which arguably would rule out any present concept of time too. If the nowhere argument where plausible it would be impossible for us to even travel one second into the future, yet we are constantly doing so all the time[ix]. One example which specifically shows the weakness of the nowhere argument is the case of astronauts orbiting the Earth. They orbit at several thousand miles per hour, for days on end, and in this time, relativity theory say that they gain a fraction of a second of time ahead of people on Earth, meaning that they have time travelled ever so slightly into the future[x]. Keller and Nelson conclude, on the basis of similar considerations that, ‘One way or the other, the presentist has to make room for travel to non-existent times’[xi].
The arguments given against the nowhere argument by Keller and Nelson can be seen illustrated in the plot of the 1989 film ‘Bill and Ted’s Excellent Adventure’[xii]. The film follows two best friends who are about to fail high school come into contact with a visitor from the future named Rufus, who provides them with a time machine to help them work on their history project. Bill and Ted travel through time picking up various historical figures and bringing them to the present to help them do well on their project. Time travel in this movie, as in Lewis’s account, is treated one-dimensionally[xiii]. This film presents quite simplistically the counter argument given by Keller and Nelson of the nowhere argument. It argues against the presentist view and shows that in fact we constantly use the past to help us with the present and in turn, much of what we do in the present is to benefit our future. In the first time travel scene, Bill and Ted travel back to 1805 to the moment when the French army were invading Austria. They do so to begin improving their knowledge of history for the test they have been set at school. Similarly in regular life, we use the past to help us improve the present or future. Bill and Ted wish to do well on their test, in order to complete high school which they hope will lead to a better future. As Lewis argues in his paper ‘The Paradoxes of Time Travel’, the passage of time is a process guided by mental continuity and one cannot be in the present without direction from the past and the motivation of the future. This film cleverly uses a time travel plot to demonstrate the contradictory nature of the nowhere argument, proving the necessary existence of the past and future and thus dissolving the paradox.
The Self-Visitation Paradox
The final paradox to be considered is known as ‘The Self-Visitation Paradox’ which Theodore Sider aptly defines like so,
‘Suppose I travel back in time and stand in a room with my sitting 10-year-old self. I seem to be both sitting and standing, but how can that be?’[xiv]
It would seem that time travel has provided us with a way in which the time traveller could travel backwards in time and stand in a room with a sitting version of his younger self. However, it is surely impossible for one person to be both sitting and standing at the same time and furthermore impossible for there to be two of one person at one time. One solution to this paradox, Lewis may have argued would be to simply accept that the sitting and standing can occur and be done simultaneously by one single person. This assumption that a person cannot be both sitting and standing is one which comes naturally to us, because we are used to thinking about situations which do not involve time travel. For Lewis, accepting that the time travelling world would be strange and different to ours and thus accepting that its possibility exists, would mean accepting that sitting and standing are not mutually exclusive actions.
Ned Markosian argues that this paradox arises from the thought that the sitting and standing traveller are two of the one person, and that confusion follows as to how one person can be simultaneously in two places. He argues that in fact it may be the case that they are only two parts of one traveller. He suggests that we consider one part is the younger traveller and one part is the older traveller, and not assume that they are one person, but instead each a different spatial part of the traveller. He explains that the different spatial parts of an object may have different properties without being contradictory[xv]. A further resolution of the self-visitation paradox can be seen in the relativist approach offered by Paul Horwich who maintains that the sitting and standing are relative to the personal time of the time traveller. By this he means that the time traveller would be sitting at a certain initial point in his personal time but would not be standing relative to that time, and similarly, the traveller would be standing relative to a later personal time, but not sitting relative to that time. The relativist relies on location as the key to finding consistency and they would argue that the traveller can be both sitting and standing as long as these actions are not done in the exact same location. For the relativist, the traveller would be, for example sitting there and standing here, and therefore contradiction would then only occur if the traveller were to be both sitting and standing there or both here, which is not the case[xvi].
The arguments given to resolve the self-visitation paradox by both Ned Markosian and Paul Horwich can be seen illustrated in a particular scene from the 1984 film version of ‘A Christmas Carol’[xvii]. The film tells the story of Ebenezer Scrooge, an old man who hates Christmas and so is taught the true meaning and spirit of the holiday by ghosts who show him his own past and present. He is also shown what the future holds for him if he does not change his behaviour. His first visit is from the ghost of Christmas past who takes him to watch parts of his childhood. One scene in particular shows an older version of Ebenezer standing next to a younger version of himself in a church on Christmas day in the past. This scene illustrates Markosian’s argument that it would not be the case that there were two of Ebenezer but instead that there are two different spatial parts of him; one older and one younger. The scene also illustrates the resolution put forward by Horwich, which argues that the sitting and standing are relative to the personal time of the time traveller. The older stage of Ebenezer can be understood as located in his personal time, having travelled back to his younger self who is located in external time. Further, the scene shows Horwich’s point that there need be no paradox or problem since the two parts of Ebenezer are not located in the exact same position; one is standing and one is sitting. Even when they are both sitting, they are not sitting in the same place. ‘A Christmas Carol’ and in particular the scene discussed above shows how the idea of self-visitation within time travel can work successfully without contradiction, providing further support for Lewis and his quest to maintain the logical possibility of time travel.