While, in a sense, then, even the indefinite has number, inasmuch as it is capable of having number or order imposed upon it (and only in so far as it has this imposed upon it, does it become knowable or intelligible), yet, as a positive factor, Number belongs only to the first class; as such it is the source of all knowledge and of all good. In reality the Pythagoreans had not got any further by this representation of nature than was reached, for example, by Anaximander, and still more definitely by Heraclitus, when they posited an Indefinite or Infinite principle in nature which by the clash of innate antagonisms developed into a knowable universe (see above, pp. 12, 16). But one can easily imagine that once the idea of Number became associated with that of the knowable in things, a wide field of detailed development and experiment, so to speak, in the arcana of nature, seemed to be opened. Every arithmetical or geometrical theorem became in this view another window giving light into the secret heart of things. Number became a kind of god, a revealer; and the philosophy of number a kind of religion or mystery. And this is why the {26} second grade of disciples were called Mathematicians; mathematics was the essential preparation for and initiation into philosophy.
Whether that which truly exists was actually identical with Number or Numbers, or whether it was something different from Number, but had a certain relation to Number; whether if there were such a relation, this was merely a relation of analogy or of conformability, or whether Number were something actually embodied in that which truly exists—these were speculative questions which were variously answered by various teachers, and which probably interested the later more than the earlier leaders of the school.
[56]
A further question arose: Assuming that ultimately the elements of knowable existence are but two, the One or Definite, and the Manifold or Indefinite, it was argued by some that there must be some third or higher principle governing the relations of these; there must be some law or harmony which shall render their intelligible union [57] possible. This principle of union was God, ever-living, ever One, eternal, immovable, self-identical. [58] This was the supreme reality, the Odd-Even or Many in One, One in Many, in whom was gathered up, as in an eternal harmony, all the contrarieties of lower [61] existence. Through the interchange and intergrowth of these contrarieties God realises Himself; the {27} universe in its evolution is the self-picturing of God. [62] God is diffused as the seminal principle throughout [68] the universe; He is the Soul of the world, and the world itself is God in process. The world, therefore, is in a sense a living creature. At its heart and circumference are purest fire; between these circle the sun, the moon, and the five planets, whose ordered movements, as of seven chords, produce an eternal music, the 'Music of the Spheres.' Earth, too, like the planets, is a celestial body, moving like them around the central fire.
[71]
By analogy with this conception of the universe as the realisation of God, so also the body, whether [72] of man or of any creature, is the realisation for the time being of a soul. Without the body and the life of the body, that soul were a blind and fleeting ghost. Of such unrealised souls there are many in various degrees and states; the whole air indeed is full of spirits, who are the causes of dreams and omens.
[73]
Thus the change and flux that are visible in all else are visible also in the relations of soul and body. Multitudes of fleeting ghosts or spirits are continually seeking realisation through union with bodies, passing at birth into this one and that, and at death issuing forth again into the void. Like wax which takes now one impression now another, yet remains in itself ever the same, so souls vary in the outward {28} [74] form that envelops and realises them. In this bodily life, the Pythagoreans are elsewhere described as saying, we are as it were in bonds or in a prison, whence we may not justly go forth till the Lord calls us. This idea Cicero mistranslated with a truly Roman fitness: according to him they taught that in this life we are as sentinels at our post, who may not quit it till our Commander orders.
On the one hand, therefore, the union of soul with body was necessary for the realisation of the former ((Greek) soma, body, being as it were (Greek) sema, expression), even as the reality of God was not in the Odd or Eternal Unity, but in the Odd-Even, the Unity in Multiplicity. On the other hand this union implied a certain loss or degradation. In other words, in so far as the soul became realised it also became corporealised, subject to the influence of passion and [75] change. In a sense therefore the soul as realised was double; in itself it partook of the eternal reason, as associated with body it belonged to the realm of unreason.
This disruption of the soul into two the Pythagoreans naturally developed in time into a threefold division, pure thought, perception, and desire; or even more nearly approaching the Platonic division (see below, p. 169), they divided it into reason, passion, and desire. But the later developments were largely influenced by Platonic and other doctrines, and need not be further followed here.