George enjoyed and hated the privileged position of being the grandson of Edgar the Tyrant, the man who had killed his kindly brother Sam. Edgar had conquered the Seven Systems with alien technology and established the most crushing despotism in human history. Like his grandfather, George was a brilliant scientist with a special talent for understanding alien technology. Unlike his grandfather, George was burdened with ethics and compassion. After discerning the secrets of an alien time machine, George nobly decided to sacrifice himself by going back in time and killing his grandfather before he discovered the trove of alien technology that enabled his reign of terror.

After travelling back in time and locating his target, George took careful aim with the alien plasma rifle, confident that the heavy weapon would guarantee the death of his grandfather. It did exactly that, vaporizing not only him but several meters of ground.

George expected to be erased from time instantly, but in realizing that he still existed he realized he still existed. Thinking that it might take some time for the effects to catch up to him (or head back to him, however it worked) he sat down to wait. And wait. When nothing happened, he thought “hmm, maybe that rumor about grandma and Uncle Sam was true after all” and travelled back to his time.

Time travel, as any time traveler will tell you, is problematic. One of the classic problems is the Grandfather Paradox. If you can travel in time, then you should be able to go back in time and kill your grandfather (or grandmother, to avoid sexism in temporal murder). However, if you kill your grandfather, then you would never exist and would not be able to go back and kill him. As such, time travel would make it possible to kill your grandfather but killing him would make it impossible for you to kill him. Hence the paradox.

One solution is to take it as a reductio ad absurdum of time travel. If time travel were possible, it would lead to an unacceptable paradox. Therefore, time travel is not possible. Another approach is to address the paradox with a bit of temporal deus ex machina: you can travel back and time and try to kill your grandfather, but you will never be able to succeed. If you, for example, try to run him over with a car, you will run out of gas or get a flat tire. If, as another example, you try to shoot him with a rifle, every round will miss or misfire. Or you will get caught by the police. There is an obvious question of how this temporal enforcement mechanism would work.

One could, of course, invoke a teleological explanation: there is a purposeful agent that ensures that you will never succeed. As with non-time travel teleological agents, this could be a supernatural being (God or a god of time), mortal agents (time cops, perhaps) or some sort of Aristotelian temporal paradox-preventer (perhaps related to the first mover).

In the context of doing metaphysics in accord with the economic style of argumentation, using a teleological metaphysical entity to solve the paradox would raise the cost of the theory. As per Occam’s razor, entities should not be multiplied beyond necessity. Metaphysical teleological explanations also tend to be out of favor in philosophy, especially those of the supernatural sort. This will tend to impose both a “weirdness” and implausibility cost on the theory.

But this cost can be offset if the entity provides enough benefits, such as explanatory power. On this economic model one chooses between metaphysical theories in a way analogous to choosing between smartphones: the one with the best benefits for the lowest cost would be the winner.

Having mortal agents prevent the paradox could make for interesting science fiction (and imposes no metaphysical cost) but there is an obvious problem: mortal agents could fail. While one could argue that time police would have a huge advantage over a lone time-traveler, there are easy-to-imagine scenarios where even a lone time-traveler succeeds. One could imagine, for example, a rogue time cop deciding to kill their grandparent. Because of this, fallible protectors of time would not solve the problem.

Another approach would be to embrace a form of non-teleological determinism: while one could travel back in time one can never succeed in killing one’s grandfather because one failed. This would seem to have broader implications for time travel as well in terms of making any changes to the past. This does raise the question of how this determinism would work but determinism (in its various forms) is already a well-established philosophical position. As such, if you are already a determinist, then you can presumably apply it to time at no extra cost and solve this problem.

Science fiction has other options that could solve the problem. One approach taken by Alfred Bester  in “The Men Who Murdered Mohammed” is that going back in time to commit murders does not affect the timeline, but instead affects the traveler by gradually removing them from reality. While the mechanism for this would need to be explained, it does solve the paradox: you could go back and kill your grandfather, but this would have no impact on the timeline. You would just fade a bit, metaphysically speaking, and history would remain unchanged.

Another approach is that time travel creates alternative timelines. The traveler goes back and murders his grandfather and thus creates a new timeline in which this occurred. The original timeline (whatever that might mean) remains intact. The time traveler might also split and they would exist in the original timeline because nothing changes there. But they would not exist in the “new” timeline: they killed their grandfather in that timeline and hence would never be born. Since time travel is mysterious and messy, perhaps the time traveler would be exempt from the split in some manner. Or perhaps not.

This approach does raise some obvious problems. One is that time travel would seem to create new timelines ex nihilo: they seem to simply come into existence from nothing. Unless, of course, the original timeline gets sliced like a pizza, something that would seem to be, at least in theory, detectable. Then again, if the original timeline is infinite, dividing infinity results in infinities. Another set of problems would involve personal identity. If the split occurs, what happens to the identity of the people in the original timeline and those “created” in the new timeline? For example, if Sally goes back and kills her grandfather and splits the timeline, then there would be a new timeline with the people from the original “duplicated” (perhaps including her grandfather if a there is an afterlife). To illustrate, consider Sally’s grandmother Sarah. When Sally kills her grandfather and splits the timeline, then there would now be at least two Sarahs. Both arose from the unsplit Sarah, so they would both seem to be Sarah. But they are now two people unless there is some form of cross timeline personal identity. Some theories of personal identity can easily handle this. For example, Locke’s consciousness-based theory would entail that both Sarahs were the original Sarah (if their memories remain) but they are no longer the same person after the split because they have different memories. Theories, like Descartes’, that make the person the soul would need to account for there being two souls: does the original divide like an amoeba or does a new soul get created? Or something else? All these issues (and others) need to be addressed to make this solution work.

While there are numerous problems that arise from this approach, it does not require postulating the existence of new types of metaphysical entities: one just needs multiples of what we already have, namely the timeline. This does not raise the ontological cost of the theory. To use an analogy, if one accepts the existence of one supernatural god, accepting a second or tenth god comes with no extra ontological cost. The price is paid for each metaphysical type rather than each token of that type. There might be other costs arising from this, though, such as matters of weirdness or plausibility.

The last approach I will consider is that time travel is dimensional travel. That is, when you travel in “time” you are going to another reality that is at a different time than your reality. On this view, when someone travels “in time” to kill “their” grandfather, they are travelling to an alternate reality and killing an alternate version of their grandfather. In that reality, “they” would not exist, but they could return to their own reality, which would be one in which their grandfather was not killed by a time traveler. This would be analogous to killing the grandfather’s twin brother: this kills someone like him but not him.

While this approach does require explaining how dimensional travel would work, it has fewer problems than the split timeline approach. While it does require multiple dimensions, so does the split timeline approach. But it does not require that they appear ex-nihilo or form from division. It also does not face the problems with personal identity: the person in the other reality is not the traveler’s grandfather, just someone similar. The obvious downside to this approach is that it solves the problem by eliminating time travel. But maybe that is a good thing.