I don't think of it as a literal logical paradox. Perhaps it's more of a causal anomaly. Imagine that you go back in time and kill your grandfather before your father is conceived. You are arrested by the police in that day and tell them some cock-and-bull story about being a time traveler from the future, the dead man's grandson in fact. The court declares you insane and you are committed. Things continue to unfold in a natural manner from their point of view - although different from how you "remember", you are never born etc. So if you do change how the future unfolds, who are you and where did you come from? In one interpretation, you just popped out of nowhere with (false?) "memories" of a future that never happens. That's a causal anomaly, not a logical paradox. Something happening (you appearing) with no cause. On another interpetation, one that posits a much more abundant 'many-worlds' ontology, at each and every moment the future consists of many different possibilities, each one associated with a timeline, a possible world in which that possibility actually occurred. (And each of those timelines multiplying into its own tree, as new possibilities continually emerge at each moment.) So in this ontology, you would have originated in one possible timeline (timeline A, where your grandfather wasn't murdered). You went back down your branch to a point where his living of dying were real possibilities and caused yourself to move into the future along another timeline (timeline B, where he was murdered). Where did you come from? Not 'out of nowhere' as in the causal anomaly model, but from timeline A. Even though from the perspective of timeline B, timeline A never happens. Equally, from the perspective of timeline A, timeline B never happened (it's the "grandfather paradox" in fact). In other words, time travel might be a lot more complicated than travel backwards and forwards along a single one-dimensional past -> future line. There might be an effectively infinite number of possible futures (and presents, since all this was presumably happening in the past too), each real in its own way and where time travelers are capable of influencing which direction they take from the point of interference, provided that they are equipped with time-machines. It's an old science-fiction plot device.