Grandfather paradox
The “grandfather paradox” is an argument used to prove the impossibility of time travel.
The idea is that an individual (usually called "Tim" because the name looks a lot like "time") who could
travel backwards in time, could kill his grandfather, prior to the conception of his father. But this would
imply that Tim’s father would never have been born, and that in turn would imply that Tim would never
be born. And if Tim was not born, Tim could not go back in time. This situation leads to a contradiction.
Tim both could and could not kill his grandfather. He could (because he would by hypothesis be in the
right time and place with a weapon) yet he could not (because he would have to have been born!) And
since our “Tim” could be anyone this means that nobody could - that time travel is impossible.
travel backwards in time, could kill his grandfather, prior to the conception of his father. But this would
imply that Tim’s father would never have been born, and that in turn would imply that Tim would never
be born. And if Tim was not born, Tim could not go back in time. This situation leads to a contradiction.
Tim both could and could not kill his grandfather. He could (because he would by hypothesis be in the
right time and place with a weapon) yet he could not (because he would have to have been born!) And
since our “Tim” could be anyone this means that nobody could - that time travel is impossible.
Syllogistically, the macro argument is this: Premise 1. If time travel is possible, then contradictions are
possible. Premise 2. Contradictions are not possible. Conclusion. Time travel is not possible.
possible. Premise 2. Contradictions are not possible. Conclusion. Time travel is not possible.
The hypothesis about Tim is one of a number of arguments that support P1. One philosopher who
believed that time travel is possible was David Lewis. Lewis argued that P1 is wrong: time travel does
not make contradictions possible, so the conclusion does not follow. So he has to deal with Tim. Here is
the alleged contradiction:
believed that time travel is possible was David Lewis. Lewis argued that P1 is wrong: time travel does
not make contradictions possible, so the conclusion does not follow. So he has to deal with Tim. Here is
the alleged contradiction:
- If time travel is possible, the Tim could kill his grandfather
- If time travel is possible, then Tim could not have killed his grandfather
Lewis presumes that Tim has a gun with him when he goes back a few decades; that he is a good shot, and
that he comes within close range of grandpa.In all of those respects, he “could have” taken the paradoxical
action.
that he comes within close range of grandpa.In all of those respects, he “could have” taken the paradoxical
action.
What Lewis says is that the argument as discussed above uses “could” in two distinct meanings, so it is
an equivocation. Whenever we say that somebody “could” do something we mean that the something
could happen holding certain things fixed. What we mean to hold fixed for purposes of the “could” depends
on the context. So when we say Tim “could kill his grandfather” give time travel we mean, “holding fixed
the past, Tim might kill his grandfather.” But when we say that Tim “could not have killed his grandfather”
we mean ”holding fixed the future -- events such as the birth of Tim’s Dad and of Tim himself -- Tim must
not have killed his grandfather.”
an equivocation. Whenever we say that somebody “could” do something we mean that the something
could happen holding certain things fixed. What we mean to hold fixed for purposes of the “could” depends
on the context. So when we say Tim “could kill his grandfather” give time travel we mean, “holding fixed
the past, Tim might kill his grandfather.” But when we say that Tim “could not have killed his grandfather”
we mean ”holding fixed the future -- events such as the birth of Tim’s Dad and of Tim himself -- Tim must
not have killed his grandfather.”
Since “could” means different things, the two contradictory assertions A and B mean different things, and
they do not directly contradict each other.
they do not directly contradict each other.
That's Lewis' argument anyway. I'm not sure it resolves the issue. Its an amusing paradox, though, which is
why it so often shows up in fiction.
why it so often shows up in fiction.
A variant: if I go back in time specifically to change something that will make the future (my time) a
better place, won't that action too prove paradoxical?
better place, won't that action too prove paradoxical?
To take the stereotypical example, I go back in history to, say, 1922 and kill Hitler. I then come back to 2018 to encounter whatever the world would be like had that been done. But ... this is now the time line I grew up in, isn't it? So I have never known any world other than the Hitlerless one. So where on this timeline would I ever have gotten the idea that I should invent a time machine and go back and kill some random aspiring painter?
