While the scientific faculty was gathering strength and leading the way to a more rational consideration of the world and natural phenomena, really advancing beyond the earlier ideas which had been almost wholly mythical, myth was still the matrix of thought, although its envelopment was partly rent asunder and was becoming transparent.  From this brief notice of the Ionic philosophy, sufficient for our purpose, let us return to the Pythagorean school, in which, although the faculty at work is essentially objective, there is a closer consideration of the analogies between thought and the world, and the ground is more often retraced, so that theory assumes a more intellectual form.

The Pythagoreans represented the origin of the world as the union of the two opposite principles of the illimitable and the limited, of the equal and the unequal.  Yet they conceive this to be a primitive union, since they formulated the supreme principle as equal—­unequal (Arist. Met. xii. 7.) They held the infinite to be the place of the one.  There was an attraction between the two principles, which was termed the act of breathing; hence the void entered into the world and separated things from each other.  Thus their conception of the world was that of a concourse of opposite principles.  They represented its limits as a unity and as the true beginning of multiplicity.  They regarded the development of the world as a process of life regulated by the primitive principles contained in the world; its breath or life depended on the breaking forth of the infinite void in Uranus, and the time which is termed the interval of all nature penetrates at once and with the breath into the world.  All therefore emanates from one, and all is at the same time governed by one supreme power.  Number is everything, and is the essence of things, but the triad includes all number, since it contains the beginning, middle, and end.  Everything is derived from the primitive one and from the principal number; and since this number in breathing its vital evolution into the void is divided into many units, everything is derived from the multiplicity of these units or numbers.

Since, by his idea of the source of universal order, Pythagoras partly accepted the theocosmic monad as the final and necessary root of all life, and of all that is knowable, he could not fail to see the convertibility of the unit into the Being.  But if the unit must always precede the manifold, there is a first unit from which all the others proceed; if this first and eternal unit is at the same time the absolute being, it follows that number and the world have a common origin and a common essence, and that the intrinsic causes and possible combinations of number are virtually accomplished in the development of the world, and these causes and combinations are ideal forms of this development.  The monad is developed by these laws through all the generative processes of nature,