I consider Swiggers and Wouters to be correct: /kath' hauton/ refers to /logou/ as in 'as on its own'.
A personal checklist of memorable wordings in Part I and Part II of Richard P. Martin’s Mythologizing Performance
Sappho’s Aphrodite, the goddess Chryse, and a primal ordeal suffered by Philoctetes in a tragedy of Sophocles
Glimpses of two different myths about two different visits by Philoctetes to the sacred island of the goddess Chryse