PHILOLAUS OF CROTONA

(fi second half of fifth century b.c.)

Philosophy, astronomy, medicine

Like the majority of the Pythagoreans living in the Pythagorean centers of Crotona and Metapontum in the middle of the fifth century B.C., Philolaus fled after the oubreak of the democratic rebellion, during which the meeting houses of the Pythagoreans were burned down. He first went to Thebes but later settled in Tarentum, the only remaining center of Pythagorean political activity in southern Italy. There he is said to have taught the mathematician Archytas.

The ancient tradition concerning Philolaus’ writings and doctrine is so confused and contradictory that some modern scholars have questioned his very existence, others have doubted that he ever wrote or published anything, and still others have tried to show that none of the fragments that have come down to us under his name are genuine. His existence, however, is established beyond reasonable doubt by Plato’s Phaedo (61e). That there existed at least one genuine work by Philolaus is attested by Menon, a disciple of Aristotle and a conscientious historian who lived only about a century later than Philolaus. In his history of medicine, of which fragments have been discovered on a papyrus, Menon quotes Philolaus’ medical doctrines.

According to a widespread ancient tradition, Philolaus had written, but did not publish, a comprehensive work of Pythagorean doctrine, the manuscript of which was purchased by Plato at a very high price and then copied. Thus Philolaus’ work became public. After the book had become famous, other books, not written by Philolaus, appear to have been published under his name. Since all later Pythagoreanism was strongly influenced by Plato, however, it is possible to distinguish between pre-Platonic and post-Platonic Pythagorean literature. This criterion has been used especially by W. Burkert to separate the probably genuine from the spurious fragments of Philolaus’ work.

According to this criterion, the fragments that can be considered genuine contain many rather abstruse speculations concerning the relation between certain numbers and certain gods of traditional Greek mythology, as well as speculations about numbers, places, and things that were more noble or more deserving of honor (τμώτερα) than others. The fragments also reveal a tendency to combine elements of various doctrines that were prevalent in the second half of the fifth century–although not all were specifically Pythagorean—into a rather muddled whole. This approach is hardly “scientific,” and there would be little reason to mention Philoaus in the context of the history of science if it were not for the considerable influence of his astronomical system on the development of astronomy, even after Copernicus.

Knowledge of this system has evolved from three sources: Aetius, a late Greek doxographer; Achilles, a late Greek commentator on the Phaenomena of Aratus; and Aritotle. The first two, who differ from each other in some details, especially in the explanation of the light emanating from the sun, mention Philolaus by name. Aristotle, describing essentially the same system, does not mention Philolaus by name but attributes the system to“Some of the Pythagoreans, who had lived in Southern Italy,” Aristotle’s reason for this attribution may be that, according to one tradition, Philolaus’ system was further elaborated by a certain Hicetas.

Contrary to all earlier astronomical systems, and also to those accepted later by Plato and Aristotle, Philolaus’ system states that the center of the universe is occupied not by the earth but by a central fire (not identical with the sun), around which the earth moves at considerable speed. That we do not see this central fire is explained by assuming that the earth always turns the same side to the central fire and that we live on the opposite side. A“counter-earth,” or“anti-earth” exists on the opposite side of the central fire but at a lesser distance. The“auti-earth” revolves around the central fire simultaneously with the earth, which is why we can never see it. Above the earth and at greater distances from the central fire the other heavenly bodies likewise revolve around the central fire-first the moon, then the sun, and then the five planets: Mercury, Venus, Mars, Jupiter, and Saturn. Outermost is the fiery sphere of the fixed stars. The sun, according to Aetius, is a hollow mirror collecting the light from below (the central fire?) and reflecting and focusing it toward the earth. According to Achilles, it is, on the contrary, similar to a convex lens, collecting the light that emanates from the outer sphere and likewise focusing it in the direction of the earth.

To understand the position of this strange system within the history of astronomy, the following factors must be considered. From the early fifth century B.C. Greek philosophers and cosmologists were puzzled by the apparently irregular motions of certain heavenly bodies. Anaxagoras, among others, tried to explain the movements of the stars by adopting mechanics as an analogue. Others, like the early Pythagoreans, considered the heavenly bodies as living beings endowed with a higher reason than humans. These philosophers thought it unworthy of such divine beings to move as irregularly as animals on this earth, rather than moving with a constant speed in the most beautiful and simple curve-the circle. Plato, who adopted this view, asked the famous mathematician Eudoxus of Cnidus if the apparent movements of the celestial bodies could be explained on the assumption that they were combinations of circular movements with constant velocity. Eudoxus actually succeeded in constructing a model of twenty-seven spheres, one within the other and each moving at a constant speed. The inner spheres were directed by the outer spheres, which moved in different directions. Thus the apparent movements of the celestial bodies could be approximately accounted for. Because of careful observations, some disagreements remained; and the number of spheres within this system was later increased to thirty-three by the astronomer Callippus. Aristotle increased the number to fifty-five. Within all these systems, however, the earth remained in the center of the universe.

By removing the earth from the center of the universe, Philolaus anticipated modern astronomical theory and, specifically, the Copernican system. It is natural to assume that Philolaus must have tried also to account mathematically for the apparent movements of the heavenly bodies, although it is difficult to see what the assumption of an invisible central fire and an invisible anti-earth could have contributed to such an explanation. Since the system, as reported by both Aetius and Achilles, did not present such an account, B. L. Van der Waerden suspected that Philolaus’ system must have differed from that described by ancient tradition. He states that either the most important step in the development of early Greek astronomy was taken by a muddleheaded speculator (ein Wirrkopf) or Philolaus’ system must have been different.

Van der Waerden, in a most ingenious fashion, constructed a Philolaic system, accounting to some extent for the observed phenomena. Aristotle, however, when speaking of the Pythagoreans of southern Italy, who invented the system otherwise ascribed to Philolaus, states expressly that they did not try to account for the observed phenomena by means of mathematical constructions. Instead, they removed the earth from the center of the universe for the sole reason that only fire, the most noble (τiμωacute;τατατoν) of the elements, was worthy of occupying that place. The anti-earth was added to bring the number of the celestial bodies to ten, because ten was the “perfect number.” If this is so—and Aristotle, after all, is not a contemptible witness—one will have to admit that it was an unscientific, muddleheaded speculator and not a great mathematician or astronomer who first suggested, against all appearances, that the earth is not in the center of the universe and that it is not at rest but moving along at great speed. This speculator also encouraged the inventors of the heliocentric system, Aristarchus of Samos and Copernicus, who greatly admired Philolaus.

BIBLIOGRAPHY

On Philolaus and his influence, see A. Boeckh, Philolaus des Pythagoreers Lehren nebst den Bruchstucken seines Werkes (Berlin, 1819); W. Burkert, Weisheit und Wissenschaft (Nuremburg, 1962); H. Diels, “Über die Excerpte von Menons Iatrica in dem Londoner Papyrus 137,” in Hermes, 28 (1893), 428–434; K. von Fritz, Grund-problem der Geschichte der antiken Wissenschaften (Berlin, 1970), 157–166; R. Mondolfo, “Sui frammenti di Filolao. Contribuzione a una revisione del processo di falsità,” in Rivista di filolgia e di istruzione classica, n.s. 15 (1937), 225–245; B. L. Van der Waerden, “Die Astronomie der Pythagoreer,” in Verhandlingen der K. nederlandsche akademie van wetenschappen. Afdeeling natuurkunde, 20 pt. 1 (1951), 1–136; and K. von Fritz, “Philolaos” in Pauly-Wissowa, supp. XIII (1974), 453-483.

Kurt Von Fritz