Abstract

Mr. Brumbaugh gives several accounts in the course of his work of the main purpose of his study, and the emphasis falls now one way and now another. Readers may easily be misled by the opening sentence of the introduction, which suggests that Plato's mathematical illustrations are pointers to "diagrams which Plato had designed, and were intended to accompany and clarify his text." If that is what Mr. Brumbaugh intended, he has failed to make out his case. There is no direct evidence that Plato designed diagrams; and there is some good inferential evidence to the contrary. It would be surprising, for example, if Plato's diagrams had survived that long, that Aristotle should have described the Divided Line in terms of an arithmetical progression and ignored Plato's express indication of proportion between the upper and lower segments. Mr. Brumbaugh himself faces this passage and admits that "no continuous tradition connects the figures of Hellenistic scholars with Plato's original design." But it really does not matter. If we design diagrams in the light of our knowledge of Plato's mathematical imagination, it is most certainly a help to the interpretation of the passages concerned. This, as a matter of fact, seems to be Mr. Brumbaugh's main reason for ascribing the diagrams to Plato, and while the conclusion does not follow, the premiss is correct; and the premiss, not the conclusion, is the main point at issue.