Time travel and the grandfather paradox

Marty's mother would have married his father even without Marty's
heroic efforts to make sure it that it happened.

Is time travel the stuff of legend? Actually (and rather pleasingly), contemporary philosophers take the possibility much more seriously than you might think. Since it is generally considered that modern physics doesn’t conclusively rule out the possibility of time travel, room has opened up for philosophical speculation about what the possibility of time travel would mean for us as human beings. If time travel is possible after all, much of what we ordinarily assume about free will, causation, and time itself will turn out to be false.

Could you go back in time and, if you were so inclined, kill your own grandfather? Let’s assume that time travel is possible - that a human being could, given the right circumstances and resources, ‘travel’ back in time to events in the past. Let’s further suppose that such a person, Dave, is on a particular mission to kill his grandfather. Dave travels back into the past, and arrives on a sunny day in central London. Dave sees a vaguely familiar figure walking down the street - it is his grandfather, as a young man. Dave pulls a gun out of his back pocket and crouches behind a post-box, waiting for the perfect moment to strike...

But wait. What happens if Dave successfully kills his grandfather? Remember that we are in the past, and that Dave’s grandfather has yet to have a child (Dave’s father), who is in turn yet to have Dave. If Dave is successful in his assassination attempt, then his grandfather (being dead) will never have Dave’s father, and thus Dave will never be born. But if Dave is never born, then Dave could never have returned from the future in the first place to kill his grandfather in the past! Something has gone wrong.

We must ask the following question: is it within Dave’s power, given that he can travel back in time, to kill his grandfather? The answer is both 'yes' and 'no'. Insofar as Dave has a motive, willingness, and adequate resources (the gun, etc) to carry out the murder, he is able to kill his grandfather. However, in the grander scheme of things, Dave’s very existence in the future guarantees that he will not, in fact, succeed in his task. Crouching behind his post-box, Dave will suddenly have a change of heart. Or he will be grabbed by a passing policeman. Or he’ll be knocked over by a cyclist, allowing his grandfather time to escape. The specifics of the event that prevents Dave from firing the killer shot aren’t important - what is important is that whilst it is physically within Dave’s power to kill his grandfather in the past, it is logically impossible that he succeeds.

Philosophical reflection tells us that we should not try to kill our grandfathers. But then, we all knew that anyway.

(This puzzle is from David Lewis, The Paradoxes of Time Travel).