The Grandfather Paradox is one of several metaphysical arguments that attempt to prove that time travel is logically impossible (whether it is physically possible is a question left by philosophers to the physicists). These arguments all have the same basic form:
Premise 1: If time travel is possible, then X must be possible.
Premise 2: X is not possible.
Conclusion: Therefore, time travel is impossible.
The Grandfather Paradox is described as follows: a time machine is invented enabling a time traveller to go back in time to before his grandfather had fathered offspring. At that time, the time traveller kills his grandfather, and therefore, one of the time traveller’s parents would never exist and thus the time traveller himself would never exist either. If he is never born, then he is unable to travel back through time and kill his grandfather, which means he would be born, and so on.
The paradox is also described in this video cartoon.
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