Once we realize that the indivisible and infinitely repeatable One of the arithmetic lesson in Republic7 is generated by διάνοια at Parmenides 143a6-9, it becomes possible to revisit the Divided Line’s Second Part and see that Aristotle’s error was not to claim that Plato placed Intermediates between the Ideas and sensible things but to restrict that class to the mathematical objects Socrates used to explain it. All of the One-Over-Many Forms of Republic10 that Aristotle, following Plato, attacked with the Third (...) Man, are equally dependent on Images and above all on the Hypothesis of the One. (shrink)