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Aristotle as an Astronomer? Sosigenes’ Account of Metaphysics Λ.8

Aristotle as an Astronomer? Sosigenes’ Account of Metaphysics Λ.8 Ever since the detailed discussion in the (lost) Περὶ τῶν ἀνελιττουσῶν of the Peripatetic exegete Sosigenes (second century CE),On Sosigenes, see Kupreeva (2018). Simplicius, In De caelo, 492.31–510.35 Heiberg extensively paraphrases and quotes Sosigenes’ Περὶ τῶν ἀνελιττουσῶν, as Moraux (1984), pp. 344–358, very well saw. it has been received wisdom that Aristotle was responsible for adding ‘counteracting’ spheres to Callippus’ system of planetary motions in order to construct an integrated account of the celestial domain from Callippus’ allegedly piecemeal account of the motion of the individual planets. I have argued elsewhere that there is no solid indication in Metaphysics Λ.8 for ascribing to Aristotle this contribution.See Golitsis (in press). Here I argue that the major aim of the discussion in Metaphysics Λ.8 is to grasp a precise number of self-existent immaterial substances (with which first philosophy is concerned) that provoke as final causes the rotation of the celestial spheres; and since Aristotle believed that, in all cases of natural motion, there is a one-to-one correspondence between a mover and a moved (or a mover and a motion), he needed to know how many celestial spheres there are. Such use of celestial theory for specific philosophical purposes is also present elsewhere, namely in On the Heavens II.12, where Aristotle points out that the fact that the sun and the moon move with fewer motions than the higher planets (whereas one would expect them to move with more motions) is due to their being unable, unlike the higher planets, to fully attain the Good, as they are farther removed from the sphere of the fixed stars. Sosigenes’ account has its very specific context – and setting out this context in sharp relief may help us understand what was at stake when Sosigenes made his ‘historical’ claims about Aristotle.One or two generations earlier than Sosigenes, the Peripatetic exegete Adrastus of Aphrodisias, whose concise exposition of the astronomical excursus in Λ.8 is integrated into Theon of Smyrna’s On Mathematics Useful for Understanding Plato, was ready to attribute the conception of the counteracting spheres to Aristotle or Eudoxus and Callippus:After this, [Aristotle] concludes that, if [the spheres] put together were going to account for the phenomena, there should be for each of the wandering [stars] other spheres too, less in number by one with regard to the moving [spheres], [that is,] the counteracting [spheres], proclaiming this opinion either as his own or as theirs [i. e. Eudoxus’ or Callippus].Theon, Expositio rerum mathematicarum ad legendum Platonem utilium, 180.8–12 Hiller (reproducing Adrastus’ account): Eἶτα δὲ ἐπιλογίζεται, εἰ μέλλοιεν συντεθεῖσαι σώζειν τὰ φαινόμενα, καθ’ ἕκαστον τῶν πλανωμένων καὶ ἑτέρας εἶναι σφαίρας μιᾷ ἐλάττονας τῶν φερουσῶν τὰς ἀνελιττούσας, εἴτε ἑαυτοῦ δόξαν ταύτην, εἴτε ἐκείνων ἀποφαινόμενος.It was Sosigenes who ascribed this conception to Aristotle with no hesitation.Cf. Simplicius, In De caelo, 498.1–4: “Aristotle having said these things in such a concise and clear way, Sosigenes praised his acumen and tried to find the use of the [counteracting] spheres added by him” (ταῦτα τοίνυν τοῦ Ἀριστοτέλους συντόμως οὕτω καὶ [D E F : οὕτως Heiberg cum Ab] σαφῶς εἰρηκότος ὁ Σωσιγένης ἐγκωμιάσας τὴν ἀγχίνοιαν αὐτοῦ ἐπεχείρησεν εὑρεῖν τὴν χρείαν τῶν ὑπ’ αὐτοῦ προστιθεμένων σφαιρῶν). In what follows, I would like to explain why he did so.According to Simplicius’ testimony, Sosigenes tried to explain by