Philolaus

• Illustration — A page from Theorica Musicae (1492) Philolaus argued at the foundation of everything is the part played by the ideas of limit and the unlimited. One of the first declarations in the work of Philolaus was that all things in the universe result from a combination of the unlimited and the limiting; for if all things had been unlimited, nothing could have been the object of knowledge. Limiters and unlimiteds are combined in a harmony (harmonia): Philolaus, Fragment DK 44B 6a. Robert Scoon explained Philolaus' universe in 1922: Philolaus is trying to show how the ordered universe that we know came into its present condition. It arose, he says, by the action of harmony on a basic substance, which we do not know but must infer. This substance consisted of different primary elements, and harmony fitted these together in such a way that nature φύσις turns out to be an ordered world κόσμος. The book by Philolaus begins with the following: Nature (physis) in the world-order (cosmos) was fitted together out of things which are unlimited and out of things which are limiting, both the world-order as a whole and everything in it. According to Stobaeus, Philolaus did away with the ideas of fixed direction in space and developed one of the first non-geocentric views of the universe and in his new way of thinking, the universe revolved around a hypothetical astronomical object he called the Central Fire. Stobaeus, i. 22. 1d In Philolaus's system a sphere of the fixed stars, the five planets, the Sun, Moon, and Earth, all moved around a Central Fire. According to Aristotle, writing in Metaphysics, Philolaus added a tenth unseen body, he called Counter-Earth, as without it there would be only nine revolving bodies, and the Pythagorean number theory required a tenth. However, Greek scholar George Burch asserts his belief that Aristotle was lampooning Philolaus's addition. The system that Philolaus described predated the idea of spheres by hundreds of years, however. Nearly two-thousand years later, Nicolaus Copernicus would mention in De revolutionibus that Philolaus already knew about the Earth's revolution around a central fire. It has been pointed out, however, that Stobaeus betrays a tendency to confound the dogmas of the early Ionian philosophers, and in his accounts, he occasionally mixes up Platonism with Pythagoreanism.

• Illustration — Discussion of Philolaus in a book by Charles Peter Mason (1870) Pythagoras and his earliest successors do not appear to have committed any of their doctrines to writing. According to Porphyrius (Vit. Pyth. p. 40) Lysis and Archippus collected in a written form some of the principal Pythagorean doctrines, which were handed down as heirlooms in their families, under strict injunctions that they should not be made public. But amid the different and inconsistent accounts of the matter, the first publication of the Pythagorean doctrines is pretty uniformly attributed to Philolaus. In one source, Diogenes Laërtius speaks of Philolaus composing one book, but elsewhere he speaks of three books, as do Aulus Gellius and Iamblichus. It might have been one treatise divided into three books. Plato is said to have procured a copy of his book. Later, it was claimed that Plato composed much of his Timaeus based upon the book by Philolaus. One of the works of Philolaus was called On Nature. It seems to be the same work that Stobaeus calls On the World and from which he has preserved a series of passages. Other writers refer to a work entitled Bacchae, which may have been another name for the same work, and which may originate from Arignote. However, it has been mentioned that Proclus describes the Bacchae as a book for teaching theology by means of mathematics. It appears, in fact, from this, as well as from the extant fragments, that the first book of the work contained a general account of the origin and arrangement of the universe. The second book appears to have been an exposition of the nature of numbers, which in the Pythagorean theory are the essence and source of all things. He composed a work on the Pythagorean philosophy in three books, which Plato is said to have procured at the cost of 100 minae through Dion of Syracuse, who purchased it from Philolaus, who was at the time in deep poverty. Other versions of the story represent Plato as purchasing it himself from Philolaus or his relatives when in Sicily. Out of the materials which he derived from these books Plato is said to have composed his Timaeus. But in the age of Plato the leading features of the Pythagorean doctrines had long ceased to be a secret; and if Philolaus taught the Pythagorean doctrines at Thebes, he was hardly likely to feel much reluctance in publishing them; and amid the conflicting and improbable accounts preserved in the authorities above referred to, little more can be regarded as trustworthy, except that Philolaus was the first who published a book on the Pythagorean doctrines, and that Plato read and made use of it. Historians from the Stanford Encyclopedia of Philosophy, Chapter Philolaus' Book: Genuine Fragments and Testimonia, noted the following: