Pythagoras is said to have been the first who assumed the title of φιλόσοφος; but there is great uncertainty as to the most material of his philosophical and religious opinions. It is believed that he wrote nothing himself, and that the earliest Pythagorean treatises were the work of Philolaus, a contemporary of Socrates. It appears, however, that he undertook to solve by reference to one single primary principle the problem of the origin and constitution of the universe. His predilection for mathematics led him to trace the origin of all things to _number_; for “in _numbers_ he thought that they perceived many analogies of things that exist and are produced, more than in fire, earth, or water: as, for instance, they thought that a certain condition of numbers was justice; another, soul and intellect, ... And moreover, seeing the conditions and ratios of what pertains to harmony to consist in numbers, since other things seemed in their entire nature to be formed in the likeness of numbers, and in all nature numbers are the first, they supposed the elements of numbers to be the elements of all things.” (Arist. Met. i. 5.) Music and harmony too, played almost as important a part in the Pythagorean system as mathematics, or numbers. His idea appears to be, that order or harmony of relation is the regulating principle of the whole universe. He drew out a list of ten pairs of antagonistic elements, and in the octave and its different harmonic relations, he believed that he found the ground of the connexion between them. In his system of the universe _fire_ was the important element, occupying both the centre and the remotest point of it; and being the vivifying principle of the whole. Round the central fire the heavenly bodies he believed to move in a regular circle; furthest off were the fixed stars; and then, in order, the planets, the moon, the sun, the earth, and what he called ἀντίχθων, a sort of other half of the earth, which was a distinct body from it, but moving parallel to it. The most distant region he called Olympus; the space between the fixed stars and the moon he called κόσμος; the space between the moon and the earth οὐρανός. He, or at least his disciples, taught that the earth revolved on its axis, (though Philolaus taught that its revolutions were not round its axis but round the central fire). The universe itself they considered as a large sphere, and the intervals between the heavenly bodies they thought were determined according to the laws and relations of musical harmony. And from this theory arose the doctrine of the Music of the Spheres; as the heavenly bodies in their motion occasioned a sort of sound depending on their distances and velocities; and as these were determined by the laws of harmonic intervals, the sounds, or notes, formed a regular musical scale.