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Temporal Paradox
Doc: A paradox!
Marty: What?
Doc: A paradox!
Marty: You mean one of those things that destroys the universe?
—Back to the Future II
A temporal paradox is any paradox that arises due to a person, object, or information, travelling backward in time.
As discussed in Unbounded Recursion:
Time Travel paradoxes ("Temporal paradoxen") can include spontaneous creation (I travel back in time and give my younger self my favorite hat.... a hat which I have had since childhood... it was given to me by a wise old stranger), impossible destruction (I go back in time and shoot a young man... subsequent inquiries reveal him to be my own grand father), and worse. Attempts to unravel these conundrums can result in infinite regress.
....there are various categories of time travel paradox.
Spontaneous Creation
I travel back in time and give my younger self my favorite hat.... a hat which I have had since childhood... it was given to me by a wise old stranger...
In such a situation, where did the hat originally come from? Need it have come from anywhere?
Impossible destruction
I go back in time and shoot a young man... subsequent inquiries reveal him to be my own grand father.
In such a situation, how did I ever get the chance to go back in time, if I was never born, since my own father was never born?
Such situations are only unresolvable depending on the MODEL that is used to reason about time travel. (See Time Travel Models)
Time Travel usually exists inside fictional universes, and such universes are built (loosely or precisely) on a system of ideas that may or may not permit certain possibilities and which can be loosely grouped by their behavior and policies into several different formats.
Time is an arrow.
Time is a duck.
Time is a spiral.
Time is a circle.
Time is an illusion, lunchtime doubly so.
Anyway, see Time Travel Models