Philolaus: Philosophy and Science in Classical Greece

Pythagoras and Philolaus experimenting with musical pipes. From Theorica musicae by Franchino Gaffurio, 1492 (1480?). / Image via Wikimedia Commons

Philolaus is said to have claimed that mathematical reason has a certain affinity with the nature of the universe,

By Daniel Costa


Philolaus of Croton (c. 470 – c. 385 BCE) was an ancient Greek philosopher from Magna Graecia, in modern-day southern Italy. He shared the Pythagoreans’ interest in music, numbers and the soul, which shone through his output. He valued fire, heat and harmony, which he considered substantial, and is best known for introducing a cosmological model that moved the earth away from the centre of the universe, placing fire there instead.

The Pythagoreans

A contemporary of the 5th century BCE thinkers Diogenes of Apollonia and Socrates, Philolaus is considered a prominent figure of the Pythagorean movement, which emerged in Croton and included Pythagoras himself as well as Archytas. One of the central tenets of the school of thought was metempsychosis, also known as transmigration, whereby a soul leaves a body at death to be born in another one. Similarly, they valued the learning and recitation of the so-called akusmata, codified sets of questions and answers whose nature was cosmological, moral, arithmetical or religious. In doing so, the Pythagoreans’ approach to cosmology attached great importance to numbers and musical harmony. A schism took place during the fifth century BCE, prompting the emergence of two different groups: the akousmatikoi, who focused on religious and ritual issues, and the mathematikoi, who delved into the mathematical and technical aspects of the movement.

Born in Croton, Philolaus moved to mainland Greece when the Pythagorean school was destroyed and its followers dispersed, and taught at Thebes. His thought suggests he belonged to the mathematikoi:

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)

In this context, Philolaus is said to have claimed that mathematical reason has a certain affinity with the nature of the universe as it reflects intelligible truth. Geometry stands out for its ability to elevate and purify the mind, releasing it from the perils of perception.

The Limited and Unlimited

Bust of Pythagoras of Samos, display in the Capitoline Museums, Rome. / Photo by Skies, Wikimedia Commons

The first self-proclaimed Pythagorean to write a treatise, Philolaus penned On Nature, whose title echoes the naturalistic stance of the pre-Socratic philosophers’ output. Like his peers, he believed in the interaction between nature and world-order. In his view, this consisted of the combination of unlimited and limited things:

the nature in the cosmos was fitted together from unlimited and limiters, both the cosmos as a whole and everything in it. (DK44 B1).

This was based on the premise that what exists cannot be exclusively limited or unlimited and that if all things were the latter there would be no knowledge. He thus concludes that there are three classes of things which exist: those that come from the limiters, those that stem from the unlimited, and those that emerge from both the limiters and the unlimited. The nature of limiters and the unlimited has prompted different interpretations, the former often being associated with numbers or abstract geometrical shapes and the latter with unformed matter. The scholar J. Warren suggests that the unlimited are essentially continua such as heat or mass and the limiters are different points along them, generating a specific temperature or shape.

Philolaus went further by claiming that these subsisting principles that prompted the things that exist were neither similar nor of the same kind. Based on the premise that similar things do not need harmony to hold them together, he concluded that supervening harmony was needed to allow for the coexistence of different things. In line with the Pythagoreans’ approach to cosmology, Philolaus mentioned the fourth and the fifth musical intervals as the magnitude of that harmony, asserting that the One at the centre of the sphere was the first thing to have been harmonized. In essence, Philolaus introduced a dualistic ontological account that allows for the variability that permeates the world yet firmly rooted in the necessary interaction being limiters and the unlimited by means of harmony.

The Central Fire

Photo courtesy of Pexels, Pixabay, Creative Commons

While many of his peers thought the earth was at rest, Philolaus postulated that it ‘danced’ in a circle with nine other divine bodies, namely the moon, the planets, the sun, the sky and the counterearth. They revolved around a central fire, the hearth of the universe or bond of nature, in what has become known as the Pyrocentric model. Olympus was the highest and purest part, while the world beneath it contained the five planets (excluding the earth) as well as the sun and the moon. The sky, located between the moon and the earth beneath it, fostered change and generation. Wisdom was responsible for the order and perfection of heavenly bodies and virtue for the disorderliness and imperfection thereof.

Pyrocentric Model as presented by the ancient Greek philosopher Philolaus of Croton (c. 470 – c. 385 BCE). / Image courtesy of WHE, Creative Commons

The model has been praised for anticipating the heliocentric theory but also condemned for being based on a priori assertions. The counterearth, for instance, has been said to be devoid of a role, yet the scholar D. Graham suggests it can explain lunar eclipses on the grounds that their occurring at different times of the day cannot be caused by the earth blocking the sun’s light.

Body and Soul

Philolaus also made a considerable contribution to the field of biology. He contended that rational animals were governed by four principles, namely the brain, the heart, the navel and the genitals. In On Nature, he wrote:

Head of thought, heart of soul and perception, navel of rooting and first growth, genitals of depositing of seed and generation. Brain contains the principle of man, heart that of animal, navel that of plant, genitals that of all together (for all shoot and sprout from seed) (B13)

He considered heat to be the source of human bodies, who have no share in coldness. He posited that semen, which constitutes animals, is hot like the womb, the place where it is deposited, suggesting that the body needs external air, which is cold, in order to survive. As a result, after birth, the animal breathes in this air and is cooled by it. With regard to the nature of diseases, he asserted that they stem from bile, blood and phlegm. Heat plays a strong role here too since, unlike many contemporaries, he contended that phlegm is by nature hot owing to the etymology of the word phelegein, ‘to burn’. In his eyes, disease is triggered by excesses of heat, food, cooling or deficiencies. Finally, he contended that certain thoughts, reasons and feelings go beyond humans power and their ability to master them, owing to their inherent strength. He echoed thinkers who testified that the physical body is a mere limitation to the metaphysical soul.


Originally published by the World History Encyclopedia, 04.28.2021, under a Creative Commons: Attribution-NonCommercial-ShareAlike 3.0 Unported license.



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