1000 time-travelers travel back in time, each with the intention of killing their own infant-self. If there is no branching time, then on pain of bringing about a logical contradiction, all must fail. But this seems inexplicable: what is to ensure that the time-travelers are stopped?
For a time, this inexplicability objection was thought to provide evidence that there is something incoherent about the possibility of backwards time travel in a universe without branching time. There is now near-consensus, however, that the objection has no bite: there is nothing inexplicable about the mass failure. Lewis, Sider and Ismael independently argue that since it is built into the description of the class of cases considered that the time-travelers must fail – and so we consider only unsuccessful attempts – there is no mystery. Smith argues that the absence of possible worlds at which auto-infanticide is committed suffices as a complete explanation for the failures. And Baron and Colyvan maintain that available causal and logical explanations jointly account for everything that needs accounting for.
I argue that these are wrong. There is remaining, problematic inexplicability. For backwards time travel not to lead to logical contradiction, something would need to do logic’s bidding, after all.