Can I kill my younger self?

Abstract
If (backward) time travel is possible, presumably so is my shooting my younger self (YS); then apparently I can kill him—I can commit retrosuicide. But if I were to kill him I would not exist to shoot him, so how can I kill him? The standard solution to this paradox understands ability as compossibility with the relevant facts and points to an equivocation about which facts are relevant: my killing YS is compossible with his proximity but not with his survival, so I can kill him if facts like his survival are irrelevant but I cannot if they are relevant. I identify a lacuna in this solution, namely its reliance without argument on the hidden assumption that my killing YS is possible: if it is impossible, it is not compossible with anything. I argue that this lacuna is important, and I sketch a different solution to the paradox.
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