5. Pythagoras. -- Legend is practically our sole informant on the life of PYTHAGORAS OF SAMOS. Neither the date of his birth (c. 580-570 B.C.) nor of his death (end of sixth century) can be exactly fixed, nor that of his emigration into Italy. His numerous voyages, and notably his sojourn in Egypt, are not proven.

The Pythagorean doctrine holds a middle course between the teaching of the Ionians and that of the Eleatics. It is at once an explanation of the unity and of the order of the universe. Everything may be reduced to numbers. The regularity manifested in the harmonious movements of the spheres is also found in the phenomena of the terrestrial world and in those of the moral life, so that the manifold relations which exist between beings and their activities may be expressed numerically. But, furthermore, number is not only the principle of order but also the principle of reality. Number is the very substance of things: whether number is to be here understood in a strict, abstract sense, or to be identified with the sense-intuition of the material figure geometrically numbered or measured.

Number is the origin of things. But how? Since the combination of units which constitute a whole number can form odd or even series, Pythagoras held that all number is a mixture of odd and even, or of indeterminate and determinate. The conflict of odd and even explains the presence of opposing properties in one and the same subject (e.g., repose and movement, right and left, good and bad, etc.). If these conflicts do not break up the unity of being and the harmony of the universe, it is because the odd and the even are united by a third principle of number. viz., harmony. Every being is a determinate harmony, that is to say, a fixed and definite compound of odd and even. From the combinations of numbers the various elements of the world arise, -- by an arbitrary plan of determination.

As for the psychological and moral theories of Pythagoras on the soul, the future state, the union of the soul with the body, etc., they belong rather to the mysteries and religious dogmas of Pythagorism. Aristotle has clearly shown that Pythagorism as a scientific system is confined to Cosmology.

Pythagoras founded a School. And his disciples were not merely philosophers and men of science, but moralists and mystics, initiated into secret rites and ceremonies. Identified with an aristocratic doctrine, the Pythagoreans were, after the death of their master, subjected to violent persecutions. In Italy their schools were broken up; but their doctrines survived in other places, notably in Thebes and Tarentum where PHILOLAUS and KLEINIAS collected together all the old Pythagorean traditions. In the fourth century Pythagorism disappeared as a School.

Pythagorism, moreover, coloured the views of several other philosophical speculators who opened their systems to heterogeneous elements. Finally, isolated Pythagorean theories, like that of number, have found their way through the centuries, passing from school to school even down to modern times.