In ‘The Paradoxes of Time Travel’ David Lewis (1976) argues that backward time travel is possible. However, it is not possible for a time traveller to change the past. This would lead to certain paradoxes, such as the Grandfather paradox. Were a person to kill their paternal grandfather before the birth of their father then they themselves would not exist. And, if they did not exist, they would not be able to travel back in time to kill their grandfather. Lewis overcomes this paradox by stating that any attempt made by a time traveller to kill their grandfather would fail. These attempts would be thwarted by commonplace reasons such as a noise distracting the time traveller, or their nerves failing them, or a pang of mercy. These commonplace reasons have led Horwich (1975, 1987) to argue that backward time travel is improbable because it would result in innumerable coincidences foiling the attempts of time travellers to change the past. However, Smith (1997, 1998, 2017) argues for the plausibility of backward time travel. This question can be understood as having two parts. Firstly, does backward time travel entail foiling coincidences? Secondly, if it does entail foiling coincidences, is it plausible given these coincidences? Three arguments by Smith, used to defend the possibility of backward time travel, claim that backward time travel does not entail foiling coincidences. I show that these arguments fail. However, Smith’s fourth argument for the possibility of backward time travel claims that backward time travel does entail foiling coincidences, but it is not implausible given these coincidences. This is because there are no laws or principles that rule out the possibility of such coincidences occurring. I claim that this is a persuasive argument for the plausibility of backward time travel and conclude that backward time travel is plausible, despite foiling coincidences.
This paper proceeds as follows. Section two outlines Lewis’ argument that backward time travel entails foiling coincidences. Section three discusses Smith’s arguments that backward time travel does not entail foiling coincidences and concludes these arguments fail. Section four examines whether backward time travel is improbable because of foiling coincidences. I examine Horwich’s argument that it is improbable and Smith’s response that it is not improbable because of these coincidences. I claim that Smith’s argument in this section is persuasive and that, given this argument, backward time travel is possible. Section five is a conclusion.
2. Why does backward time travel entail foiling coincidences?
It is generally acknowledged that backwards time travel is possible. Most philosophers agree that the paradoxes that make backward time travel seem impossible – the grandfather paradox and the paradox of autoinfanticide (people killing their infant selves) – can be overcome. However, overcoming these paradoxes leads to another difficulty. It seems that the possibility of backward time travel gives rise to highly improbable correlations of events – these events are ‘coincidences’ that foil the attempts of time travellers to change the past (Ismael, 2003). For example, consider the following experiences of time travellers, Sue and Oskar. Both have the desire and intent to change the past but are thwarted in these attempts:
Sue hops in her newly designed and built time machine. The year is 2018. She travels back to 1936 in the hope of killing her maternal grandmother when she was pregnant (Sue doesn’t like her mother much and figures her mother’s death in utero will save her a lot of money spent in therapy). Amazing, she arrives in Sydney in 1936. As it happens, her time machine almost lands on top of her grandmother, missing her by a whisker. Sue leaps out of the time machine, grabs her grandmother by the collar of her nice ice blue frock and is ready to plunge a hypodermic needle into her neck which will kill her instantly. But as she raises her arm, a tram bell rings and she realises she is standing in the middle of the tram line about to be run down. She instantly lets go of her grandmother, who runs off screaming, and then falls to the side of the road. In the following weeks Sue searches high and low for her grandmother, intent on her demise. She finds her three times (standing by the same tram stop) and each time her grandmother runs from her screaming. The first two times Sue tackles her grandmother to the ground, but on both occasions as she’s about to deliver a fatal blow she’s prevented from doing so by a cramp in her arm that causes her arm to freeze mid-air, allowing her grandmother to escape. The third time she sees her grandmother she runs furiously after her but, alas! She slips on a banana peel just as she’s about to catch her and goes flying into the side of a building. Forlorn, and full of regret, Sue hops back in her time machine and returns to 2018.
