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{{Clean up|Answer contains conversation & extraneous material.}} A paradox is basically an impossible event in time and space, which in results, destroys the entire universe. For example, your current self says hello to your future self using a time machine, whereas there are two of you. This is an impossible event, thus destroys the universe.

Sometimes, however, instead of destroying the universe the true timeline reasserts itself, correcting the paradox. (see The "Last of the Time Lords")

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A paradox is basically something which by valid reasoning/something which appears to be valid reasoning, creates an apparently impossible or contradictory statement.


An example is "If God is all powerful, can God create a rock so heavy he himself can not lift it?"


If God is all powerful, he should be able to do anything, including creating a rock he can not lift. If God is all powerful he should be able to lift any rock, including any rock he could make. This therefore is a paradox.


The existence of a paradox may be cause to reject the theory (in this case, saying God isn't all powerful) or is cause to believe there's a flaw in your reasoning (such as suggesting that the very idea of 'a rock God can not lift' is nonsense and therefore the question is meaningless).


Technically, interacting with a version of yourself from a different time need not be a paradox. It depends on how one assumes time travel works. A common paradox is the grandfather paradox. If a man travels backwards in time and kills his grandfather before his parents were born, he'd never be born. Therefore he could not travel backwards in time and kill his grandfather.


That said, some people believe that travelling backwards in time would create a new timeline. In that case, even though the man wouldn't be born in the timeline in which he's killed his grandfather, since he was already born it doesn't create a problem.


If however you could change your own past by travelling backwards in time and that would affect you in the present, then travelling backwards in time and killing your grandfather would cause you not to exist, causing your grandfather not to be killed, causing you to exist, causing you to kill your grandfather...Effectively since there's no resolution to the situation, arguably it couldn't happen. Yet in time travel it might.


In logical analysis, a truly paradoxical sitaution (as opposed to simply a counterintuitive situation) is generally treated as impossible (indicating a flaw in logic or assumptions). Since Doctor Who sometimes assumes paradoxes are possible, the same result which means that the logic in your theory breaks down, extends to mean the universe itself breaks down.

An interesting example is this. If you and a friend are caught in a scenario where you have to be quiet and your friend doesn't realise, you have to tell your friend to be quiet which prevents them making a sound but means you must make a sound to prevent a sound from being made.