From Chapter VII., The Pythagoreans
150. The Central Fire
It is not easy to accept the statement of Aetios that this system was taught by Philolaos. Aristotle nowhere mentions him in connexion with it, and in the Phaedo Sokrates gives a description of the earth and its position in the world which is entirely opposed to it, but is accepted without demur by Simmias the disciple of Philolaos.88 It is undoubtedly a Pythagorean theory, however, and marks a noticeable advance on the Ionian views current at Athens. It is clear too that Sokrates states it as something of a novelty that the earth does not require the support of air or anything of the sort to keep it in its place. Even Anaxagoras had not been able to shake himself free of that idea, and Demokritos still held it along with the theory of a flat earth. The natural inference from the Phaedo would certainly be that the theory of a spherical earth, kept in the middle of the world by its equilibrium, was that of Philolaos himself. If so, the doctrine of the central fire would belong to a later generation.
It seems probable that the theory of the earth's revolution round the central fire really originated in the account of the sun's light given by Empedokles. The two things are brought into close connexion by Aetios, who says that Empedokles believed in two suns, while "Philolaos" believed in two or even in three. His words are obscure, but they seem to justify us in holding that Theophrastos regarded the theories as akin.89 We saw that Empedokles gave two inconsistent explanations of the alternation of day and night (§ 113), and it may well have seemed that the solution of the difficulty was to make the sun shine by reflected light from a central fire. Such a theory would, in fact, be the natural issue of recent discoveries as to the moon's light and the cause of its eclipses, if these were extended to the sun, as they would almost inevitably be.
The central fire received a number of mythological names, such as the "hearth of the world," the "house," or "watch-tower " of Zeus, and "the mother of the gods."90 That was in the manner of the school, but it must not blind us to the fact that we are dealing with a scientific hypothesis. It was a great thing to see that the phenomena could best be "saved" by a central luminary, and that the earth must therefore be a revolving sphere like the other planets.91 Indeed, we are tempted to say that the identification of the central fire with the sun was a detail in comparison. It is probable, at any rate, that this theory started the train of thought which made it possible for Aristarchos of Samos to reach the heliocentric hypothesis,92 and it was certainly Aristotle's successful reassertion of the geocentric theory which made it necessary for Copernicus to discover the truth afresh. We have his own word for it that he started from what he had read about the Pythagoreans.93
In the form in which it was now stated, however, the theory raised almost as many difficulties as it solved, and it did not maintain itself for long. It is clear from Aristotle that its critics raised the objection that it failed to "save the phenomena" inasmuch as the assumed revolution of the earth would produce parallaxes too great to be negligible and that the Pythagoreans gave some reason for the belief that they were negligible. Aristotle has no clear account of the arguments on either side, but it may be pointed out that the earth was probably supposed to be far smaller than it is, and there is no reason why its orbit should have been thought to have an appreciably greater diameter than we now know the earth itself to have.94
A truer view of the earth's dimensions would naturally suggest that the alternation of night and day was due to the earth's rotation on its own axis, and in that case the earth could once more be regarded as in the centre. It does not appear that Aristotle knew of any one who had held this view, but Theophrastos seems to have attributed it to Hiketas and Ekphantos of Syracuse, of whom we know very little otherwise.95 Apparently they regarded the heaven of the fixed stars as stationary, a thing Aristotle would almost have been bound to mention if he had ever heard of it, since his own system turns entirely on the diurnal revolution.
Both theories, that of the earth's revolution round a central fire and that of its rotation on its own axis, had the effect of making the revolution of the fixed stars, to which the Pythagoreans certainly adhered, very difficult to account for. They must either be stationary or their motion must be something quite different from the diurnal revolution.96 It was probably this that led to the abandonment of the theory.
In discussing the views of those who hold the earth to be in motion, Aristotle only mentions one theory as alternative to that of its revolution round the central fire, and he says that it is that of the Timaeus. According to this the earth is not one of the planets but "at the centre," while at the same time it has some kind of motion relatively to the axis of the universe.97 Now this motion can hardly be an axial rotation, as was held by Grote;98 for the whole cosmology of the Timaeus implies that the alternation of day and night is due to the diurnal revolution of the heavens.99 The fact that the earth is referred to a little later as "the guardian and artificer of night and day"100 proves nothing to the contrary, since night is in any case the conical shadow of the earth, which is thus the cause of the alternation of day and night. So far, Boeckh and his followers appear to be in the right.