Oskar was a rather nerdy and depressed adolescent who spent most of his time in his parents’ basement designing science experiments and listening to his one John Coltrane CD. He had been feeling rather suicidal for the past few months and decided to design a time machine to return to 2004, when he was a toddler, and kill his toddler self. Surely there was no point to life, it was far too painful, and he figured that if he killed himself before he had enough memory to know about his life he would avoid the endless torment. So, one night after his parents had retired for the evening, he hopped in his machine and miraculously found himself upstairs in his bedroom looking at his infant self in a cot. He grabbed a pillow, intent on suffocating his infant self, but suddenly the fire alarm in the house went off and he heard his parents running down the hallway. He hid in the closet as his parents raced into the room and snatched his infant self away from him. Each night, down in the basement, Oskar would attempt to travel back in time to kill himself, but each night his parents would foil his attempt by racing into baby Oskar’s room just as the deed was about to be done. In the end, Oskar gave up and resigned himself to his life of misery.
Attempts by time travellers to change the past must fail because changing the past entails a logical contradiction, leading to impossible situations. Changing the past entails that an event both did occur and did not occur, and this results in paradoxes. It is impossible that teenage Oskar kills his infant self. If baby Oskar did not survive to puberty, there would be no teenage Oskar in existence to kill infant Oskar. This equally applies to Sue. Had Sue’s mother been killed in the womb, Sue would not be paying to see her therapist. Lewis (1976) argues that backward time travel is possible but can only occur if the possibility of changing the past is ruled out.
However, if it is impossible to change the past then what is it that prevents an agent who is intent upon doing just that? Lewis (1976) responds that any attempt to change the past (‘bilking’ attempts) will be prevented by a commonplace reason such as guns jamming, people having a change of heart, or people slipping on banana peels at the crucial moment. This leads Lewis to say that “a possible world where time travel took place would be a most strange world, different in fundamental ways from the world we think is ours.” (1976, p. 145). It is the strangeness of these foiling coincidences that overcomes the paradoxes of backward time travel and enables the possibility of travelling into the past.
And yet, while these commonplace reasons overcome the paradoxes of backward time travel, it seems unlikely that each attempt by a time traveller to change the past would be foiled in this way. These commonplace reasons have led to an objection by Horwich (1975, 1987). He claims that these foiling coincidences make the possibility of local backward time travel extremely improbable. These coincidences would amount to improbable correlations of events and we have empirical reason to believe such correlations are highly unlikely. Horwich concludes that the possibility of backward time travel is unlikely.
Before discussing Horwich in section 4, I explore three arguments by Smith that are designed to support the possibility of backward time travel by attacking the premise that backward time travel entails foiling coincidences.
3. Smith’s arguments that backward time travel does not entail foiling coincidences
The main argument against the possibility of backward time travel, due to Horwich, claims that it is improbable because it entails foiling coincidences and we have empirical reason to believe that such coincidences are highly unlikely. The following three arguments by Smith are designed to defend the possibility of backward time travel by showing that it does not entail foiling coincidences. The first two arguments are from earlier papers, that is, “Banana’s enough for time travel” (1997) and “The problems of backward time travel” (1998). The third argument is from a later paper “I’d Do Anything to Change the Past (But I Can’t Do ‘That’)” (2017). I claim that these arguments fail and, thus, that backward time travel does entail foiling coincidences. His arguments are as follows:
3.1 Argument One: Improbable inputs and outputs
Smith’s (1997, 1998) first argument that backward time travel is possible as it does not entail foiling coincidences claims that the argument that backward time travel entails lots of foiling coincidence requires that there are also improbable inputs. Because these inputs are unlikely, this suggests that improbable outputs (such as foiling coincidences) are also unlikely. Smith agrees that if an agent attempts autoinfanticide a string of coincidences would occur to prevent them. However, for this to occur it would require, as an input, faulty reasoning on the part of the time traveller to continuously attempt the impossible. He argues that this ‘mass irrationality’ (1997, p. 387) is unlikely. Further, a scenario where a time traveller returns to their younger self and makes numerous attempts on the life of their younger self makes little sense if they do not remember that numerous attempts were made on their life when they were younger (Smith, 1998). Another improbable input is if a time traveller had an unlikely belief in resurrection, and for this reason kept attempting to kill someone who lived beyond the date in question (Smith, 1997).
Goddu (2007) claims that Smith has only established that lots of bilking attempts would reflect a lot of fallacious reasoning. Smith has not established that backward time travel would not entail lots of foiling coincidences. As such, Smith is arguing that there would not be lots of bilking attempts in backward time travel because it is unlikely there would be a lot of fallacious reasoning. And because there would not be lots of bilking attempts, there would not be lots of foiling coincidences. To assess the strength of this argument it is necessary to decide whether we believe that there would not be lots of bilking attempts due to fallacious reasoning. In other words, would fallacious reasoning be widespread amongst time travellers to the local past? If time travel to the local past were regularly occurring, would time travellers be aware of the futility of changing the past? Or would they constantly try to change the past, either out of ignorance or curiosity?
