The infinite runner

If you can imagine that Achilles starts but never stops running, then you can imagine that Achilles never starts but stops running. You can imagine that Achilles never starts and never stops running. If whenever you begin or end observing Achilles, he's always running, then you can't determine which of the three cases is true because you're always observing within the range that is covered by all three cases.

If you observe Achilles starting to run, then it's reasonable to suppose that either he'll stop running at some point or he will never stop running. If you observe Achilles stopping his run, then either he must have started running or he was always running. In both cases, the third case, namely, Achilles runs forever, is false. The basic case is that Achilles starts and stops running. But there is a weird case in which he stops running before he starts. If he was always running and then stopped at some point in time, a new start will do since he only starts running after he has stopped.