On Philolaus’ astronomy


In Philolaus’ cosmology, the earth revolves around a central fire along with the other heavenly bodies, including a planet called the counter-earth which orbits below the earth. His theory can account for most astronomical phenomena. A common criticism of his theory since ancient times is that his counter-earth does no work in the system. Yet ancient sources say the planet was supposed to account for some lunar eclipses. A reconstruction of Philolaus’ cosmology shows how lunar eclipses occurring at certain times of day cannot be explained by earth blocking the sun’s light. The counter-earth could explain these eclipses.

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  1. 1.

    Translations will be my own unless otherwise specified.

  2. 2.

    Contrast Furley’s view just a few years earlier (1987:58): “the system as a whole makes very little astronomical sense, and it is hard to believe it was intended to do so.”

  3. 3.

    Nor are recent commentators all as generous to Philolaus as Huffman. Concerning Philolaus’ cosmology Couprie says, “I would rather call it fantasy than creative imagination, and certainly not ‘a triumph of thought over mere appearance’ (Huffman 1993:259)” (2011:172, cf. 170–173, xxxi).

  4. 4.

    Barnes observes, “the fact is that we do not know what considerations led Philolaus to propound his startling innovations, and without such knowledge, we cannot pass judgment. Astronomically, of course, the Philolaic system is inadequate, but so are all the admirable astronomical systems of antiquity” (1982 [1979]:284). His first statement is quite correct, but the criterion of adequacy (presumably empirical adequacy) mentioned in the second provides a way to frame at least a relative judgment.

  5. 5.

    See, e.g., Herodotus on theories of the Nile floods, 2.19-29; “Hippocrates” on scientific explanation, Ancient Medicine chs. 1–3, 16, 22. Both authors are responding to philosophical/scientific theories using philosophical tools. In the early fourth century, Plato studies the hypothetical method, Meno 86e-87b, Phaedo 100a, which allows the possibility of comparing conclusions to appearances; see Robinson (1953). To recognize an interplay between theory and observation is not to presuppose that facts are given a priori, or that there is a fixed boundary between theory and observation, only that the two realms must interact in theory construction and testing. For a study of Greek theory and observation, see Lloyd (1979), ch. 3.

  6. 6.

    Most notably in Huffman (1993), ch. 4. In his reconstruction, he has been meticulous in attention to historical appropriateness.

  7. 7.

    Maniatis (2009) calls it “pyrocentric,” which is apt in one way, but fire is not confined to the center of Philolaus’ cosmos, whereas the hearth has a unique location.

  8. 8.

    Burch (1954) among others puts the counter-earth on the same orbit as the earth, positioned opposite it, so as to counter-balance its mass. Aristotle, however, makes it clear that the orbit of the counter-earth is inside that of the earth: Alexander of Aphrodisias in Metaph. 39.1-3 = Aristotle fr. 203; Simplicius in Cael. 511.19-22 = Aristotle fr. 204; cf. Aetius 2.7.7 = DK 44A16; Aet. 3.11.3 = A17.

  9. 9.

    254-7. For a history of views about the motion of the stars, and the problems the question causes, see Heath 1913:101–105.

  10. 10.

    To use Babylonian units, which were not introduced into Greece until the time of Hipparchus. But of course Greek geometry could represent the angular distance as 1/30th of a circle. In fact, Philolaus had a (mean synodic) month of 29 1/2 days (see Censorinus 18.8, 19.2 = A22 with Huffman 1993:276–279); the modern figure is 29.53059; he had a solar year of 364 1/2 days. But for purposes of the present exercise, it is enough to approximate the periods in question.

  11. 11.

    For the reconstruction, see Huffman 1993, ch. 4, and Heath 1913:98–101.

  12. 12.

    Eudemus attributes recognition of the five planets to the Pythagoreans. Philolaus provides the ultimate source; Simplicius in Cael. 471.2-6 = Eudemus fr. 146 Wehrli. See Dicks 1970:66; Vlastos 1975:46 and n. 65, 103. Zhmud 2003:258 attributes the recognition to some Pythagorean before Philolaus.

  13. 13.

    choreuein Aetius 2.7.7 = 44A16.

