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Aristotle’s Arguments for the Sphericity of the Earth

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Book cover When the Earth Was Flat

Part of the book series: Historical & Cultural Astronomy ((HCA))

Abstract

According to Aëtius, Thales stated that the earth is shaped like a ball. Diogenes Laërtius reports that Hesiod, Anaximander and Pythagoras taught that the earth was spherical. These testimonies are usually considered false. Several scholars have argued that Parmenides was the first to accept the earth’s sphericity. In the Phaedo, Plato tells us that someone has convinced Socrates that the earth is a sphere, without indicating who this “someone” was or what his arguments were. He then compares the earth with a dodecahedron. There must have been a heated debate among ancient Greek cosmologists about the shape of the earth, some of which can still be followed in the reports of the doxographers. For example, a curious argument, attributed to Anaxagoras, that is intended to prove that the earth is flat. Aristotle, who was familiar with the ins and outs of the debate, sought to terminate it by putting forward arguments for the sphericity of the earth and arguing against alleged evidence that the earth is flat. Since then, hardly any serious philosopher or astronomer has doubted that the earth is a sphere. Aristotle’s arguments can be divided into two groups: theoretical and empirical.

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Notes

  1. 1.

    P 3.9.1 (not in S) = DK 50, 4 = TP1 161; not in LM, Gr, and KRS.

  2. 2.

    Diogenes Laërtius, Vitae Philosophorum 8.48 = DK 28A44 = LM PARM. D33b = Gr Prm40, not in KRS (Pythagoras and Hesiod); Diogenes Laërtius, Vitae Philosophorum 2.1.1 = DK 12A1(1) = LM ANAXIMAND. D31 = Gr Axr 1(1) = TP2 Ar92 (Anaximander).

  3. 3.

    Although O’Grady (2002, 94–100), still broke a lance for Thales. Bakker (2016, 165–166) mentions Pythagoras without a critical note.

  4. 4.

    Recently, e.g., Panchenko (2008), Graham (2013, 105–106).

  5. 5.

    Plato, Phaedo, 108C–E and 110B.

  6. 6.

    See the section Aristotle on empirical arguments for a flat earth.

  7. 7.

    Bakker’s Epicurean Meteorologica tries to answer the intriguing question of whether Epicurus (and Lucretius) believed the earth to be flat. A notorious flat-earther was Cosmas Indicopleustes (sixth century A.D.).

  8. 8.

    Simplicius (In Aristotelis De Caelo Commentaria 542.14) counts five arguments, but the last one has to do with measuring the earth’s circumference and thus presupposes the sphericity of the earth.

  9. 9.

    Hawking (1988, 2–3).

  10. 10.

    Graham (2013, 95).

  11. 11.

    Rovelli (2015, 35).

  12. 12.

    See Bakker (2016, 169–175) (Chap. 4.2.2).

  13. 13.

    Aristotle, De Caelo 297b24ff; the text between square brackets is my addition.

  14. 14.

    The last is Kepler’s interpretation; see note 31.

  15. 15.

    See LSJ, s.v. κυρτός.

  16. 16.

    Cf. Aristotle, Meteorologica 265a31.

  17. 17.

    Rovelli (2015, 35).

  18. 18.

    Neugebauer (1975, 1093–1094). See also, e.g., Dicks (1970, 260, n. 379): “Strictly, this proves only the curvature of the earth’s surface,” and North (2008, 82): “Not a perfect argument by itself, of course.”

  19. 19.

    Neugebauer (1975, 576).

  20. 20.

    Aristotle, De Caelo 297b29–31, my italics.

  21. 21.

    Bakker (2016, 171).

  22. 22.

    Bowen and Todd (2004, 1, 157 n. 8).

  23. 23.

    Aristotle, De Caelo 293b25–29.

  24. 24.

    This phenomenon has already been mentioned in Chap. 9, section Attempts to Understand the Invisible Bodies as an Additional Cause of Lunar Eclipses.

  25. 25.

