If Eleatic thought stands over against Pythagorean thought as what is valid or grounded against what is ungrounded or invalid, we are embarked upon dialectic, or the debate in which thought is countered by thought.
As we have already intimated, Gnosticism had such a power 1 For the disciples of Valentinus, especially Marcus, after whom was named a separate sect, the Marcosians, with their Pythagorean theories of numbers and their strong tincture of the mystical, magic, and sacramental, see Valentinus And Valentinians.
The Pythagorean school of philosophers adopted the theory of a spherical earth, but from metaphysical rather than scientific reasons; their convincing argument was that a sphere being the most perfect solid figure was the only one worthy to circumscribe the dwellingplace of man.
Since the Pythagorean school of philosophy upheld the spherical as against the disk-shaped world, some of the ancient geographers, including Eratosthenes and Strabo, looked upon the hydrosphere as forming two belts at right angles to each other, one belt of ocean following the equator, the other surrounding the earth from pole to pole as in the terra quadrifida of Macrobius; while others, including Aristotle and Ptolemy, looked upon the inhabited land, or oikumene, as occupying the greater part of the earth's surface, so that the Indian Ocean was an enclosed sea and India (i.e.
He entered deeply into the distinctively Pythagorean number theory, particularly dwelling on the properties inherent in the decad - the sum of the first four numbers, consequently the fourth triangular number, the tetractys (see Vit.
He was also influenced by the Epicurean and the Academic and the revived Pythagorean schools.
He has, indeed, a system, but it is a singular medley of doctrines borrowed, not only from Saint-Simonian, but from Pythagorean and Buddhistic sources.
The Pythagorean theory of numbers, Neoplatonic ideas of emanation, the Logos, the personified Wisdom, Gnosticism - these and many other features combine to show the antiquity of tendencies which, clad in other shapes, are already found in the old pre-Christian Oriental religions.
Even these had been preceded by earlier Pythagorean constructions envisaging the divine life in divine triangles.
MUSIC OF THE SPHERES, in Pythagorean philosophy, the harmony produced by the heavenly bodies in their orbits, inaudible to human ears.