When, however, Boeckh goes on to argue that the word ἰλλομένην in the Timaeus does not refer to motion at all, but that it means "globed" or "packed" round, it is quite impossible for me to follow him. Apart from all philological considerations, this interpretation makes nonsense of Aristotle's line of argument. He says101 that, if the earth is in motion, whether "outside the centre" or "at the centre," that cannot be a "natural motion"; for, if it were, it would be shared by every particle of earth, and we see that the natural motion of every clod of earth is "down," i.e. towards the centre. He also says that, if the earth is in motion, whether "outside the centre" or "at the centre," it must have two motions like everything else but the "first sphere," and therefore there would be excursions in latitude (πάροδοι) and "turnings back " (τροπαί) of the fixed stars, which there are not. It is clear, then, that Aristotle regarded the second theory of the earth's movement as involving a motion of translation equally with the first, and that he supposed it to be the theory of Plato's Timaeus. It is impossible to believe that he can have been mistaken on such a point.102
When we turn to the passage in the Timaeus itself, we find that, when the text is correctly established, it completely corroborates Aristotle's statement that a motion of translation is involved, 103 and that Boeckh's rendering is inadmissible on grammatical and lexicological grounds.104 We have therefore to ask what motion of translation is compatible with the statement that the earth is "at the centre," and there seems to be nothing left but a motion up and down (to speak loosely) on the axis of the universe itself. Now the only clearly attested meaning of the rare word ἴλλομαι is just that of motion to and fro, backwards and forwards.105 It may be added that a motion of this kind was familiar to the Pythagoreans, if we may judge from the description of the waters in the earth given by Sokrates in the Phaedo, on the authority of some unnamed cosmologist.106
What was this motion intended to explain? It is impossible to be certain, but it is clear that the motions of the circles of the Same and the Other, i.e. the equator and the ecliptic, are inadequate to "save the appearances." So far as they go, all the planets should either move in the ecliptic or remain at an invariable distance from it, and this is far from being the case. Some explanation is required of their excursions in latitude, i.e. their alternate approaches to the ecliptic and departures from it. We have seen (p. 63) that Anaximander already busied himself with the "turnings back" of the moon. Moreover, the direct and retrograde movements of the planets are clearly referred to in the Timaeus a few lines below.107 We are not bound to show in detail that a motion of the kind suggested would account for these apparent irregularities; it is enough if it can be made probable that the fifth-century Pythagoreans thought it could. It may have seemed worth while to them to explain the phenomena by a regular motion of the earth rather than by any waywardness in the planets; and, if so, they were at least on the right track.
To avoid misunderstanding, I would add that I do not suppose Plato himself was satisfied with the
theory which he thought it appropriate for a Pythagorean of an earlier generation to propound. The idea
that Plato expounded his own personal views in a dialogue obviously supposed to take place before he
was born, is one which, to me at least, is quite incredible. We know, moreover, from the
unimpeachable authority of Theophrastos, who was a member of the Academy in Plato's later years,
that he had then abandoned the geocentric hypothesis, though we have no information as to what he
supposed to be in the centre of our system.108
It seems clear too from the Laws that he must have
attributed an axial rotation to the earth.109
85. For the authorities see R. P. 81-83. The attribution of the theory to Philolaos is perhaps due to Poseidonios. The "three books" were doubtless in existence by his time.
86. Plato makes Timaios attribute an axial rotation to the heavenly bodies, which must be of this kind (Tim. 40 a 7). The rotation of the moon upon its axis takes the same time as its revolution round the earth; but it comes to the same thing if we say that it does not rotate at all relatively to its orbit, and that is how the Greeks put it. It would be quite natural for the Pythagoreans to extend this to all the heavenly bodies. This led ultimately to Aristotle's view that they were all fixed (ἐνδεδεμένα) in corporeal spheres.
87. This seems more natural than to suppose the earth and counter-earth to be always in conjunction. Cf. Aet. iii. 11, 3, τὴν οἰκουμένην γῆν ἐξ ἐναντίας κειμένην καὶ περιφερομένην τῇ ἀντίχθονι.
88. Plato, Phaed. 108 e 4 sqq. Simmias assents to the geocentric theory in the emphatic words καὶ ὀρθῶς γε.
89. Aet. ii. 20, 13 (Chap. VI. p. 238, n. 3) compared with ib. 12 Φιλόλαος ὁ Πυθαγόρειος ὑαλοειδῆ τὸν ἥλιον, δεχόμενον μὲν τοῦ ἐν τῷ κόσμῳ πυρὸς τὴν ἀνταύγειαν, διηθοῦντα δὲ πρὸς ἡμᾶς τὸ φῶς, ὤστε τρόπον τινὰ διττοὺς ἡλίους γίγνεσθαι, τό τε ἐν τῷ οὐρανῷ πυρῶδες καὶ τὸ ἀπ' αὐτοῦ πυροειδὲς κατὰ τὸ ἐσοπτροειδές· εἰ μή τις καὶ τρίτον λέξει τὴν ἀπὸ τοῦ ἐνόπτρου κατ' ἀνάκλασιν διασπειρομένην πρὸς ἡμᾶς αὐγήν. This is not, of course, a statement of any doctrine held by "Philolaos," but a rather captious criticism such as we often find in Theophrastos. Moreover, it is pretty clear that it is inaccurately reported. The phrase τὸ ἐν τῷ κόσμῳ πῦρ, if used by Theophrastos, must surely mean the central fire and τὸ ἐν τῷ οὐρανῷ πυρῶδες must be the same thing, as it very well may, seeing that Aetios tells us himself (ii. 7. 7, R. P. 81) that "Philolaos" used the term οὐρανός of the sublunary region. It is true that Achilles says τὸ πυρῶδες καὶ διαυγὲς λαμβάνοντα ἄνωθεν ἀπὸ τοῦ ἀερίου πυρός, but his authority is not sufficiently great to outweigh the other considerations.
90. Aet. i. 7, 7 (R. P. 81).Proclus in Tim. p. 106, 22 (R. P. 83 e).
91. Aristotle expresses this by saying that the Pythagoreans held τὴν . . . γῆν ἓν τῶν ἄστρων οὐσαν κύκλῳ φερομένην περὶ τὸ μέσον νύκτα τε καὶ ἡμέραν ποιεῖν (De caelo, B, 13. 293 a 23).
92. I do not discuss here the claims of Herakleides to be the real author of the heliocentric hypothesis.
93. In a letter to Pope Paul III., Copernicus quotes Plut. Plac. iii. 13, 2-3 (R. P. 83 a) and adds Inde igitur occasionem nactus, coepi et ego de terrae mobilitate cogitare.
94. Cf. Ar. De caelo, B, 13. 293 b 25 ἐπεὶ γὰρ οὐκ ἔστιν ἡ γῆ κέντρον, ἀλλ' ἀπέχει τὸ ἡμισφαίριον αὐτης ὅλον, οὐθὲν κωλύειν οἴονται τὰ φαινόμενα συμβαίνειν ὁμοίως μὴ κατοικοῦσιν ἡμῖν ἐπὶ τοῦ κέντρου, ὥσπερ κἂν εἰ ἐπὶ τοῦ μέσου ἧν ἡ γῆ· οὐθὲν γὰρ οὐδὲ νῦν ποιεῖν ἐπίδηλον τὴν ἡμισεῖαν ἀπέχοντας ἡμᾶς διάμετρον. (Of course the words τὸ ἡμισφαίριον αὐτης ὅλον refer to Aristotle's own theory of celestial spheres; he really means the radius of its orbit.) Now it is inconceivable that any one should have argued that, since the geocentric parallax is negligible, parallax in general is negligible. On the other hand, the geocentric Pythagorean (the real Philolaos?), whose views are expounded by Sokrates in the Phaedo, appears to have made a special point of saying that the earth was πάμμεγα (109 a 9), and that would make the theory of the central fire very difficult to defend. If Philolaos was one of the Pythagoreans who held that the radius of the moon's orbit is only three times that of the earth's (Plut. De an. procr. 1028 b), he cannot have used the argument quoted by Aristotle.