  14. 14.

    Huffman 2007 provides a strong cosmological and cosmogonical motivation for the hearth and even a biological analogy, in rejecting the interpretation of Kingsley 1995, chs. 13–14, who identifies the central fire with the mythological Tartarus in a religious context. But Huffman’s account does not entail any astronomical advantages.

  15. 15.

    Hippolytus Haer. 1.8.9-10 = 59A42; Graham and Hintz (2007) and Graham and Hintz (2010), Graham (2013a).

  16. 16.

    See Wöhrle (1995), Graham (2002) and Mourelatos (2012).

  17. 17.

    See Graham and Hintz 2007, Graham 2013b:177 ff. On Philolaus’ astronomy as au courant of the latest theoretical developments, see Guthrie 1962:286–287; Huffman 1993:241, 250.

  18. 18.

    APo. 90a15-18; 93a30-b7; 98b16-24; 87b39-88a2; Metaph. 1044b9-15.

  19. 19.

    Heath 1913:99–100, 119; Burnet 1930 [1892]:305–306; Cherniss 1935:198–199. For contrary views, see n. 25 below.

  20. 20.

    One question that arises is what role the central fire might play in the illumination of the moon. We get no information about whether it might by itself light up the moon. But as long as the counter-earth lies between the central fire and the moon it could block the light from both the central fire and the sun.

  21. 21.

    I observed such an eclipse on Dec. 10, 2011 in Utah, commencing at about 6 a.m. local time.

  22. 22.

    epiphraxis Eusebius.

  23. 23.

    Bicknell (1968) speculated that Anaxagoras interpreted a sunspot as a fragment broken off from the sun, but this seems far-fetched.

  24. 24.

    Heath 1913:100–101 notes that the lack of observed parallax of the planets would suggest the same result.

  25. 25.

    “It has been suggested that the counter-earth might have performed the same function [of causing lunar eclipses] in the Philolaic scheme. This, however, is impossible, since the orbit of the moon is outside the earth’s, while that of the counter-earth is inside it ...” (Dicks 1970:66–67). “[S]ince the counter-earth is inside the orbit of the earth and the moon is outside the orbit of the earth, there is no way that it could serve such a function [of causing a lunar eclipse]” (Huffman 1993:247). “[O]n any account of the relative orbits of the sun, moon, and earth, it is hard to see how the counter-earth could interpose itself between sun and moon ...” (Hankinson 1998:41). “[I]t is hard to see how the counter-earth that is supposed to orbit between the earth and the central fire could ever cause an eclipse of the moon, as Dicks rightly remarks” (Couprie 2011:171).

  26. 26.

    Aristotle Cael. 293a23-24, which Guthrie translates, “they invent another earth, lying opposite our own” (my italics). The Greek, however, is not clear as to what sense of opposition is meant and has no verb or participle corresponding to ‘lying.’

  27. 27.

    Alexander Aphr. in Metaph. 40.32 = Aristotle fr. 203. “The counter-earth always remains and moves opposite to the earth, as denoted by its name ...” (Maniatis 2009:404).

  28. 28.

    In fact, the meaning ‘taking the place of’ appears only in relatively late nominal compounds, but the meaning ‘like’ is suitably early; antitheos is found in Homer Il. 5.663 et passim.

  29. 29.

    Thus the Pythagoreans called the moon antichthōn as being a heavenly earth and blocking (antiphrattousa) sunlight (Simplicius in Cael. 512.17-20).


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I presented this paper to the International Association for Presocratic Philosophy at a meeting in Mérida, Mexico, on Jan. 9, 2012. I am grateful to the participants for discussion, as well as to Carl Huffman for written comments and to my colleague David Grandy for oral comments.

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Correspondence to Daniel W. Graham.

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Communicated by : A. Jones.

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Graham, D.W. On Philolaus’ astronomy. Arch. Hist. Exact Sci. 69, 217–230 (2015). https://doi.org/10.1007/s00407-014-0147-3

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  • Solar Eclipse
  • Full Moon
  • Empirical Adequacy
  • Lunar Eclipse
  • Heavenly Body