himself the position and function of the counteracting spheres as rotational components of the concentric planetary motions. This was not just a standard and expected endeavour by a Peripatetic exegete but also an important rectification of previous accounts of the planetary theory espoused by the Master. Eudemus’ Astronomical History, on which Sosigenes otherwise relied for his knowledge of ancient astronomical theories, especially of Eudoxus’, may have included a quite succinct and insufficient account of the counteracting spheres. At any rate, the absence of an authoritative account was probably the reason why Aristotle’s ἀνελίττουσαι were seriously distorted in the course of history. The very title of Sosigenes’ work Περὶ τῶν ἀνελιττουσῶν also reflects this distortion.The explanation of Aristotle’s counteracting spheres, as they are presented in Λ.8, was, as it can be deduced with certainty from Simplicius’ commentary on On the Heavens, an important part of Sosigenes’ work. The title of a work, however, reflects the whole: the ἀνελίττουσαι that Sosigenes primarily had in mind are not the counteracting spheres, as in Aristotle, but all concentric spheres. This is why his treatise began with a detailed exposition of the theory of Eudoxus, the first mathematician who allegedly responded to “Plato’s problem”, namely how the apparent orbits of the planets can be accounted for through the primitive explanatory principle of circular, uniform and ordered motion:Eudoxus of Cnidus is said to be the first among the Hellenes to have made use of such hypotheses – as Eudemus recorded in the second book of his Astronomical History and Sosigenes [recorded too] taking this over from Eudemus – after Plato, as Sosigenes says, put the following problem to those who were dealing with those issues, namely ‘given what circular, uniform and ordered motions will the phenomena of the wandering [stars] be preserved?’.Simplicius, In De caelo, 488.18–24: Καὶ πρῶτος τῶν Ἑλλήνων Εὔδοξος ὁ Κνίδιος, ὡς Εὔδημός τε ἐν τῷ δευτέρῳ τῆς Ἀστρολογικῆς ἱστορίας ἀπεμνημόνευσε καὶ Σωσιγένης παρὰ Εὐδήμου τοῦτο λαβών, ἅψασθαι λέγεται τῶν τοιούτων ὑποθέσεων Πλάτωνος, ὥς φησι Σωσιγένης, πρόβλημα τοῦτο ποιησαμένου τοῖς περὶ ταῦτα ἐσπουδακόσι, τίνων ὑποτεθεισῶν ὁμαλῶν καὶ <ἐγκυκλίων καὶ> [addidi] τεταγμένων κινήσεων διασωθῇ τὰ περὶ τὰς κινήσεις τῶν πλανωμένων φαινόμενα. See Zhmud (1998) for a critical discussion of whether the report about the problem set by Plato was present in Eudemus or rather only in Sosigenes.And further:We have said also earlier that Plato assigned without hesitation to the heavenly motions circularity, uniformity and order and put forward to the mathematicians the following problem: given what hypotheses will it be possible that the phenomena of the wandering [stars] be preserved by means of uniform, circular and ordered motions? And [we said following Sosigenes] that Eudoxus of Cnidus was the first to conceive of the hypotheses that use the so-called anelittousai spheres.Simplicius, In De caelo, 492.31–493.5: Kαὶ εἴρηται καὶ πρότερον, ὅτι ὁ Πλάτων ταῖς οὐρανίαις κινήσεσι τὸ ἐγκύκλιον καὶ ὁμαλὲς καὶ τεταγμένον ἀνενδοιάστως ἀποδιδοὺς πρόβλημα τοῖς μαθηματικοῖς προὔτεινε, τίνων ὑποτεθέντων δι’ ὁμαλῶν καὶ ἐγκυκλίων καὶ τεταγμένων κινήσεων δυνήσεται διασωθῆναι τὰ περὶ τοὺς πλανωμένους φαινόμενα, καὶ ὅτι πρῶτος Εὔδοξος ὁ Κνίδιος ἐπέβαλε ταῖς διὰ τῶν ἀνελιττουσῶν καλουμένων σφαιρῶν ὑποθέσεσι. Translation by Mueller (2005), modified. As it is unlikely that Eudemus used the word ὑπόθεσις for qualifying Eudoxus’ theory, we may surmise that Simplicius is here wholly relying on Sosigenes.The ἀνελίττουσαι are not only the name of a class of spheres, as in Aristotle, but have also evolved to become the name of a hypothesis. By the time of Sosigenes, this hypothesis had become an obsolete one, since it could not account for the planetary motions as accurately and as simply as the posterior hypotheses of the eccentric circles and the epicycles.Cf. Simplicius, In De caelo, 507.9–12: “Thus, in giving judgment against the hypothesis of turning [spheres] especially because it does not preserve the difference in depth, that is, the anomaly of the [planetary] motions, those who came later rejected the homocentric [turning] spheres and hypothesized eccentric and epicyclic ones” (κατεγνωκότες οὖν τῆς τῶν ἀνελιττουσῶν ὑποθέσεως οἱ μεταγενέστεροι μάλιστα διὰ τὸ τὴν κατὰ βάθος διαφορὰν καὶ τὴν ἀνωμαλίαν τῶν κινήσεων μὴ ἀποσώζειν τὰς μὲν ὁμοκέντρους ἀνελιττούσας παρῃτήσαντο, ἐκκέντρους δὲ καὶ ἐπικύκλους ὑπέθεντο). Translation by Bowen (2013). As Bowen explains, the term ἀνωμαλία is used here to signify the mean motion of a planet on its epicycle: the difference “in depth” is accounted for by the epicyclic anomaly, which is measured from the apogee of the epicycle.Simplicius himself takes ἀνελίττουσας lato sensu as equivalent to ὁμοκέντρους, as his expression ἡ διὰ τῶν ἀνελιττουσῶν σφαιροποιία readily makes clear.Simplicius, In De caelo, 504.16–17: “The spherical construction by means of the anelittousai, which [actually] cannot preserve the phenomena, is somewhat like this [i. e. as described]” (τοιαύτη τίς ἐστιν ἡ διὰ τῶν ἀνελιττουσῶν σφαιροποιία μὴ δυνηθεῖσα διασῶσαι τὰ φαινόμενα). Cf. also 488.7–9: “Those who hypothesize eccentric and epicyclic [motions], as well as those who hypothesize concentric [motions] (the ones called anelittousai), admit a greater number of motions [than one] for each [planet] in order that these [apparent motions] be saved” (διὰ γὰρ τὸ ταύτας σώζεσθαι πλείονας καθ’ ἕκαστον κινήσεις παραλαμβάνουσιν, οἱ μὲν ἐκκέντρους καὶ ἐπικύκλους, οἱ δὲ ὁμοκέντρους τὰς ἀνελιττούσας καλουμένας ὑποτιθέμενοι) and 493.8–11: “The hypothesis of anelittousai, which hypothesizes the anelittousai as concentric with the universe and not eccentric, as later [astronomers suppose], was pleasing to Aristotle, who thought that all heavenly [bodies] must move about the centre of the universe” (τῷ γὰρ Ἀριστοτέλει νομίζοντι δεῖν τὰ οὐράνια πάντα περὶ τὸ μέσον τοῦ παντὸς κινεῖσθαι ἤρεσκεν ἡ τῶν ἀνελιττουσῶν ὑπόθεσις ὡς ὁμοκέντρους τῷ παντὶ τὰς ἀνελιττούσας ὑποτιθεμένη καὶ οὐκ ἐκκέντρους, ὥσπερ οἱ ὕστερον). Translations by Bowen (2013), slightly modified. The loose sense of the term ἀνελίττουσαι has been put into light and explained through pars pro toto synecdoche by Mendell (2000), p. 92 nn. 40 and 41. Stricto sensu, however, the ἀνελίττουσαι were the spheres that Theophrastus had previously called ἄναστροι, namely the spheres that move for the sake of the star but do not themselves have the star:Thus, [Aristotle] says that the sphere having the single star said to wander moves by virtue of being fastened in many spheres called anelittousai or, as Theophrastus calls them, starless [spheres], being the last of the entire system of spheres.Simplicius, In De caelo, 491.17–20: Λέγει οὖν ὅτι ἡ σφαῖρα ἡ τὸ ἓν ἄστρον ἔχουσα τὸ πλανᾶσθαι λεγόμενον ἐν πολλαῖς σφαίραις ταῖς ἀνελιττούσαις καλουμέναις ἤ, ὡς ὁ Θεόφραστος αὐτὰς καλεῖ, ταῖς ἀνάστροις ἐνδεδεμένη φέρεται τελευταία οὖσα τῆς ὅλης αὐτῶν συντάξεως.Such are three of the four spheres of Saturn and Jupiter according to the system of Eudoxus, which of course did not include ἀνελίττουσαι strictiore sensu, that is, counteracting spheres. It is in virtue of the loose sense of ἀνελίττουσαι that Simplicius, obviously following Sosigenes, is justified in saying “The first who conceived of the hypotheses [that preserve the phenomena] through the so-called ἀνελίττουσαι spheres was Eudoxus of Cnidus”. Of course, the use of the term in the loose sense does not imply that Theophrastus himself identified the ἀνελίττουσαι of Λ.8 with all the spheres that move for the sake of a planet but do not contain the planet. It does show, however, that at some point the need was felt to distinguish between the ἀνελίττουσαι of Λ.8, the counteracting spheres which constitute only a subset of Theophrastus’ ἄναστροι, and the ἀνελίττουσαι as applying to all the spheres of a by then obsolete astronomical theory. Labelling all of them as ἀνελίττουσαι accentuated the contrast between that old account and the modern accounts, which do not posit counteracting spheres at all but deploy eccentric or epicyclic spheres. Sosigenes seems aware of this semantic development when he speaks of “the spheres which Aristotle calls counteracting” (ἃς ἀνελιττούσας καλεῖ).Simplicius, In De caelo, 498.3. When Alexander of Aphrodisias, who was a disciple of Sosigenes, says, in his commentary on the Metaphysics, that Aristotle will discuss how many immaterial forms there are in “the theory about the ἀνελίττουσαι”,Cf. Alexander of Aphrodisias, In Metaphysica, 146.8–9 Golitsis (= 179.1–2 Hayduck): Καὶ εἰ ἔστιν ὅλως ἄυλά τινα εἴδη, ὁπόσα ταῦτά ἐστι […] ποιήσεται λόγον ἐν τῇ περὶ τῶν ἀνελιττουσῶν θεωρίᾳ (“And if there are any immaterial forms at all, he will discuss how many these are in the theory about the ἀνελίττουσαι”). i. e. in Λ.8, he certainly does not mean the term in the Aristotelian sense; for to arrive at a definite number of immaterial forms, one needs, in addition to the spheres in which the planets are fastened, not only the counteracting spheres but also the moving ones.The identification of the ἀνελίττουσαι with all the spheres that do not have a star – and, thus, their parallelism with Theophrastus’ ἄναστροι – was probably intended as a rectification by Sosigenes of a previous account.Simplicius, In De caelo, 493.17–20, says that the three spheres posited by Eudoxus for the sun were called starless by Theophrastus, as well as “bringing back in turn” (ἀνταναφέρουσαι), i. e. the lower spheres, and “reversing” (ἀνελίττουσαι), i. e. the higher spheres (διὰ τοῦτο οὖν ἐν τρισὶν αὐτὸν φέρεσθαι ἔλεγον σφαίραις, ἃς ὁ Θεόφραστος ἀνάστρους ἐκάλει ὡς μηδὲν ἐχούσας ἄστρον καὶ ἀνταναφερούσας μὲν πρὸς τὰς κατωτέρω, ἀνελισσούσας δὲ πρὸς τὰς ἀνωτέρω). The information that Theophrastus called those spheres ἀνταναφέρουσαι that Aristotle called ἀνελίττουσαι comes from Sosigenes, as is made clear by the quotation at 504.4–9: “Sosigenes also adds the following when he says that ‘it is clear from what has been said that Aristotle calls [the spheres] reversing [anelittousai] in one sense, whereas Theophrastus calls them bringing back in turn [antanapherousai] in another. Indeed, both [designations] apply to them. That is to say, [these spheres] reverse the upper motions and bring back in turn the poles of the spheres beneath by removing the former [motions] and bringing the latter to what is required” (προστίθησι δὲ καὶ τοῦτο ὁ Σωσιγένης δῆλον εἶναι λέγων ἐκ τῶν εἰρημένων, ὅτι κατ’ ἄλλο μὲν ἀνελιττούσας αὐτὰς ὁ Ἀριστοτέλης προσαγορεύει, κατ’ ἄλλο δὲ Θεόφραστος ἀνταναφερούσας· ἔστι γὰρ ἄμφω περὶ αὐτάς· ἀνελίττουσι γὰρ τὰς τῶν ὑπεράνω κινήσεις καὶ ἀνταναφέρουσι τοὺς τῶν ὑπ’ αὐτοὺς σφαιρῶν πόλους, τὰς μὲν ἀφαιροῦσαι, τοὺς [scripsi: τὰς codd.] δὲ εἰς τὸ δέον καθιστῶσαι). Translation by Bowen (2013), adapted. Of course, the claim that all three Eudoxean spheres of the sun are starless is wrong. I find it difficult to explain this as a misleading account by Simplicius. Rather, ἃς ὁ Θεόφραστος … ἀνωτέρω looks like an erroneous gloss based on a parallel reading of 491.17–20 (λέγει οὖν ὅτι ἡ σφαῖρα ἡ τὸ ἓν ἄστρον ἔχουσα τὸ πλανᾶσθαι λεγόμενον ἐν πολλαῖς σφαίραις ταῖς ἀνελιττούσαις καλουμέναις ἤ, ὡς ὁ Θεόφραστος αὐτὰς καλεῖ, ταῖς ἀνάστροις ἐνδεδεμένη φέρεται τελευταία οὖσα τῆς ὅλης αὐτῶν συντάξεως) and 504.4–9, since it reproduces the erroneous τὰς instead of τοὺς (sc. πόλους). Before Sosigenes, Adrastus of Aphrodisias (or, at any rate, his contemporary Theon of Smyrna)As said earlier, Adrastus’ concise exposition of the astronomical excursus in Λ.8 is integrated into Theon’s On Mathematics Useful for Understanding Plato. There is some discussion as to how much Theon draws from Adrastus for describing the concentric planetary theory. See lately Petrucci (2012), who maximizes Adrastus’ presence in Theon’s exposition. identified as ἀνελίττουσαι a class of spheres more restricted than Aristotle’s and, what is more, a class of spheres that he took to be non-concentric and to “move according to a certain proper motion about their own centres” (i. e. epicycles). Once his concise exposition of the astronomical excursus of Λ.8 has been completed, Adrastus goes on to explain:Since they [i. e. Eudoxus, Callippus and Aristotle] thought that it is natural that everything should move in the same direction [i. e. westward] but observed that the planets move also in the opposite direction too, they assumed that among the moving [spheres] there must be some other spheres, obviously solid, which by their motion will reverse the moving [spheres] in the opposite direction, since they touch them, in the way the so-called rollers [touch larger whoops] in the spherical machines: while they move according to a certain proper motion about their [own] centres, they move in the opposite direction and reverse what are underneath them and are attached to them beneath because of the entanglement of their cogs. It is indeed natural for all the spheres to move in the same direction, as they are carried around by the outermost [sphere], but because of the ordering of their positions, of their places and their sizes, they move, some slower, some faster, in the opposite direction according to their own motion and about their own axes that are oblique to the sphere of the fixed [stars]. The result is that, although the stars [i. e. the planets] that are fastened in them are carried in accordance with the simple and uniform motion [of the spheres], they seem to perform per accidens some composite, non-uniform and intricate motions. And they describe [against the background of the fixed stars] circles of various sorts, some being concentric [i. e. they account for their diurnal motion], some eccentric [i. e. they account for their latitudinal motion along the ecliptic], and some epicyclic [i. e. they account for their motion in depth].Theon, Expositio rerum mathematicarum …, 180.13–181.9: Ἐπεὶ γὰρ ᾤοντο κατὰ φύσιν μὲν εἶναι τὸ ἐπὶ τὸ αὐτὸ φέρεσθαι πάντα, ἑώρων δὲ τὰ πλανώμενα καὶ ἐπὶ τοὐναντίον μεταβαίνοντα, ὑπέλαβον δεῖν εἶναι μεταξὺ φερουσῶν ἑτέρας τινάς, στερεὰς δηλονότι, σφαίρας, αἳ τῇ ἑαυτῶν κινήσει ἀνελίξουσι τὰς φερούσας ἐπὶ τοὐναντίον, ἐφαπτομένας αὐτῶν, ὥσπερ ἐν ταῖς μηχανοσφαιροποιίαις τὰ λεγόμενα τυμπάνια, κινούμενα περὶ τὸ κέντρον ἰδίαν τινὰ κίνησιν, τῇ παρεμπλοκῇ τῶν ὀδόντων εἰς τοὐναντίον κινεῖν καὶ ἀνελίττειν τὰ ὑποκείμενα καὶ προσυφαπτόμενα. ἔστι δὲ τὸ μὲν φυσικὸν ὄντως, πάσας τὰς σφαίρας φέρεσθαι μὲν ἐπὶ τὸ αὐτό, περιαγομένας ὑπὸ τῆς ἐξωτάτω, κατὰ δὲ τὴν ἰδίαν κίνησιν διὰ τὴν τάξιν τῆς θέσεως καὶ τοὺς τόπους καὶ τὰ μεγέθη τὰς μὲν θᾶττον, τὰς δὲ βραδύτερον ἐπὶ τὰ ἐναντία φέρεσθαι περὶ ἄξονας ἰδίους καὶ λελοξωμένους πρὸς τὴν τῶν ἀπλανῶν σφαῖραν· ὥστε τὰ ἐν αὐταῖς ἄστρα τῇ τούτων