“Imagine you had a time machine. Nothing would stop you from going back in time and killing yourself as an infant, before you ever entered the timemachine. But then a contradiction would ensue: you would never have entered any time machine since you were killed before doing so (let “killing” be understood throughout as implying permanent death), and yet you would have entered a time machine, in order to travel back in time to kill yourself. Some conclude that time travel is impossible, since it would lead to this contradiction.
“There is nothing special about autoinfanticide: similar problems arise whenever a time traveler resolves to go back in time and do something that did not in fact occur. A time traveler who remembers owning a 1974 Plymouth Gold Duster could, it would seem, go back into the past and prevent herself from ever owning such a fine automobile; a time traveler could, it would seem, go back and prevent Lincoln from giving the Gettysburg address, and so on. But autoinfanticide is an especially vivid example.
“As it stands, this argument is very weak. All it shows is that autoinfanticide is impossible, as are related scenarios, such as one in which an address is given but in which someone travels back in time and prevents that address from being given. The impossibility of a certain kind of time-travel scenario does not impugn the possibility of time travel in general, any more than the existence of an impossible story about an empty box containing a figurine impugns the possibility of boxes.
“We have admitted the possibility of time travel, though not the possibility of autoinfanticide. But these possible time travelers who do not kill their earlier selves: some have the desire as well as the means. What stops them?
“No one thing. Some have a sudden change of heart. Some fear awful forces they think would be unleashed by a violation of the laws of logic. Some attempt the deed but fail for various reasons: non-lethal wounds, slips on banana peels, and the like. Others succeed in committing a murder, only to find they killed the wrong person. And there are possible worlds in which time travelers are shackled by gods, or are by other means prevented from doing mischief, though surely this is not required for time travel to occur.
“But focus now on cases in which time travelers are not shackled in ways we do not take ourselves to be shackled. These time travelers would then have the ability to do the sorts of things we could do, in their circumstances. If I, who do not travel back in time, had a gun, had the evil desire to kill, and were suitably positioned near an unprotected victim, I would have the ability to kill that victim. So a time traveler relevantly like me could likewise kill her victim. But the time traveler’s victim is her earlier self, and surely the time traveler cannot kill her earlier self, since contradictions would be true if she did. Thus, this argument concludes, unless time travelers are strangely shackled by gods or whatnot, time travel is impossible. An unshackled time traveler would both have and lack the ability to kill her earlier self.”
Text: Theodore Sider, “Time Travel, Coincidences and Counterfactuals”. Philosophical Studies, #110, 2002.