THE METAPHYSICS

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Among these, and even before them, those called the Pythagoreans Followers of Pythagoras, active in the 6th and 5th centuries BCE, who famously integrated mathematics, music, and mysticism. were the first to devote themselves to mathematics. They advanced this study and, having been nurtured in it, they believed that its principles were also the principles of all existing things. Since, by nature, numbers are prior to physical things, they seemed to see in numbers many similarities to things that exist and things that are coming into being—more so than they saw in fire, earth, or water. For instance, they considered a certain property of numbers to be Justice, another to be the Soul and Intellect, another to be Time, and so on for almost everything else, so to speak. Furthermore, seeing the properties and ratios of musical harmonies in numbers, and since everything else in its whole nature seemed to be modeled after numbers, and numbers were the first things in all of nature, they concluded that the elements of numbers were the elements of all beings, and that the entire heaven is harmony and number. Whatever they could demonstrate in numbers and harmonies that agreed with the properties and parts of the heavens and the arrangement of the universe, they collected and applied. If anything was missing anywhere, they supplied it, so that their entire treatise would be consistent. By this I mean, for example, since the number ten original: "denarius" is seen as perfect and encompasses the whole nature of numbers, they say that the bodies moving in the heavens are also ten. But since only nine are clearly visible, they create a tenth, the Counter-Earth original: "oppositam terram"; an invisible celestial body hypothesized by the Pythagoreans to bring the number of orbiting spheres to ten.. ¶ We have determined these matters more exquisitely elsewhere. But the reason we repeat them here is this: so that we may learn from them what they pose as principles, and how these fall into the causes we have mentioned. For these men also appear to think that number is the principle—acting as the matter for existing things, and also as their properties and states. The elements of number are the Even and the Odd; of these, one is Limited original: "finitum" and the other is Unlimited original: "infinitum". The One original: "vnum", however, comes from both of these (for it is said to be both even and odd). Number comes from the One, and numbers, as has been said, make up the whole heaven. ¶ Others among them say there are ten principles, arranged in parallel columns: the Limited, the Unlimi-

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Among these, and before them, those who are called Pythagoreans were the first to touch upon and increase these teachings. They believed that their own principles were the principles of all things. And since numbers are first by nature, it seemed to them that they saw in numbers many more similarities to those things which exist and are created than in fire, earth, and water; as if a certain state of numbers were Justice, another the Soul and Mind, another Time, and almost everything else similarly. Moreover, observing the states and ratios of musical chords in numbers—since, I say, all other things in every nature seemed to be similar to numbers, and numbers were first and prior to every nature—they believed the elements of numbers to be the elements of all things that exist, and the whole heaven to be a chord original: "concentum"; a musical harmony or symphony and a number. And whatever they could show in numbers and chords to be adapted to the states and parts of heaven and to the whole universe, they gathered and adapted; and if anything was lacking anywhere, they brought it into being so that their whole treatment might be perfect and connected. For example, since the number ten is seen to be perfect and to encompass every nature of numbers, they say that those things which are carried in heaven are indeed ten. But because only nine are manifest, they make the tenth the Counter-Earth. ¶ Truly, we have determined these things more exactly in other places. But the reason we relate these things is this: so that we may receive from these men the things they propose as principles, and see in what way they fall into the mentioned causes. And these men also seem to think that number is the principle of those things which exist—both as matter and as properties or states. The elements of number are the Even and the Odd; and of these, one is Limited, the other Unlimited. And the One itself is from both of these; for they said the One was both even and odd. Moreover, number consists of the One. And number itself is the whole heaven, as we have said. ¶ But others of the same group say there are ten principles, which they have presented in a series: the Limited and the Unlimi-