Kitap 14
7
Nor is it in any way defined in which sense numbers are the causes of substances and of Being; whether as bounds,The theories criticized from this point onwards to Aristot. Met. 14.6.11 are primarily Pythagorean. See Introduction. e.g. as points are the bounds of spatial magnitudes,e.g. the line by 2 points, the triangle (the simplest plane figure) by 3, the tetrahedron (the simplest solid figure) by 4. and as EurytusDisciple of Philolaus; he flourished in the early fourth century B.C. determined which number belongs to which thing—e.g. this number to man, and this to horse—by using pebbles to copy the shape of natural objects, like those who arrange numbers in the form of geometrical figures, the triangle and the square.cf. Burnet, E.G.P. sect. 47.
8
Or is it because harmony is a ratio of numbers, and so too is man and everything else? But in what sense are attributes—white, and sweet, and hot—numbers?This is an objection to the view that numbers are causes as bounds. And clearly numbers are not the essence of things, nor are they causes of the form; for the ratioOr formula. is the essence, and numberIn the sense of a number of material particles. is matter.
9
E.g. the essence of flesh or bone is number only in the sense that it is three parts of fire and two of earth.Cf. Empedocles Fr. 96 (Diels). And the number, whatever it is, is always a number of something; of particles of fire or earth, or of units. But the essence is the proportion of one quantity to another in the mixture; i.e. no longer a number, but a ratio of the mixture of numbers, either of corporeal particles or of any other kind. Thus number is not an efficient cause—neither number in general, nor that which consists of abstract units—nor is it the matter, nor the formula or form of things. Nor again is it a final cause.
