Philolaus

“Philolaus by Carl Huffman, Stanford Encyclopedia of Philosophy”

“Such... being the middle nature of the soul, Plato, with great propriety, in the Phædrus, and in his tenth book of laws, defines it to be number moving itself; which definition he received from Philolaus, and Philolaus from Pythagoras.”

“Pythagoras, in the sacred discourse, calls number "the ruler of forms and ideas." But Philolaus, "the commanding and self-begotten container of the eternal duration of mundane concerns." And {{w|Hippasus}} and all those... under the probation of the quinquennial silence... "the first exemplar of the mundane fabric, and the judiciary instrument of its artificer."”

“Plato was instructed in their nature by Philolaus his preceptor, and the disciple of Pythagoras.”

“In regard to Philolaus, we are told... that he derived geometrical determinations (the point, the line, the surface, the solid) from the first four numbers, so he derived physical qualities from five, the soul from six; reason, health, and light, from seven; love, friendship, prudence, and inventive faculty from eight. Herein (apart from the number schematism) is contained the thought that things represent a graduated scale of increasing perfection; but we hear nothing of any attempt to prove this in detail, or to seek out the characteristics proper to each particular region.”

“The importance of the decuple system in relation to the Pythagoreans is much greater. For as they considered numbers over ten to be only the repetition of the first ten numbers, all numbers and all powers of numbers appeared to them to be comprehended in the decad, which is therefore called by Philolaus, great all-powerful and all-producing, the beginning and the guide of the divine and heavenly, as of the terrestrial life.”

“Philolaus, in a fragment preserved by {{w|Stobaeus}} (Eclog. Phys. p. 51), says, "that there is a fire in the middle at the centre, which is the Vesta of the universe, the house of Jupiter, the mother of the Gods, and the basis, coherence, and measure of nature." Hence... they are greatly mistaken who suppose the Pythagoreans meant the Sun by the fire at the centre...”

“Philolaus divided the world into three parts—viz. Olympus, which holds within itself the purity of the elements, i. e. probably the central fire and the fire outwardly embracing the world; Kosmus, or the world in a limited sense, i. e. the perfectly ordered world, which comprises all mundane bodies except the earth; and Uranus, i. e. the part of the universe which belongs to the terrestrial sphere.”

“According to the Pythagorean Philolaus, "the Dekad, the full and perfect number, was of supreme and universal efficacy as the guide and principle of life, both to the Kosmos and to man. The nature of number was imperative and lawgiving, affording the only solution of all that was perplexing or unknown; without number, all would be indeterminate and unknowable."”

“In the old Pythagorean representation of the celestial system, according to Philolaus, the five planets were mentioned... among the ten deified bodies which revolve round the central fire (the focus of the universe έστἱα) "immediately beneath the region of fixed stars;" these were succeeded by the Sun, Moon, Earth, and... the anti-Earth...”

“Fragment 3. The harmony is generally the result of contraries; for it is the unity of multiplicity, and the agreement of discordances. (Nicom.Arith.2:509).”

“Fragment 2. All things, at least those we know, contain number; for it is evident that nothing whatever can either be thought or known, without number. Number has two distinct kinds: the odd, and the even, and a third, derived from a mingling of the other two kinds, the even-odd. Each of its subspecies is susceptible of many very numerous varieties; which each manifests individually.”

“Fragment 1. (Stob.21.7; Diog.#.8.85) The world's nature is a harmonious compound of infinite and finite elements; similar is the totality of the world in itself, and of all it contains.b. All beings are necessarily finite or infinite, or simultaneously finite and infinite; but they could not all be infinite only.”

“There is a fire in the middle at the centre, which is the Vesta of the universe, the house of Jupiter, the mother of the Gods, and the basis coherence and measure of nature.”

“The ancient theologists and priests... testify that the soul is united with the body as if for the sake of punishment; and so is buried in body as in a sepulchre.”

“[Number is] the commanding and self-begotten container of the eternal duration of mundane concerns.”