Unclarity and the Intermediates in Plato’s Discussions of Clarity in the Republic

In this paper, I argue that the two versions of divided line (the first in Book VI and the recalled version in Book VII) create problems that cannot be solved — with or without the hypothesis that the objects belonging to the level of διάνοια on the divided line are intermediates.  I also argue that the discussion of arithmetic and calculation does not fit Aristotle’s attribution of intermediates to Plato and provides no support for the claim that Plato had such intermediates in mind when he talked about διάνοια in the Republic. The upshot of my argument is negative: even if Aristotle’s report about Plato and intermediates is correct, there is no evidence for such objects provided in the passages I review from the Republic. If they are to be found in Plato, it will have to be elsewhere that they are found.