A temporal paradox is a thought experiment where a time traveler goes to the past, and does something that would prevent him from time travel in the first place. If he does not go back in time, he does not do anything that would prevent his traveling to the past, so time travel would be possible for him. However, if he goes back in time and does something that would cause him/her to not make a time machine he would not travel back in the first place causing him to make one then go back and not make one.
A typical example of this kind is the grandfather paradox, where a person goes back in time to kill his grandfather before he had any biological descendant. If they succeed, one of their parents would never exist and they themselves would never exist either. This would make it impossible for them to go back in time in the first place, making them unable to kill their grandfather, who would continue to produce offspring and restart the situation. But if they fail, their grandfather would live and produce offspring. This has the same affect as prevailing.
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The Daily Omnivore 