I criticize Lockwood’s solution to the “paradoxes” of time travel, thus endorsing Lewis’s more conservative position. Lockwood argues that only in the context of a 5D space-time-actuality manifold is the possibility of time travel compatible with the Autonomy Principle (according to which global constraints cannot override what is physically possible locally). I argue that shifting from 4D space-time to 5D space-time-actuality does not change the situation with respect to the Autonomy Principle, since the shift does not allow us to have (...) a coincidence-free local dynamical theory. (shrink)