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Philolaus of Croton (c. 470–385 BCE)

(c. 470385 BCE)

Philolaus of Croton (a Greek city in southern Italy) was a philosopher/scientist in the Pythagorean tradition. He was a contemporary of Socrates, being born c. 470 BCE, twenty years after Pythagoras died, and living until c. 385. On his first trip to Italy, Plato may have met an aged Philolaus; he mentions him as a teacher of the Thebans Simmias and Cebes in the Phaedo. A large body of pseudo-Pythagorean writings appeared in the first century BCE, and a number of these were forged in Philolaus's name, because he was one of the three most famous early Pythagoreans (along with Pythagoras himself and Archytas). Some fifteen fragments and a number of testimonia survive from these forged works. Philolaus, in fact, wrote one book, On Nature, which was probably the first book in the Pythagorean tradition (Pythagoras wrote nothing). Approximately eleven genuine fragments of that book have survived along with a number of testimonia. Aristotle discusses Pythagorean philosophy extensively but does not assign this philosophy to Pythagoras himself but rather to the "people called Pythagoreans," whom he treats as slightly older contemporaries of the atomists. This dating fits Philolaus exactly, and the agreement between the philosophy described by Aristotle and the fragments of Philolaus's book shows that Philolaus was the primary source for Aristotle's account.

Philolaus argued that the nature of the cosmos as a whole and of all things in it was to be explained in terms of two types of elements, unlimiteds and limiters. The unlimiteds include the material elements favored by his predecessors in the pre-Socratic tradition, such as earth, air, fire, and water but also continua such as space and time. Philolaus is emphatic, however, that such principles are not adequate to explain the cosmos because (1) limits, such as shapes, are also part of the cosmos humans can observe, and (2) such limiting features cannot have arisen from what is unlimited. Philolaus's cosmogony illustrates the role of these principles; the first thing to emerge was the central fire, which is a combination of the unlimited, fire, and the limiter, center. This central fire then draws in other unlimiteds such as time, void, and breath, which will be combined with limits to produce the cosmos known to humans.

Philolaus introduces harmony as an essential third principle, which specifies the way in which limiters and unlimiteds are combined. The central example is the musical scale in which the unlimited continuum of sound is limited by specific notes; harmony insures that these notes do not have a haphazard order, however, but are "fitted together" in accordance with whole number ratios. This idea depends on the earlier Greek discovery that, if a person plucks two strings, one of which is twice the length of the other, we will hear the interval of the octave between the two sounds, so that the octave corresponds to the ratio 2: 1. Similarly, the fifth will correspond to the ratio 3: 2 and the fourth to the ratio 4: 3. Philolaus appears to regard the cosmos as a whole as structured according to the ratios that determine diatonic scale. Plato may be influenced by Philolaus in using this same scale to construct the world soul in the Timaeus.

By specifying the "formula" according to which limiters and unlimiteds combine, numbers also define the essence of a given thing and thus play an important epistemological role for Philolaus: "And indeed all things that are known have number. For it is not possible that anything whatsoever be understood or known without this" (Fr. 4). On the one hand, Aristotle is clearly right that numbers are not separate from things in this system, as they were later in Plato; Philolaus and his successor Archytas were interested in the numbers of things, not in numbers separated from things. On the other hand, Aristotle's suggestion that the Pythagoreans thought that things just were numbers or that they were made of numbers is not supported by the fragments of Philolaus, where it is clear that things are made of limiters and unlimiteds. According to Philolaus, our senses reveal a world composed of unlimiteds and limiters (e.g., stuffs and shapes), but on further examination the phenomena point to the numerical ratios that govern them. It is doubtful that Philolaus had explicitly addressed the metaphysical status of these ratios. Aristotle may have thought that if numbers reveal the essence of things, then things are, in an important sense, numbers; but this is Aristotelian interpretation. Philolaus prefers to say that things are composed of limiters and unlimiteds and known through the numerical ratios in accordance with which the limiters and unlimiteds are combined.

Philolaus is the first person to move the earth from the center of the universe and make it a planet, and Copernicus saw Philolaus as an important predecessor. The earth does not orbit around the sun in Philolaus's system, however; the fixed stars, five planets, sun, moon, earth, and an enigmatic counter-earth all orbit around the central fire. The system may have some origins in a religious cosmology in which the central fire is identified with Tartarus, a region under the earth where the guilty are punished in Greek mythology. Aristotle suggests that the counter-earth was introduced to satisfy the a priori requirement that there be ten heavenly bodies around the central fire, because the Pythagoreans regarded ten as the perfect number. On the other hand, there is clear evidence that Philolaus intended the system to explain astronomical phenomena as well as satisfying a priori or religious requirements. The system can explain basic phenomena and is the first to include the five known planets in correct order, although it cannot account for such things as the apparent retrograde motion of planets. Philolaus clearly responded to objections to his system, which were based on the phenomena, arguing that the motion of the earth around the central fire did not produce a parallax effect, because the distance from the earth to the central fire was small in comparison to the distance between the earth and the planets. Similarly human beings never see the central fire or counter-earth, because the side of the earth on which they live is always turned away from the center, the earth rotating once on its axis during each orbit of the central-fire.

Philolaus argued that in each area of inquiry it was necessary to begin by identifying the minimum number of principles required to explain the phenomena. Limiters, unlimiteds, and harmony are the basic metaphysical principles; bile, blood, and phlegm explain disease; intellect, sensation, nutrition/growth, and generation are the basic psychic faculties. Philolaus drew an analogy between the birth of the cosmos and the birth of a human being, arguing that the embryo is initially hot and draws in cooling breath immediately upon birth, just as the cosmos begins with the central fire drawing in breath from the unlimited. It may be that he regarded the soul as a harmony of physical opposites, a view that Plato, perhaps in criticism of Philolaus, shows in the Phaedo to be inconsistent with a belief in an immortal soul.

In the Philebus, "the method of the men before our time," which Plato adapts to address problems in his own metaphysics, is clearly the metaphysical system of Philolaus, which thus had a significant impact on Plato's later metaphysics. Some have argued that Philolaus's metaphysics must go back to Pythagoras, but Aristotle clearly dates it to the time of Philolaus, and the system itselfwith its emphasis on the necessity of limiters in addition to unlimiteds makes most sense, if it arose after Pythagorasat a time when Parmenides had championed the role of limit in explaining reality.

See also Archytas of Tarentum; Pythagoras and Pythagoreanism.


texts and commentary

Huffman, C. A. Philolaus of Croton: Pythagorean and Presocratic. Cambridge, U.K.: Cambridge University Press, 1993.


Barnes, J. The Presocratic Philosophers. London: Routledge, 1982.

Burkert, W. Lore and Science in Ancient Pythagoreanism. Translated by E. Minar. Cambridge, MA: Harvard University Press, 1972.

Kahn, Charles H. Pythagoras and the Pythagoreans. Indianapolis: Hackett, 2001.

Kingsley, Peter. Ancient Philosophy, Mystery and Magic. Oxford: Clarendon, 1995.

Meinwald, Constance Chu. "Plato's Pythagoreanism." Ancient Philosophy 22 (1) (2002): 87101.

Schibli, H. S. "On 'The One' in Philolaus, Fragment 7." The Classical Quarterly, n.s., 46 (1) (1996): 114130.

Sedley, David. "The Dramatis Personae of Plato's Phaedo." In Philosophical Dialogues: Plato, Hume, Wittgenstein, edited by T. J. Smiley, 326. Oxford: Oxford University Press, 1995.

Carl A. Huffman (2005)

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