What's in a circle?

Spinoza, Leibniz, Marlowe, Shakespeare, Keats

pp. 85-96

in: Emily Rolfe Grosholz, Great circles, Berlin, Springer, 2018

Abstract

Both mathematics and poetry search for the conditions of intelligibility—the conditions of order, organization, meaningfulness—of the world and human life. Plato's Socrates proposed, in the Republic, Book VI, that the things of mathematics and the things in the heavens inhabit the realm of Being, of eternity and truth, whereas we human beings find ourselves down here in the world, in the realm of Becoming, of generation and corruption, of opinion. As I noted earlier, we owe to Aristotle, and to Euclid, the useful notion of a middle term; they are both indebted to Plato's analogy of the Divided Line in the Republic, Book VI, 509d-511e. The analogy is stated in terms of a proportion, the assertion of a similitude (not an equality) between two ratios: the ratio A:B is similar to the ratio C:D and also to the ratio A + B:C + D.