I suggest that fallacious reasoning would be widespread amongst time travellers. There is much work that supports the irrationality of human decision making, such as Kahneman (2011). In Thinking, Fast and Slow, he suggests that our decision making is based on two cognitive systems, system 1 and system 2. System 1 is rapid and intuitive, whereas system 2 is effortful. A main premise of the book (that is substantially supported with empirical evidence) is that, in general, humans make many irrational decisions as they rely on the quick heuristics of system 1 rather than engaging in the cognitive effort required to reason well.
I suggest that, in the case of time travel, people would rely on false intuitions rather than reason. As (weak) empirical support for this, the handful of people I discussed time travel with do not understand why changing the past is impossible. It could be argued that people’s attitudes would change if travelling to the past became common. However, in response to this, another example where the public has had the opportunity to become more informed but have not necessarily taken advantage of this is the internet. We have access to vast amounts of information since the introduction of the internet. And yet, despite widespread access, we are not necessarily more well-informed.
3.2 Argument Two: Counterfactual argument
Smith’s (1997) second argument for the possibility of backward time travel attempts to show how autoinfanticide does not automatically lead to foiling coincidences because it does not automatically lead to failure. Smith agrees that when you attempt the impossible you will fail. However, he argues that in the case of autoinfanticide the problem can be phrased in a way that suggests you will not always fail. He claims that Horwich’s argument for autoinfanticide rests on the following counterfactual:
Counterfactual A: If the time traveller were to kill the child who lives at his old address, then a contradiction would hold.
If counterfactual A were true, backward time travel would entail many foiling coincidences. However, Smith suggests an alternative counterfactual:
Counterfactual B: If the time traveller were to kill the child who lives at his old address, then the child would not be his younger self.
Counterfactual B allows for the possibility of the child being someone other than the time traveller’s younger self. From this, Smith claims that attempts by the time travellers to kill the child at their old address are not doomed to failure.
Smith realises that an objection is to explicitly state that the child at the old address is the time traveller’s younger self. If this is the case, the time traveller’s attempt to kill this child will fail. However, Smith claims that, if we accept the truth of counterfactual B then it means that the identity of the child and the time traveller are not automatically the same. While counterfactual A assumes they are the same, Counterfactual B means that the identity of the child is the same as the time traveller partly because of the coincidences that stopped the child from dying. As a result, the child grew up to become the time traveller. He states; “The coincidences contribute to the identity rather than the identity requiring the coincidences” (1997, p. 376).
However, analytically the term ‘autoinfanticide’ means that the identity of the time traveller is the same as the child they are attempting to kill. It does not make sense to claim that attempts of autoinfanticide can include attempts on someone other than the time traveller’s younger self. If we accept that, by definition, attempts of autoinfanticide refer to attempts the time traveller makes to kill their younger self, we must accept that these attempts will fail. Vihvelin (1996) agrees that these attempts will fail. She states that when we evaluate counterfactuals we try to work out what would be true at the closest world where the antecedent is true. In worlds most like ours, where teenage Oskar tries to kill the infant at his home and the child is himself, he must fail. To find a world where Oskar succeeds we would have to imagine a world quite different to our own. For example, a world where resurrection was possible.
Sider (2002) suggests another way of looking at counterfactuals in the case of these time travel paradoxes. He states that coincidences are things that ‘might’ happen, they are not things that ‘would’ happen. He claims that counterfactuals that state that the agent would always fail are wrong. It is wrong to say, “If a time traveller attempted to kill that child at their old address and that child was themselves, then they would fail because of a foiling coincidence”. A better way to phrase a counterfactual about autoinfanticide is to build the failure of the agent into the antecedent. For example, “If a time traveller tried to kill their younger self and they failed, then a foil coincidence will have prevented them”. By building the failure of the agent into the antecedent, we more clearly state the reality of these scenarios and illustrate how these counterfactuals are true.
