Time travel paradoxes are not really so tough. In fact, as Looper unwinds, we find that time travel relatively light-weight stuff compared everything else that happens in the story. It’s a little bit like The Matrix, where you discover that a modestly talented hacker has been sent careening into Alice’s nightmare chasm.
Looper takes place in 2044, but this version of the future looks like '70s urban squalor with a splash of Studio 54. We get the sense that life is cheap in this brave old world, and that’s because just about everybody we meet is a killer, or a boss (Jeff Daniels), or an underling, or a stripper.