I consider Swiggers and Wouters to be correct: /kath' hauton/ refers to /logou/ as in 'as on its own'.
What thoughts you have of me, and what thoughts I have of you, in poems by Walt Whitman and Allen Ginsberg
“Dream of a Shade”: Refractions of Epic Vision in Pindar’s Pythian 8 and Aeschylus’ Seven against Thebes