for what evidently united and distinguished them was their community of principles and life—whether anything was good for the commonwealth or not, was by them publicly and openly discussed. The Greeks are above having particular clothing, maintaining special customs of washing, rising, practising music, and distinguishing between pure and impure foods. This, they say, is partly the affair of the particular individual and of his personal freedom, and has no common end in view, and partly it is a general custom and usage for everybody alike. What is most important to us is the Pythagorean philosophy—not the philosophy of Pythagoras so much as that of the Pythagoreans, as Aristotle and Sextus express it. The two must certainly be distinguished, and from comparing what is given out as Pythagorean doctrine, many anomalies and discrepancies become evident, as we shall see. Plato bears the blame of having destroyed Pythagorean philosophy through absorbing what is Pythagorean in it into his own. But the Pythagorean philosophy itself developed to a point which left it quite other than what at first it was. We hear of many followers of Pythagoras in history who have arrived at this or that conclusion, such as Alcmæon and Philolaus; and we see in many cases the simple undeveloped form contrasted with the further stages of development in which thought comes forth in definiteness and power. We need, however, go no further into the historical side of the distinction, for we can only consider the Pythagorean philosophy generally; similarly we must separate what is known to belong to the Neo-Platonists and Neo-Pythagoreans, and for this end we have sources to draw from which are earlier than this period, namely the express statements found in Aristotle and Sextus. The Pythagorean philosophy forms the transition from realistic to intellectual philosophy. The Ionic school said that essence or principle is a definite material. The next conclusion is (_α_) that the absolute is not grasped in natural form, but as a thought determination. (_β_) Then it follows that determinations must be posited while the beginning was altogether undetermined. The Pythagorean philosophy has done both.