While this is an interesting approach, I argue that Horwich and Vihvelin correctly phrase how counterfactuals should be understood in autoinfanticide. Autoinfanticide is attempting the impossible if we allow that it occurs in a world like our own (and not one where such things as resurrection are possible). It seems undeniable that attempts will fail. For this reason, counterfactuals that deal with autoinfanticide should build this failure into the consequent. The consequence of autoinfanticide, were it attempted, is that this attempt would fail.
In sum, I disagree with Smith’s counterfactual argument against Horwich. Analytically, autoinfanticide entails that the time traveller attempt to kill their younger self. If a child is not their younger self, then it is not a case of autoinfanticide. In addition, while all attempts at autoinfanticide must fail, it seems that the best way to phrase a counterfactual about autoinfanticide is to build this failure into the consequent.
3.3 Argument Three: Self-contradictory and non-existent events argument
The third (and later) argument by Smith (2017) that backward time travel is possible and does not entail foiling coincidences states that the paradox scenarios that backward time travel describes are self-contradictory events. Consequently, foiling coincidences cannot be said to occur because the events that give rise to them are non-existent. Smith claims that Horwich’s reasoning (that backward time travel is unlikely because of the foiling coincidences it gives rise to) is not sound because, in the case of time travel paradoxes such as autoinfanticide, there is no possible scenario that fits this description. It is not possible for teenage Oskar to kill his infant self. Or for Sue to kill her grandmother. The descriptions themselves are self-contradictory. Smith further claims that Lewis’ ‘commonplace reason’ response to the Grandfather paradox is mistaken. It assumes that there is a possibility of killing grandfather, and consequently that we must answer why these attempts are thwarted. However, if we reject the possibility of these scenarios, then there is no need to ask what foils agents’ attempts to change the past in these scenarios.
This argument begs the question because it relies on the assumption that backward time travel is not possible. However, this is what we are trying to determine. If we allow for the possibility of backward time travel, then it is possible for an agent to be present at a former time when they themselves were younger. While Smith is correct in asserting that there is “no scenario at all” (2017, p. 14) that fits the description of autoinfanticide, this does not mean that scenarios in which autoinfanticide could be attempted do not exist. For example, it is possible for teenage Oskar to be in the situation where he attempts to kill his younger self. What is not possible is for him to succeed in this attempt. To claim that a scenario where this attempt was made was impossible would first require ruling out the possibility of backward time travel, and I take it this is not what Smith assumes.
In sum, Smith fails to show that situations in which attempted autoinfanticide could happen are impossible and, consequently, he does not show that foiling coincidences would not occur to stop time travellers attempting to change the past in these situations.
4. Smith versus Horwich: Is backward time travel improbable given foiling coincidences?
The fourth argument by Smith more directly addresses the concerns of Horwich that backward time travel is improbable because of foiling coincidences. Smith’s argument, found in “Banana’s enough for time travel” (1997), agrees that backward time travel entails foiling coincidences, but claims that it is still plausible despite these coincidences. To assess the conflict between Horwich and Smith, I first explain Horwich’s argument and then address Smith’s response.
4.1 Horwich’s argument: Backward time travel is improbable because of foiling coincidences
Horwich (1987) claims that backward time travel is highly improbable because of the foiling coincidences it would give rise to. His argument can be understood as follows. If backward time travel were possible it would lead to lots of bilking attempts (attempts to change the past). These would lead to lots of commonplace reasons (foiling coincidences) that would thwart these attempts. These commonplace reasons would be correlated events that were causally unrelated, and we have empirical reason to believe that such correlations are highly improbable. Consequently, the possibility of local backward time travel is highly improbable.
Horwich supports these claims in various ways. Firstly, he gives a physical reason for why backward time travel must entail foiling coincidences if it is to be possible. Gödel (1949) proved that backwards time travel is possible due to his solutions to field equations in Einstein’s theory of general relativity. These show that closed timelike curves are possible. The backward part of these curves allows for backward time travel. However, if backward time travel to the local past occurred, it would entail that two events that are normally separated by time occur together on a closed timelike curve. For example, infant Oskar would be killed while teenage Oskar is alive, and this is not possible. Horwich states that we can conclude from this that either backward time travel is impossible, or it leads to foiling coincidences that stop the time traveller from changing the past and prevent the contradictions of these paradoxes. These coincidences are highly improbable and would mean that time travellers “are constrained by mysterious forces which conspire to prevent them from bringing about such contradictions” (Horwich, 1975, p. 9). Horwich concludes that these improbable coincidences mean that local backward time travel is unlikely to occur.