ἁπλῇ καὶ ὁμαλῇ κινήσει φερόμενα κατὰ συμβεβηκὸς αὐτὰ δοκεῖν συνθέτους καὶ ἀνωμάλους καὶ ποικίλας τινὰς ποιεῖσθαι φοράς. καὶ γράφουσί τινας κύκλους διαφόρους, τοὺς μὲν ἐγκέντρους, τοὺς δὲ ἐκκέντρους, τοὺς δὲ ἐπικύκλους. What comes next (181.9–11: ἕνεκα δὲ τῆς ἐννοίας τῶν λεγομένων ἐπὶ βραχὺ καὶ περὶ τούτων ἐκθετέον, κατὰ τὸ δοκοῦν ἡμῖν ἀναγκαῖον εἰς τὰς σφαιροποιίας διάγραμμα) suggests that up to that point Theon was quoting from a source that, pace Petrucci, did not provide geometrical illustrations. Theon’s diagram (see Petrucci [2015], p. 179 for a helpful reconstruction) clearly identifies the epicycle as the proper motion of the planet.According to this account, the ἀνελίττουσαι are spheres that accomplish the epicyclic motion, which is per se uniform and in the same direction as the natural motion of the outermost sphere (i. e. westward), but at the same time move in the opposite direction (i. e. eastward) the two moving spheres between which they are placed (the lower one belongs to the next planet); the result for the observer of the wandering star is its intricate (ποικίλη) and per accidens non-uniform motion.ποικίλη (φορά) is reminiscent of Plato’s Timaeus, 39d2: ὡς ἔπος εἰπεῖν οὐκ ἴσασιν χρόνον ὄντα τὰς τούτων (sc. τῶν ἄστρων [without the moon and the sun]) πλάνας, πλήθει μὲν ἀμηχάνῳ χρωμένας, πεποικιλμένας δὲ θαυμαστῶς. The ἀνελίττουσαι are the last spheres of each planetary system and are obviously not hollow, like the moving spheres, but solid in order that they can bear the heavenly body of the wandering stars.Cf. also Theon, Expositio rerum mathematicarum …, 178.17–179.1: “How can it indeed be possible that bodies of such size are fastened in bodiless circles? It is appropriate that there are some spheres constituted of the fifth body which are placed and move across the depth of the whole heaven; some of them are higher, whereas others are arranged below them, and some are bigger, whereas others are smaller, and moreover some are hollow, whereas the ones in their depth are in turn solid; the planets are fixed in these [latter] spheres, like fixed stars” (πῶς γὰρ καὶ δυνατὸν ἐν κύκλοις ἀσωμάτοις τηλικαῦτα σώματα δεδέσθαι; σφαίρας δέ τινας εἶναι τοῦ πέμπτου σώματος οἰκεῖον ἐν τῷ βάθει τοῦ παντὸς οὐρανοῦ κειμένας τε καὶ φερομένας, τὰς μὲν ὑψηλοτέρας, τὰς δὲ ὑπ’ αὐτὰς τεταγμένας, καὶ τὰς μὲν μείζονας, τὰς δὲ ἐλάττονας, ἔτι δὲ τὰς μὲν κοίλας, τὰς δ’ ἐν τῷ βάθει τούτων πάλιν στερεάς, ἐν αἷς ἀπλανῶν δίκην ἐνεστηριγμένα τὰ πλανητά …).It is obvious that Adrastus tried to adjust the ἀνελίττουσαι of Λ.8 to the epicycles explaining the retrograde and prograde motions of the planets, as well as their apogees and perigees, which were first conceived of in the second century B. C. by Hipparchus of Nicaea and were dominant in the theory of planetary motion in Adrastus’ time. Such an adjustment was possible only through an obvious misinterpretation of Aristotle’s statement at 1074a1–3 (καθ᾽ ἕκαστον τῶν πλανωμένων ἑτέρας σφαίρας μιᾷ ἐλάττονας εἶναι τὰς ἀνελιττούσας), as if it read “there should be for each of the wandering stars other spheres too, one in number [and] lesser [in size than its moving spheres], that is, the counteracting spheres”. The result was that there should be one ἀνελίττουσα in each planetary system, namely the sphere in which the star is fastened. This far-fetched interpretation is the exact opposite of the interpretation of Sosigenes, who, by appealing to the authority of Theophrastus, identified the ἀνελίττουσαι with the starless spheres.Adrastus was a Platonizing Aristotelian and was apparently interested in presenting the theory of planetary motion of the ancient Platonist astronomers and Aristotle as more “accurate” than