Re-entrant reality
The grandfather paradox is no paradox at all, it seems to me. Any sequence of events that is impossible has a probability of zero. Even if such a sequence begins, it must end as a possible sequence. You get lost, and fail to visit grandad. The weapon fails. The weapon fails catastrophically and you kill yourself instead. You are seduced by a totally hot and kinky chick and your priorities change. Anything with a non-zero probability is more likely and will happen instead.
Nearly all the consequences of time travel are implausible. Just about the only one that isn’t involves you arriving to tell yourself how to effect the time travel. This is the only way you can simultaneously be the first person to do it and observe someone else do it first: re-entrant reality.