    Bakker (2016, 171, 174–175, Table 4.2), also notes this curious fact. His suggestion, however, that this could be due to the idea that the same effect of shadow lines on the moon could be caused by a flat, disk-shaped earth, is not right.

  26. 26.

    Ptolemy, Almagest I.4.

  27. 27.

    Ptolemy, Almagest VI.

  28. 28.

    Cf. Cleomedes in Bowen and Todd (2004, I.5).

  29. 29.

    Cleomedes in Bowen and Todd (2004, II.6). This text is not mentioned in Table 4.2 in Bakker (2016, 174–175).

  30. 30.

    See Copernicus (1543, not in I.2) (“Quod terra quoque sphaerica sit”), but at the end of 1.3 (“Quomodo terra cim aqua unum globum perficiat”).

  31. 31.

    See Kepler (1635, I, 25): “Terminos umbrae terrestris, in corpore lunae deficientis, tam qui sunt ad septentriones, quam qui ad Austrum, tam ad Orientem, quam ad Occidentem [sc. partem Lunae], esse arcus perfecti circuli.” The text between square brackets is my addition.

  32. 32.

    Aristotle, De Caelo 297b31ff, the numbers between brackets are my addition.

  33. 33.

    Bakker (2016, 172).

  34. 34.

    Bakker (2016, 238, Fig. 4), cf. Furley (2010, 429, n. 41): “Given the same figures as attributed to Eratosthenes, the sun would have to be only 39,579 stades from the earth (less than 5000 miles)”.

  35. 35.

    Pliny, Natural History 2.182–184.

  36. 36.

    This is more specific than a “reference to the unevenness of the earth’s surface” (Bakker 2016, 172).

  37. 37.

    Panchenko (1999, 32) dismisses somewhat too easily Cleomedes’ remark (in Bowen and Todd 2004, I.5.12) that those who taught that the earth was concave did so because otherwise the water would flow off the earth.

  38. 38.

    In fact, as will be explained in Part Two of this book, this argument was used by ancient Chinese astronomers of the gai tian system to explain why stars appear and disappear when we move around on a flat earth. See also the section Empirical arguments that Aristotle did not use.

  39. 39.

    See Panchenko (2015).

  40. 40.

    Hippolytus, Refutatio Omnium Haeresium 1.7.6 = DK 13A7(6) = LM ANAXIMEN. D3(6) = Gr Axs12 = TP2 Aa 56 = KRS 156.

  41. 41.

    Manilius, Astronomica, 1.215–220.

  42. 42.

    Copernicus (1543, I.2).

  43. 43.

    Aristotle, De Caelo 298a9–16. Perhaps Aristotle obtained this information from Eudoxus. See Bigwood (1993, 546–547).

  44. 44.

    Aristotle, Meteorologica 362b28–30.

  45. 45.

    Strabo, Geographica 1.1.20.18–27.

  46. 46.

    Cleomedes in Bowen and Todd (2004, I.5.30).

  47. 47.

    Hippolytus, Refutatio Omnium Haeresium 1.9.4 = DK 60A4(4) = LM ARCH. D2(4), KRS 515(4); not in Gr.

  48. 48.

    Cf. Tannery (1887, 279). See for more scholars on this subject: Panchenko (1999, 23).

  49. 49.

    Ptolemy, Almagest, I.4.

  50. 50.

    Pliny, Natural History 2.72.

  51. 51.

    Pliny, Natural History, 2.73.

  52. 52.

    Pliny, Natural History, 2.72.

  53. 53.

    See Part Two of this book.

  54. 54.

    This crucial proof is not mentioned in Bakker’s list (2016, 174–175, Table 4.2).

  55. 55.

    Herodotus, Historiae 4.42; the remarks between square brackets are my additions.

  56. 56.

    Panchenko (2008, 192).

  57. 57.

    Ibidem.

  58. 58.

    Pliny, Natural History 2.75.

  59. 59.

    See Aristotle, De Caelo 284b6–286a2, where Aristotle also argues that the South Pole is the uppermost and the North Pole the lowest. See also Meteorologica 362a32–b9.

