Philolaus was the first Pythagorean philosopher to have written a book, and a contemporary of Socrates. He interpreted the world as a composition of limiters and unlimiteds; this composition is configured in harmony. His theses had an impact on Plato's late philosophy.

Life and Work

Little is known about Philolaus' life. He came from Croton, Alkmaeon's land, in Southern Italy, and also lived in Taranto and Thebes. His philosophical peak is placed in the end of the 5th c., and this allows the assumption that he was of the same generation as Socrates. We know that he was the first Pythagorean to have written a book: On Nature. This book was the only one Philolaus composed - a practise customary among the Presocratic philosophers. Ancient tradition echoed the derogatory fame that Plato took the cue for Timaeus from Philolaus book, which had come to his possesion during his first expedition in Sicily.

The authenticity of the about 25 extant fragments from Philoalus' book had been impugned in the past. Modern scholars, however, concede that approximately 10 of them should be considered genuine.

Principles and Cosmos

Diogenes quotes the first phrase of Philolaus' book: "Nature in the ordered universe was composed of unlimited and limiting elements, and so was the whole universe and all that is therein" (Lives 8.85; Philolaus, frag. 1). Limit and unlimitedness figure here, for the first time, as principles of the beings. And, since the Pythagoreans deemed numbers to be the principles, it is plausible that Philolaus' "unlimited and limiting elements" hinged on mathematics (for example, limiters could indicate shapes or specific numbers). At any rate, Philoalus declares that "indeed all the things that are known have number. For it is not possible that anything whatsoever be understood or known without this" (Philolaus frag. 4). This fitting together between the unlimiteds and the limiters confers harmony upon the universe. Philolaus argues for the necessity of his central notion of harmony by claiming that divergent things, such as the unlimiteds and the limiters, "would have been impossible to be ordered, if a harmony had not come upon them, in whatever way it came to be" (frag. 6).

What is discernible in Philolaus' fragments is the reconciliation between the Pythagorean philosophy and the physiocracy of the Presocratics. The new element is the connection of the cosmic order with numbers and harmony. There are indications that Philolaus developed some kind of cosmogony, according to which the first outcome of the combination between limit and unlimitedness appears "in the center of the sphere, [and] is called the hearth" (frag. 7). It is reasonable to compare Philoalus' Hearth with the Fire situated in the centre of the universe according to the cosmology of the Pythagoreans.

Philolaus' Astronomy

The astronomical system, that Aristotle credited to the Pythagoreans, involved the Earth, the planets and the immobile stellar sphere, which rotated around the central Fire. However, a celestial system of 9 orbiting bodies could not suffice the Pythagoreans. Their demand to instil the number 10 (the "tetractys") into the world led them to assume the existence of a second Earth, the counter-Earth, which also revolved around the Fire. Scholars agree that it was Philolaus who conjured up this invention. This was, to be sure, a bold theory, for it ascribed motion to the Earth; for all that, it could not account even for the most blatant planetary phenomena. It does not seem that Philolaus was intent on that; rather, he aimed at finding a way to confer harmony unto the heavens. With the introduction of 10, which is the sum of the first four numbers (1+2+3+4), the universe acquired a harmonic musical structure: the ratios 1/2, 2/3, and 3/4, the foundation of the Pythagorean theory of music, found their way into the heavens.

A similar understanding of the universe is also hinted by the famous Pythagorean doctrine of the "harmony of the spheres"; that is, a heavenly music produced by the motion of the planets and the stars. This music is audible only to the insiders. This fascinating and durable theory could have also been worked out by Philolaus himself.

Phiolaus and Plato Plato mentions Philoalus in his dialogue Phaedo at the point where Socrates asks his partners to discuss Philolaus' theory that the soul is a kind of harmony between the constituents of the body - this being the case, it is inferred that the soul does not survive the demise of the body. Since the concept of harmony comes into play, we must assume that Philolaus had in mind "limiters" and "unlimiteds" that fit together in the soul. Even tough we do not know what these "limiters" and "unlimiteds" were, we should not be much in error to presume that they must have been numbers; in which case, it would be hard to attribute them to the body. On top of that, it would be rather improbable for a Pythagorean to disavow the immortality of the soul.

At any rate, the influence of Philolaus on mature Plato does not require an explicit reference to him. It is most clearly discerned in Philebus, where Plato construes the cosmic phenomena as harmonic mixtures of the Limit and the Unlimited. Again, the world in the Timaeus is created by a good Demiurge who employs numbers in shaping the pre-cosmic indefinite (i.e., "unlimited") "space". Finally, in his so-called "unwritten doctrines", Plato identifies the Forms with the numbers because he thinks that the number yields the organic relation between the one and the many, the unity and the multitude, the limit and the unlimited.

Author: Vassilis Kalfas
  • Hicks, R.D. Diogenes Laertius, Lives of Eminent Philosophers. Cambridge, 1972.
  • Huffman, C.A. Philolaus of Croton: Pythagorean and Presocratic. Καίμπριτζ, 1993.
  • Huffman, C.A. "Philolaus." Zalta, E.N ed. Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/philolaus/. .
  • Kirk, G.S, Raven, J.E., Schofield, M, The Presocratic Philosophers. Cambridge, 1983.
  • Timpanaro Cardini, M. ed. Pitagorici, Testimonianze e frammenti (τόμ. 2, σ. 262–385). Φλωρεντία, 1958–64.
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