ABSTRACT
The great dream of Pythagoras was to uncover the bond between the proportions indigenous to number, music, and the movement observable in the heavens. This chapter traces—in very broad strokes—the Pythagorean notion of number in Plato and tries thereby to illustrate something of the role that this notion plays in the Platonic conception of the forms, in the unfolding of the movement of the dialectic, and even in the articulation of the moral order of the universe. In order to do this, some elements of ancient mathematics need to be rehearsed. The reason for this is twofold. First, our understanding of the nature of counting and even our way of writing numbers (and so the way we represent them to ourselves) is different from that found in ancient Greece. Second, it might help us to see something of the innovation that Plato introduces into these elements.