95. Aet. iii. 13, 3 Ἡρακλείδης ὁ Ποντικὸς καὶ Ἔκφαντος ὁ Πυθαγόρειος κινοῦσι μὲν τὴν γῆν· οὐ μήν γε μεταβατικῶς, ἀλλὰ τρεπτικῶς [1. στρεπτικῶς] τρόχου δίκην ἐνηξονισμένην, ἀπὸ δυσμῶν ἐπ' ἀνατολὰς περὶ τὸ ἴδιον αὐτῆς κέντρον. Cicero attributes the same doctrine to Hiketas (Acad. pr. ii. 39), but makes nonsense of it by saying that he made the sun and moon stationary as well as the fixed stars. Tannery regarded Hiketas and Ekphantos as fictitious personages from a dialogue of Herakleides, but it seems clear that Theophrastos recognised their existence. It may be added that the idea of the earth's rotation was no novelty. The Milesians probably (§ 21) and Anaxagoras certainly (p. 269) held this view of their flat earth. All that was new was the application of it to a sphere. If we could be sure that the geocentric Pythagoreans who made the earth rotate placed the central fire in the interior of the earth, that would prove them to be later in date than the system of "Philolaos." Simplicius appears to say this (De caelo, p. 512 9 sqq.), and he may be quoting from Aristotle's lost work on the Pythagoreans. The point, however, is doubtful.
96. The various possibilities are enumerated by Sir T. L. Heath (Aristarchus, p. 103). Only two are worth noting. The universe as a whole might share in the rotation of the ἀπλανές, while the sun, moon and planets had independent revolutions in addition to that of the universe. Or the rotation of the ἀπλανές might be so slow as to be imperceptible, in which case its motion, "though it is not the precession of the equinoxes, is something very like it" (Heath, loc. cit.).
97. Arist. De caelo, B, 13. 293 b 5, ἔνιοι δὲ καὶ κειμένην ἐπὶ τοῦ κέντρου [τὴν γῆν] φασὶν αὐτὴν ἴλλεσθαι καὶ κινεῖσθαι περὶ τὸν διὰ παντὸς τεταμένον πόλον, ὥσπερ ἐν τῷ Τιμαίῳ γεγραπται.. The text and interpretation of this passage are guaranteed by the reference in the next chapter (296 a 25) οἱ δ' ἐπὶ τοῦ μέσου θέντες ἴλλεσθαι καὶ κινεῖσθαί φασι περὶ τὸν πόλον μέσον. All attempts to show that this refers to something else are futile. We cannot, therefore, with Alexander, regard καὶ κινεῖσθαι as an interpolation in the first passage, even though it is omitted in some MSS. there. The omission is probably due to Alexander's authority. Moreover, when read in its context, it is quite clear that the passage gives one of two alternative theories of the earth's motion, and that this motion, like the revolution round the central fire, is a motion of translation (φορά), and not an axial rotation.
98. Plato's Doctrine respecting the Rotation of the Earth (1860).
99. Plato, Tim. 39 c 1, νὺξ μὲν οὖν ἡμέρα τε γέγονεν οὕτως καὶ διὰ ταῦτα, ἡ τῆς μιᾶς καὶ φρονιμωτάτης κυκλήσεως περίοδος. This refers to the revolution of the "circle of the Same," i.e. the equatorial circle, and is quite unambiguous.
100. Plato, Tim. 40 c 1 [γῆν] φύλακα καὶ δημιουργὸν νυκτός τε καὶ ἡμέρας ἐμηχανήσατο. On this cf. Heath, Aristarchus, p. 178.
101. Arist. De caelo, B, 14. 296 a 29 sqq. The use of the word ὑπολειπόμενα of the apparent motion of the planets from west to east is an interesting survival of the old Ionian view (p. 70). The idea that the earth must have two motions, if it has any, is based on nothing more than the analogy of the planets (Heath, Aristarchus, p. 241).
102. Aristotle must have been a member of the Academy when the Timaeus was published, and we know that the interpretation of that dialogue was one of the chief occupations of the Academy after Plato's death. If he had misrepresented the doctrine by introducing a motion of translation, Alexander and Simplicius would surely have been able to appeal to an authoritative protest by Krantor or another. The view which Boeckh finds in the Timaeus is precisely Aristotle's own, and it is impossible to believe that he could have failed to recognise the fact or that he should have misrepresented it deliberately.