Christopher,
ReplyDeleteYour post is fascinating and clearly explained. There seems no reason to speak of Tim's grandfather; he could kill his father before he, Tim, was born. Or he could kill his father soon after he, Tim, was born and grow up fatherless, thereby creating a contradiction. In fact, he could land in the past in his time machine and do nothing, and the future might not be what it had been. Suppose that he landed the time machine on a public street, and his father, on his way home from work, saw it and joined the crowd that was marveling at it. As a result, he got home late and his wife got angry at him because she had to reheat dinner, and they quarreled. But, before Tim arrived in his time machine, that had been the night that Tim was conceived, but, because of the quarrel, he was not conceived! Or, because he stopped to look at the time machine, someone else's father got home late, quarreled with his wife, and did not conceive the son, who, before Tim's time travel, had been kidnapping migrant children and otherwise making the world worse than it had been.
I should have written that Tim could kill his father before he, Tim, was conceived, not before he was born. If Tim killed his father while Tim's mother was pregnant with Tim, then Tim could still be born.
DeleteI also do not see how Lewis' argument, valid as it may be, resolves the issue. The contradiction remains, and it goes far beyond whether Tim exists or not. If Tim kills his grandfather, then the world as a whole is different. Every interaction that Tim's grandfather had with other people would not occur, and their lives would change as a result. For example, Tim's grandfather, if Tim kills him, would not go to a ball game with a friend that he went to before Tim killed him, and that friend would do something else that day, which would affect other people in countless ways.
ReplyDeleteIn addition, the existence of a contradiction does not rule out time travel, because of the possibility that alternate worlds--the world with Tim before Tim kills his grandfather, and the world without Tim after Tim kills his grandfather--could both exist. Don't ask me how; I just raise the possibility. The contradiction might not preclude the possibility of time travel, but might be evidence of its impossibility. If so, what might preclude it? Perhaps something in the nature of time. You'll have to ask Einstein about that, however, as I am not qualified to answer it.
Henry,
ReplyDeleteWith regard to what I called the macro argument above, you are saying that the conclusion does not follow if we deny Premise 2. Lewis approach is to keep P2 (that contradiction implies impossibility) while denying P1 (that time travel involves contraction). Your suggestion is that we can keep P1, and deny P2 (by way of accepting the branching off of time lines).
I'm inclined to believe in a multiverse, but a rather different sort of multiverse than the one this suggests. Personally, I'm inclined to accept both premises and thus the conclusion of the macro argument. But the lines of reasoning involved in maintaining any possible position here are intricate and weird, which is why they're fun. And why they've kept science fiction writers busy for decades.
Are you familiar with the classic Star Trek episode "City on the Edge of Forever"? Joan Crawford's character had to die because she was a charismatic pacifist in circa 1930, and it was too early for pacifism. If she had lived, the western allies would have disarmed, Hitler would have prevailed, and the Federation would never have come into existence.
No, I did not see that (or any) Star Trek episode. What Federation? Joan Crawford's character must have been quite a gal (is that word permitted these days? "Guy" wouldn't work) to have the ability to persuade nations to disarm.
DeleteThe "Federation of Planets" of course! In the world of Star Trek, the Federation in an idealization of mid-20th century liberalism on a galaxy wide level, engaged in warfare with the more spartan civilization of the Klingon Empire.
ReplyDeleteThe Crawford episode was my first encounter with such time travel paradoxes. The plot is intricate: McCoy goes back in time first. He must have seen Crawford's character about to walk into the street and be hit by a car, so he reflexively rescued her, with no idea the disastrous consequence that would have. Kirk and Spock travel back in pursuit of him, then Kirk meets Crawford some time before the traffic accident "fork" of the two timelines. He and Spock figure out what has happened (in meta-time, I suppose) to the time line, and Kirk has to prevent McCoy from saving Crawford's life so premature pacifism will not prevail.