  60. 60.

    Aristotle, Meteorologica 362b6–9. See also Heidel (1937, 86).

  61. 61.

    For a survey of the sources until the end of the thirteenth century, see Hamel (1996, 38–109).

  62. 62.

    Kepler [1635, I.3 (p.19)].

  63. 63.

    Aristotle, De Caelo 291b23.

  64. 64.

    Cf. Aristotle, De Caelo 287a6–12 and 291b11–23.

  65. 65.

    Aristotle De Caelo 294a1–4; the text between square brackets is my addition. See Panchenko (1997).

  66. 66.

    Aristotle, De Caelo 294a5–7; the text between square brackets is my addition.

  67. 67.

    Furley (1987, 198), Heath (1913, 235). For a detailed discussion of this argument, see Couprie (2011, 181–188).

  68. 68.

    Simplicius, In Aristotelis De Caelo Commentaria 519.30–33.

  69. 69.

    Simplicius, In Aristotelis De Caelo Commentaria 519.33–520.2.

  70. 70.

    Simplicius, In Aristotelis De Caelo Commentaria, 520.7–8.

  71. 71.

    Aristotle, De Caelo 294a8.

  72. 72.

    Aristotle, De Caelo 294a9–10; texts between square brackets my additions.

  73. 73.

    Aristotle, De Caelo 294b14–15.

  74. 74.

    Aristotle, De Caelo 294b23–24.

  75. 75.

    Cf. Kahn (1994, 118): “In Aristotle’s demonstration of the earth’s sphericity, general cosmological arguments take precedence over τὰ φαινόμενα κατὰ τὴν αἴσϑησιν.”

  76. 76.

    Dreyer (1953, 109): “In his general conception of the Kosmos Aristotle is guided by purely metaphysical arguments.” Dicks (1970, 196): “His arguments are largely a priori.”

  77. 77.

    Aristotle, De Caelo 294b33.

  78. 78.

    Plato, Phaedo 97D–E.

  79. 79.

    Cf. Aristotle, Analitica Posteriora I.xiii and xxxi.

  80. 80.

    Aristotle, Analitica Posteriora 78b39. In the same sense, Aristotle states in De Caelo 297a2–7: “This belief finds further support in the assertions of mathematicians on astronomy: that is, the observed phenomena (…) are consistent with the hypothesis (…) that the earth lies at the centre.” (my italics).

  81. 81.

    Cf. Aristotle, De Caelo 292b20.

  82. 82.

    Aristotle, De Caelo 296b18–21.

  83. 83.

    Aristotle, De Caelo 297b20.

  84. 84.

    Moraux (1965, CXXXI, n. 2), see also Jori (2009, 473).

  85. 85.

    Simplicius, In Aristotelis De Caelo Commentaria 545.30.

  86. 86.

    Aristotle, De Caelo 296b7; Guthrie has: “the natural motion of the earth as a whole, like that of its parts.”

  87. 87.

    Aristotle, De Caelo 297a22–26.

  88. 88.

    Aristotle, De Caelo 296b13–15.

  89. 89.

    See more extensively: Couprie (2011, 213–220).

  90. 90.

    Copernicus (1543), Preface and Dedication to Pope Paul III.

  91. 91.

    Copernicus (1543, I.8 and I.9).

  92. 92.

    Copernicus (1543, I.9).

  93. 93.

    • P = Aëtius in pseudo-Plutarch, Placita (numbering according to Dox).

      S = Aëtius in Stobaeus, Anthologium (numbering according to Wachsmuth and Hense).

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  1. Department of Philosophy, Faculty of Philosophy and Arts, University of West Bohemia, Pilsen, Czech Republic

    Dirk L. Couprie

  2. Amsterdam, The Netherlands

    Dirk L. Couprie

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Couprie, D.L. (2018). Aristotle’s Arguments for the Sphericity of the Earth. In: When the Earth Was Flat. Historical & Cultural Astronomy. Springer, Cham. https://doi.org/10.1007/978-3-319-97052-3_12

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