from this supreme power, the State, for even if they try to separate themselves, they unconsciously remain beneath this universal. The speculative meaning of the practical philosophy of Pythagoras thus is, that in this signification, the individual consciousness shall obtain a moral reality in the brotherhood. But as number is a middle thing between the sensuous and Notion, the Pythagorean brotherhood is a middle between universal, actual morality and maintaining that in true morality the individual, as an individual, is responsible for his own behaviour; this morality ceases to be universal spirit. If we wish to see practical philosophy reappear, we shall find it; but, on the whole, we shall not see it become really speculative until very recent times. We may satisfy ourselves with this as giving us an idea of the Pythagorean system. I will, however, shortly give the principal points of the criticism which Aristotle (Met. I. 8) makes upon the Pythagorean number-form. He says justly, in the first place: “If only the limited and the unlimited, the even and odd are made fundamental ideas, the Pythagoreans do not explain how movement arises, and how, without movement and change there can be coming into being and passing away, or the conditions and activities of heavenly objects.” This defect is significant; arithmetical numbers are dry forms and barren principles in which life and movement are deficient. Aristotle says secondly, “From number no other corporeal determinations, such as weight and lightness, are conceivable;” or number thus cannot pass into what is concrete. “They say that there is no number outside of those in the heavenly spheres.” For instance, a heavenly sphere and a virtue, or a natural manifestation in the earth, are determined as one and the same number. Each of the first numbers may be exhibited in each thing or quality; but in so far as number is made to express a further determination, this quite abstract, quantitative difference becomes altogether formal; it is as if the plant were five because it has five stamens. This is just as superficial as are determination through elements or through particular portions of the globe; it is a method as formal as that by which men now try to apply the categories of electricity, magnetism, galvanism, compression and expansion, of manly and of womanly, to everything. It is a purely empty system of determination where reality should be dealt with.