To assess the likelihood of local backward time travel, Horwich (1987) also explores the bilking argument. The bilking argument against backward causation can be applied to backward time travel as this involves backward causation. Horwich applies bilking attempts to autoinfanticide, such as teenage Oskar attempting to kill infant Oskar. We know that teenage Oskar’s attempts will always fail. Bilking attempts fail as their success would lead to logically impossible situations. However, Horwich states “we recognise that there is a considerable strangeness in this – something ad hoc and unsatisfying about explaining the repeated failures”(Horwich, 1987, p. 122). Again, these failures would lead to foiling coincidences that make backward time travel seem improbable. Horwich states:
Failure is indeed possible for a variety of reasons; but an indefinitely long string of failures…constitutes a very striking coincidence. Given our experience of the infrequency with which such coincidences occur, we have good reason to believe that the persistent failure of bilking attempts is highly improbable (1987, p. 122).
Huw Price agrees with Horwich and claims:
…the bilking argument…shows us that the hypothesis of time travel can be made to imply propositions of arbitrarily low probability. This is not a classical reductio, but it is as close as science ever gets (1996, p. 278).
Horwich (1987) explains that the coincidences of bilking attempts are improbable because they violate what he terms the Principle of V-correlation. According to Horwich, highly correlated events result in a V-shaped pattern that he calls fork asymmetry. If two events, A and B, are correlated then this correlation is the result of either a chain of events connecting them, or a third event, C, that links A and B by two chains of events. He terms this the Principle of V-correlation. Correlations that violate this principle are highly improbable and this is what we find in failed bilking attempts. These attempts violate this principle because they lead to inverse forks where A and B are connected by a subsequent event, not a proceeding one. For example, if A is Sue’s attempt to kill her grandmother before her mother’s birth, and B is the foiling coincidences that prevent Sue from doing this – such as slipping on a banana peel – then these two events are not causally connected by a preceding event. Instead, they are connected by the subsequent event, C, which is Sue’s failure to bilk. Because bilking attempts violate the Principle of V-correlation these correlations are inexplicable and, consequently, are highly improbable.
Phil Dowe (2003) agrees that backward time travel entails the type of coincidences that Horwich suggests. However, he suggests that these are causally connected. As such, he challenges Horwich’s claim that these correlations are inexplicable. Dowe argues that there is a causal connection between A and B. If A is Sue’s attempt to kill her grandmother before her mother’s birth, and B are the foiling coincidences that happen to Sue, then the correlation between A and B in the case of backward time travel is 1. According to Horwich, there would be no correlation between A and B were there no backward time travel. However, while Horwich argues that there is no common cause of both A and B, Dowe argues that B is part of the causal history of A. For example, the banana skin (that is, B) causes Sue to slip. And the fact that she slips leads to her grandmother surviving in 1936. The fact that her grandmother survives was one of the reasons that caused Sue to decide to go back in time and attempt to kill her (that is, A). Thus, there is a causal chain connecting B and A.
While Dowe argues that the correlations that arise because of bilking are not coincidental because they are causally related, Ismael (2003) argues that these correlations are not coincidental because they are not analytically independent. Ismael uses the example ‘Earman rockets’ to discuss these correlations. An Earman rocket is programmed to fire a probe into the past. If the probe is not detected, no safety switch is activated. But if the probe is detected, a safety switch is activated to stop the probe. This means that the probe is only fired if it is not fired. This is in line with other time travel paradoxes except that it avoids the complication of human agency. Ismael states that a coincidental correlation between X and Y occurs when X and Y are neither analytically or causally connected. However, there is no coincidental correlations in the failure of Earman rockets to fire. In these cases, when the rocket attempts to fire it attempts to implement a self-defeating chain. However, this will be thwarted (a failed bilking attempt, for example the system malfunctions). But these are not analytically independent. “Being self-defeating is not analytically independent of being thwarted because saying that a launch is thwarted is just a way of saying that it is defeated and defeating oneself is just a special way of getting defeated.” (2003, p. 310).
While both Dowe and Ismael agree that correlations arise in backward time travel, but that these correlations are not coincidental, Smith argues that there are no laws preventing such correlations and, thus, no reason to believe that they could not occur.
4.2 Smith’s response: There are no laws preventing foiling coincidences
While Horwich claims that backward time travel is highly improbable because of foiling coincidences, the fourth argument by Smith (1997) responds to Horwich’s claim that coincidences that violate the Principle of V-correlation are highly improbable. He refutes this by arguing that this improbability is only based upon our observation. It is not based on any law or principle. In addition, no such law or principle exists. He states the Horwich’s argument that these coincidences violate the principle of V-correlations is based on “what has been observed; it is a purely de facto principle and has no modal force.” (1997, p. 368). In other words, coincidences of the sort that bilking attempts give rise to seem improbable because we have not witnessed many of them. However, they could become more frequent and, in this case, they would not seem so strange to us. Smith states:
Suppose that any day prior to tomorrow lies outside the local past of the departure of the first backward time traveller. We have not the slightest reason to suppose that we will not see extraordinary coincidences occurring tomorrow, as our time traveller attempts to murder her grandfather…Thus, the most that Horwich can argue – assuming that local backward time travel does entail coincidences – is that no time traveller from our local future has visited us – that is, that time travel to the local past will not occur within the next few generations, at least not around here. And that is something we know anyway, simple on technological grounds (Smith, 1997, p. 371).
I take this to be the most persuasive way to understand this issue. It suggests that, while we do not see many of these foiling coincidences, this is not a reason to believe that they are improbable and that it would not be possible to witness them in the future. Smith argues that even if we assume that backward time travel entails lots of coincidences, it does not follow from this assumption that backward time travel can be expected to occur only rarely. At most, the fact that we do not witness these violations suggests that there are not many (or any) time travellers from the future currently walking amongst us. If they did start visiting us in droves, we would perhaps start to see lots of improbable coincidences (violations of the Principle of V-correlation). For this reason, local backward time travel is plausible, even if we have reason to doubt that there are currently any time travellers from the future in our midst.
In conclusion, I argue that backward time travel is plausible. I suggest that backward time travel would entail foiling coincidences due to failed bilking attempts. As such, I disagree with Smith’s augments that foiling coincidences would not arise in these situations. However, I agree with Smith’s claim that foiling coincidences do not prove that backward time travel is improbable. At most, it can be claimed that we currently do not witness many of these improbable coincidences. This suggests we are not currently being visited by many (or any) time travellers. But this does not establish that time travel is improbable or impossible. Rather, it shows that we currently are not seeing many (or any) consequences of time travel.
Dowe, P. (2003). The Coincidences of Time Travel. Philosophy of Science, 70(3), 574-589. doi:10.1086/376926
Goddu, G. C. (2007). Banana Peels and Time Travel. Dialectica, 61(4), 559-572. doi:10.1111/j.1746-8361.2007.01126.x
Godel, K. (1949). A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy. La Salle: Harper & Row.
Horwich, P. (1975). On Some Alleged Paradoxes of Time Travel. The Journal of Philosophy, 72(14), 432-444. doi:10.2307/2025013
Horwich, P. (1987). Asymmetries In Time. Massachusetts, US: MIT Press.
Ismael, J. (2003). Closed Causal Loops and the Bilking Argument. Synthese, 136(3), 305-320. doi:10.1023/A:1025170026539
Kahneman, D. (2011). Thinking, Fast and Slow. London, UK: Penguin Books.
Lewis, D. (1976). The Paradoxes of Time Travel. American Philosophical Quarterly, 13(2), 145-152.
Price, H. (1996). Time’s Arrow & Archimedes’ Point: New directions for the physics of time. Oxford, UK: Oxford University Press.
Sider, T. (2002). Time Travel, Coincidences and Counterfactuals. Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, 110(2), 115-138. doi:10.1023/A:1020205802833
Smith, N., J. J. (1997). Bananas Enough for Time Travel? The British Journal for the Philosophy of Science, 48(3), 363-389. doi:10.1093/bjps/48.3.363
Smith, N., J. J. (1998). The problems of backward time travel. Endeavour, 22(4), 156-158. doi:10.1016/S0160-9327(98)01154-5
Smith, N., J. J. (2017). I’d Do Anything to Change the Past (But I Can’t Do ‘That’). American Philosophical Quarterly, 54(2), 153-168.
Vihvelin, K. (1996). What Time Travelers Cannot Do. Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, 81(2/3), 315-330. doi:10.1007/BF00372789