David Lewis proposed a solution to the Grandfather Paradox; the Paradox which was used to disprove the possibility of time travel. His successful analysation allows for comparable paradoxes to be solved using the same logic. Specifically, there is a reason to believe that Lewis' solution can be used to solve the problem outlined in Earman's logically pernicious self-inhibitor problem. Firstly, I will be exploring what the Grandfather Paradox entails and David Lewis' solution to it. Secondly, I will present the logically pernicious self-inhibitor problem by John Earman and how it maps onto the Grandfather Paradox, showing all parallels and how they are comparable. Finally, I will provide a solution to Earman's problem using the logic outlined in Lewis' grandfather paradox solution.
The Grandfather Paradox exemplifies the argument that time travel has logical impossibilities. This paradox refers to the hypothetical that involves a young time traveller, Tim, and their grandfather. Tim goes back in time to kill his grandfather at a time before he or his father had been born. On a linear timeline, this would mean that Tim can now have never been born to kill his grandfather in the first place. In this hypothetical Tim exists and does not exist at the same time. (Hohwy et al. 2018, p.2)
David Lewis' proposed solution to the paradox presents as context-dependent with a focus on the different meanings of 'can.' Lewis' solution presents both possibilities and arguments in the paradox. Lewis writes that Tim has the physical capability to kill his grandfather. Assuming Tim can load the rifle and aim and be close enough to shoot, then Tim can kill his grandfather. (Lewis. 1976, p.150-151) Concerning the other part of the paradox, Lewis presents that both Tim's existence, as well as his grandfather's life after the supposed killing, is factual evidence that not only did Tim not kill his grandfather but that Tim cannot kill his grandfather. In both of these cases, Tim either can or can't complete the task, relevant to a different set of facts present. This solutions of these two hypotheticals are separate with a different set of elements, and therefore distinct conclusions. Lewis argues that he cannot consider both scenarios in unison as a way to prove a contradiction that doesn't exist. (Lewis. 1976, p.151)
John Earman famously presented a self-defeating causal loop to disprove the possibility of time travel. A self-defeating causal loop is where the cause of the event occurs after the event, and this event harms the time traveller. An example is a time traveller going back in time to kill themselves at a younger age. (Ismael. 2003, p.305) 'The Logically Pernicious Self-Inhibitor' imagines a rocket ship that fires a probe into the past. The rocket ship is programmed to fire the probe unless the safety switch is turned on. The safety switch only turns on if the return of a probe is detected by a sensor attached to the ship. The rocket ship only fires the probe if it does not fire the probe, this is a logical impossibility. (Hohwy et al. 2018, p.3)
The logically pernicious self-inhibitor hypothetical is comparative to the Grandfather Paradox. The probe firing from the rocket into the past is parallel to Tim time travelling to the past. The sensor on the rocket ship detecting the return of a probe and then firing is parallel to Tim successfully killing his grandfather. In the rocket ship example, the probe will fire as long as it does not fire. (Ismael. 2003, p.305) And in the grandfather paradox, Tim goes back in time to kill his grandfather and continues to exist. (Hohwy et al. 2018, p. 8)
Lewis' solution of the Grandfather Paradox can help solve Earman's logically pernicious self-inhibitor problem. In the Grandfather Paradox, when the two conclusions are presented that Tim either can or can't kill his grandfather, Lewis responds that both are possible given the circumstances and that they 'are compatible because 'can' is equivocal' (Lewis. 1976, p. 150). Using this logic to solve the logically pernicious self-inhibitor problem, you find the hypotheticals to be unusually familiar as they both involve some kind of time travel. In Earman's hypothetical, it appears to be a casual loop given all assumptions. However, if we were to take away certain assumptions, the paradox begins to collapse. Earman’s example assumed that such a rocket ship can be built and that the sensor detecting the probe is functional. Using Lewis' logic, we can conclude that given the physical and technological possibilities of the time, the rocket ship either can or can't be built. Additionally, given the casual loop by the probe, the presence or absence of a working sensor would result in the device working or not working. (Hohwy et al. 2018, p.308) The solution to John Earman's problem is context-dependent, and either can or cannot be possible depending on the specificities of the case.
While Earman's illustration is more complicated than the grandfather paradox, it is plausible that the solution proposed by Lewis can apply to both cases. Lewis successfully solves the Grandfather Paradox by accepting both possibilities (that Tim either can or can't kill his grandfather) but under different premises. (Lewis. 1976, p.151) There are distinct parallels between this as well as Earman's problem. Both examples involve time travel into the past, and something not happening for it to happen. These parallels make it possible to apply Lewis' logic of multiple context-dependent solutions depending on valid assumptions. While the logically pernicious self-inhibitor isn't as plausible as Tim's travel to murder, the parallels between the two examples make the proposed solution more reasonable.
I have shown that David Lewis' solution and logic in tackling the grandfather paradox has been successful beyond its original intent. Lewis' thorough account of the solution made an application to other paradoxes possible. Earman's logically pernicious self-inhibitor problem is comparable to the grandfather paradox as there are parallels that make solutions transferable. Both hypotheticals involve some level of time travel, causal loops, and a seemingly illogical paradox. By focusing on contextual dependencies and using the word 'can' as equivocal, we can conclude that depending on the technical possibilities such a probe shooting rocket ship either can or cannot be built. Additionally, depending on the functionality or dysfunctionality of the probe sensor, the device either can or cannot work.
References
Lewis, D. (1976). The Paradoxes of Time Travel. American Philosophical Quarterly, 13(2), 145-152. viewed 20 October 2019 http://www.jstor.org/stable/2000961
Hohwy, H, Chadha, M, Townsend, A, May, J, Deery, O. (2018) Time Travel. online course materials, Semester 2, 2019, Monash University.
Ismael, J. (2003). Closed Causal Loops and the Bilking Argument. Synthese, 136(3), 305-320. viewed 22 October 2019 http://www.jstor.org/stable/20118337