103. The best attested reading in Tim. is γῆν δὲ τροφὸν μὲν ἡμετέραν, ἰλλομένην δὲ τὴν περὶ τὸν διὰ παντὸς πόλον τεταμένον. The article τὴν is in Par. A and also in the Palatine excerpts, and it is difficult to suppose that any one would interpolate it. On the other hand, it might easily be dropped, as its meaning is not at once obvious. It is to be explained, of course, like τὴν ἐπὶ θάνατον or Xenophon's προεληλυθότος . . . τὴν πρὸς τὰ φρούρια, and implies a path of some kind, and therefore a movement of translation.
104. In the first place, the meaning globatam, "packed," "massed" would have to be expressed by a perfect participle and not a present, and we find accordingly that Simplicius is obliged to paraphrase it by the perfect participle, δεδεμένη or δεδεσμηνένη. Sir T. L. Heath's "wound " (Aristarchus, p. 177) ought also to be "winding." In the second place, though Par. A has εἰλλομένην, the weight of authority distinctly favours ἰλλομένην, the reading of Aristotle, Proclus and others. The verbs εἵλλω (εἴλλω), εἰλῶ and ἴλλω are constantly confused in MSS. It is not, I think, possible to regard ἴλλω as etymologically connected with the other verbs. It seems rather to go with ἰλλός and ἰλλαίνω, which are both used in Hippokrates. For its meaning, see below, n. 2.
105. Cf. Soph. Ant. 340 ἰλλομένων ἀρότρων ἔτος εἰς ἔτος, clearly of the ploughs going backwards and forwards in the furrows. Simplicius makes a point of the fact that Apollonios Rhodios used ἰλλόμενος in the sense of "shut in," "bound," εἰργόμενος (cf. Heath, Aristarchus, p. 175, n. 6). That, however, cannot weigh against the probability that the scribes, or even Apollonios himself, merely fell into the common confusion. Unless we can get rid of the article τὴν and the testimony of Aristotle, we must have a verb of motion.
106. Cf. Plato, Phaed. 111 c 4, where we are told that there is an αἰώρα in the earth, which causes the waters to move up and down in Tartaros, which is a chasm extending from pole to pole. See my notes in loc.
107. Proclus, in his commentary, explains the προχωρἡσεις and ἐπανακυκλήσεις Of Tim. 20 c as equivalent to προποδισμοί and ὑποποδισμοί. In a corrigendum prefixed to his Aristarchus, Sir T. L. Heath disputes this interpretation, and compares the application of the term ἐπανακυκλούμενον to the planet Mars in Rep. 617 b, which he understands to refer merely to its "circular revolution in a sense contrary to that of the fixed stars." It is to be observed, however, that Theon of Smyrna in quoting this passage has the words μάλιστα τῶν ἄλλον after ἐπανακυκλούμενον, which gives excellent sense if retrogradation is meant. In fact Mars has a greater arc of retrogradation than the other planets (Duhem, Système du monde, vol. i. p. 61). As I failed to note this in my text of the Republic, I should like to make amends by giving two reasons for believing that Theon has preserved Plato's own words. In the first place he is apparently quoting from Derkyllides, who first established the text of Plato from which ours is derived. In the second place, μάλιστα τῶν ἄλλων is exactly fifteen letters, the normal length of omissions in the Platonic text.
108. Plut. Plat. quaest, 1006 c (cf. V. Numae, c. 11). It is important to remember that Theophrastos was a member of the Academy in Plato's last years.
109. In the passage referred to (822 a 4 sqq.) he maintains that the planets have a simple circular motion, and says that this is a view which he had not heard in his youth nor long before. That must imply the rotation of the earth on its axis in twenty-four hours, since it is a denial of the Pythagorean theory that the planetary motions are composite. It does not follow that we must find this view in the Timaeus, which only professes to give the opinions of a fifth-century Pythagorean.
Created for Peithô's Web from Early Greek Philosophy by John Burnet, 3rd edition (1920). London: A & C Black Ltd. Burnet's footnotes have been converted to chapter endnotes. Greek unicode text entered with Peithô's Younicoder.
Web design by Larry Clark and RSBoyes (Agathon). Peithô's Web gratefully acknowledges the assistance of Anthony Beavers in the creation of this web edition of Burnet. Please send comments to: