ABSTRACT
THERE are many passages in Plato which look as if they alluded to well-worn practices, discussions, or lessons in the Academy. As is natural with allusions, they are often marked by a puzzling brevity or oddity of expression. One need not assume that they are always conscious allusions; for every writer has moments of obscurity which are due not so much to his conclusions as to his reaching them along lines that have been familiar to him. To appreciate his whole meaning the reader has then to infer as best he can the writer's train of thought. I wish to suggest that the language in which Dialectic is described in the later Dialogues presupposes a particular and probably familiar method of illustrating it. This was a geometrical illustration of the rules of Division by means of a divided line. By failing to notice it readers have not been led into any important misunderstanding of the Academy's rules. But I hope it will appear that the recognition of it makes Plato's manner of describing Division intelligible to an extent that is otherwise difficult. It is only a tentative suggestion, and would perhaps not have been worth making but for the possibility that some points of interest might at the same time emerge for those who were unconvinced by it.
