Ἀνα τὸν αὐτὸν λόγον

Answering articles by Smith (PJ 18) and Matoso (PJ 22) about the Divided Line, I argue that the problems Smith raised and Matoso pretended to solve don’t exist in a proper reading of the analogy and the ensuing allegory of the cave in light of one another and stem from a misunderstanding of the expression ἀνα τὸν αὺτον λόγον at Rep. VI, 509d7: the λόγος to be used to split both segments is not the one used to split the line in the first place, and it is not a numerical ratio, but a logical rationale.