I was off to study again today. I finished off Chapter 6 of the Physics, for now, without much additional enlightenment.
I can understand the need for contraries. I see a white thing; and it becomes a black thing. It was white, and now it’s black. These are contraries. To change means to be different, to be now A and then not-A. So far, so good. And I can see why you need something underlying A and not-A that remains through the change. (At least, I think I do; I might be fooling myself.)
But I don’t really understand the relationship between contrarieties and genera, or why there can only be a single primary contrariety in a genus, or how one pair of contraries can necessarily reduce to another pair, or how all things that are can be generated from one kind of “stuff” and one pair of contraries. That seems too simple.
Can anyone help me out with this?
In addition, I read Copleston’s chapter on the Pythagoreans, who are interesting to me on two grounds. First, unlike the Miletians, they had the notion of an immortal soul and believed in transmigration of souls. This appears to be an innovation in Greek thought. I’ll also note that it’s not completely clear just what they thought the soul was, only that it was what gave the person identity and that it was more important than the body. Second, they described the universe in terms of Number and Geometry. They attached mystical significance to particular numbers; but they seemed to be inspired in this by the amazing ways you can use numbers to describe what is. They were especially taken with the relationship between lengths of harp strings and the tones they produce. Apparently they mostly thought of numbers geometrically; for example, the number 9 is a square number, and thus can be thought of as filling an area.