He would walk 500 miles and he would walk 500 more. Just to be the man that walks a 1000 miles till he can't no more.
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While fun it just seems like something made up. How accurate is an anecdotal record from this time ? Why would anyone argue about "the existence of motion" what does that even mean
The one he was "arguing" against by walking away was Zeno discussing his paradox about having to go halfway to a target, then halfway again, etc., so therefore you could never truly get there. Whether it happened or not is another question, but given Diogenes seemed to be the anti-philosopher of many names, if he didn't, then had he been there and heard it he would have.
Or he might have done something a bit more interesting than leaving.
Records of events in Greece past the 5th century BCE are about as reliable as any other bit of history. Diogenes was a philosopher famous for being something of a wit and an iconoclast, so this would have been very in-character for him to do.