Doesn't the end of Looper create a time paradox?

I guess this is more a question about the nature of time travel more than anything else.

At the end of the movie,

Joe shoots himself in a field and changes the course of history.

Does this create a paradox as it changes the history that led up to that point?

If his future self had never existed he'd never have gone on the mission he did and thus he never would have ended up in the field.

Once he did what he did, he could no longer have done it, and so theoretically, time and space should have just folded in on itself and popped out of existence.

Is there something I'm missing that would explain how the movie could have ended where it did without the events at the beginning to lead it there?

Comments

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