it actually was. But his interpretation could not be retained as valid by any diligent reader of Λ.8 – e. g. it cannot possibly provide the Aristotelian tallies of celestial spheres. Sosigenes probably conceived of his work Περὶ τῶν ἀνελιττουσῶν also as a response to any account which tried to make sense of the astronomical excursus of Λ.8 by combining concentric, eccentric and epicyclic spheres and motions. Sosigenes endeavoured to show what the ἀνελίττουσαι (stricto sensu) really are according to Aristotle by providing thanks to his own ingenuity a solid physical interpretation of the Eudoxean scheme of concentric spheres and a geometrical reconstruction that proved the necessity of adding the counteracting spheres.Sosigenes believed that Aristotle used two different words, namely ἀνελίττουσας and ἀποκαθιστώσας, in order to capture two different functions performed by the counteracting spheres: the rectilinearization of the axis of the first moving sphere of the lower planet with the axis of the sphere of the fixed stars (ἀποκαθιστᾶν) and subsequently the restoration of the diurnal speed to this and the rest of its moving spheres (ἀνελίττειν); cf. Simplicius, On Aristotle’s On the Heavens, 498.4–10 (quoting Sosigenes): “It is necessary for these spheres, which Aristotle calls counteracting, to be added to the hypotheses for two reasons: so that there will be the proper position for both the fixed sphere for each planet and for the spheres under it; and so that the proper speed will be present in all the spheres. For it was necessary both that a sphere move in the same way as the sphere of the fixed around the same axis as it and that it rotate in an equal time, but neither [property] could possibly belong to it without the addition of the spheres mentioned by Aristotle” (δυοῖν ἕνεκα ταύτας, ἃς ἀνελιττούσας καλεῖ, φησὶν ἀναγκαῖον εἶναι προσγενέσθαι ταῖς ὑποθέσεσιν, ἵνα τε θέσις ἡ οἰκεία εἴη τῇ τε καθ’ ἕκαστον ἀπλανεῖ καὶ ταῖς ὑπ’ αὐτῇ, καὶ ὅπως τάχος τὸ οἰκεῖον ἐν πάσαις ὑπάρχοι· ἔδει γὰρ τήν γε ὁμοίαν τῇ τῶν ἀπλανῶν [ἢ ἄλλῃ τινὶ σφαίρᾳ delevi cum Bowen] περί τε τὸν αὐτὸν ἄξονα ἐκείνῃ φέρεσθαι καὶ χρόνῳ ἴσῳ αὐτὴν περιστρέφεσθαι, ὧν οὐδὲν ἄνευ τῆς προσθέσεως τῶν ὑπὸ Ἀριστοτέλους λεγομένων σφαιρῶν ὑπάρξαι δυνατόν). Translation by Mueller (2005). At first glance, this was a mere exegetical task. For Sosigenes followed the astronomical science of his day and had no other verdict to pronounce than this: the model that tried to account for the phenomenal planetary motions by means of the ἀνελίττουσαι (now meant lato sensu) had failed:The spherical construction by means of the ἀνελίττουσαι is approximately as described. It cannot preserve the phenomena, as Sosigenes also remarks critically when he says: “Nevertheless, the [hypotheses] of the Eudoxans do not in fact save the phenomena, not as they have been recorded later, nor even as they had been known before and accepted by those same people. And what necessity is there to speak about the other [phenomena], some of which even Callippus of Cyzicus tried to preserve when Eudoxus was not successful, whether or not [Callippus] did preserve [them]?”Simplicius, In De caelo, 504.16–22: Τοιαύτη τίς ἐστιν ἡ διὰ τῶν ἀνελιττουσῶν σφαιροποιία μὴ δυνηθεῖσα διασῶσαι τὰ φαινόμενα, ὡς καὶ ὁ Σωσιγένης ἐπισκήπτει λέγων· “οὐ μὴν αἵ γε τῶν περὶ Εὔδοξον σώζουσι τὰ φαινόμενα, οὐχ ὅπως τὰ ὕστερον καταληφθέντα, ἀλλ’ οὐδὲ τὰ πρότερον γνωσθέντα καὶ ὑπ’ αὐτῶν ἐκείνων πιστευθέντα. καὶ τί δεῖ περὶ τῶν ἄλλων λέγειν, ὧν ἔνια καὶ Κάλλιππος ὁ Κυζικηνὸς Εὐδόξου μὴ δυνηθέντος ἐπειράθη διασῶσαι, εἴπερ ἄρα καὶ διέσωσεν;”. Translation by Bowen (2013), modified. Bowen supplies ‘spheres’ (αἵ γε, sc. σφαῖραι) instead of ‘hypotheses’ (αἴ γε, sc. ὑποθέσεις) supplied by Mueller (2005). He also takes the quote from Sosigenes to be ending with πιστευθέντα on the grounds that “its syntax does not require such an attribution [i. e. to Sosigenes]” (p. 165); but it does not require either that the rest of the passage be attributed to Simplicius. Until 506.8sqq., where the testimony of Porphyry is adduced, there is no real indication that Simplicius is commenting by himself (even if he does not always “quote” Sosigenes).Callippus’ rectifications were only the beginning of a critical distance vis-à-vis the theory of Eudoxus. Sosigenes insists on the failure of this theory to account for the most important empirical observation that needed to be “saved”, namely the variation of planets in distance, which is particularly evident in the cases of Mars and Venus. We are told that a younger contemporary of Callippus, namely Autolycus of Pitane, undertook to provide a rectification that would be explanatory also of this phenomenon but with no satisfying results.Cf. Simplicius, In De caelo, 504.22–26: “But this very thing, which is also manifest to the eye, none of them until Autolycus of Pitane conceived of showing it by means of hypotheses, although not even Autolycus himself was able to establish it […]. What I mean is that there are times when the planets appear near, but there are times when they appear to have moved away from us” (ἀλλ’ αὐτό γε τοῦτο, ὅπερ καὶ τῇ ὄψει πρόδηλόν ἐστιν, οὐδεὶς αὐτῶν μέχρι καὶ Αὐτολύκου τοῦ Πιταναίου ἐπεβάλετο διὰ τῶν ὑποθέσεων ἐπιδεῖξαι, καίτοι οὐδὲ αὐτὸς Αὐτόλυκος ἠδυνήθη […]. ἔστι δέ, ὃ λέγω, τὸ ποτὲ μὲν πλησίον, ἔστι δὲ ὅτε ἀποκεχωρηκότας ἡμῶν αὐτοὺς φαντάζεσθαι). Translation by Mueller (2005), modified. We are also told that Callippus’ fellow countryman and master, namely Polemarchus, was aware of the inequality of distances of each planet in relation to itself but was completely unready to abandon the principle of concentricity of all celestial spheres.Cf. Simplicius, In De caelo, 505.19–23: “But yet it is not admissible to say that the inequality of the distances of each [planet] in relation to itself really escaped their notice. For, evidently, Polemarchus of Cyzicus recognizes it but neglects it on the grounds that it is not perceptible, because he loves more the positioning of the spheres themselves in the universe about its very centre” (ἀλλὰ μὴν οὐδὲ ὡς ἐλελήθει γε αὐτοὺς ἡ ἀνισότης τῶν ἀποστημάτων ἑκάστου πρὸς ἑαυτόν, ἐνδέχεται λέγειν. Πολέμαρχος γὰρ ὁ Κυζικηνὸς γνωρίζων μὲν αὐτὴν φαίνεται, ὀλιγωρῶν δὲ ὡς οὐκ αἰσθητῆς οὔσης διὰ τὸ ἀγαπᾶν μᾶλλον τὴν περὶ αὐτὸ τὸ μέσον ἐν τῷ παντὶ τῶν σφαιρῶν αὐτῶν θέσιν). Translation by Bowen (2013), slightly modified. Nevertheless, in this short history of the reception of the concentric theory of Eudoxus, Aristotle’s own voice is presented by Sosigenes as dissonant:Aristotle, too, is obviously aware [of this phenomenon] in his Problemata physica, when he sets forth further difficulties for the hypotheses of the astronomers, [difficulties] which derive from the fact that the sizes of the planets do not appear to be the same.The Problemata physica transmitted under Aristotle’s name do not contain such a discussion. Thus, he was not completely satisfied with the anelittousai, even if [the thesis] that they are concentric with the universe and move about its centre won him over.Heiberg ends here the quote from Sosigenes. But there is no reason to think that it was Simplicius who thought to adduce the testimony of Λ.8 ad extra, when Sosigenes had practically provided already a commentary on the astronomical excursus. And, further, from what he says in Metaphysics Lambda, he is evidently not one to think that the motions of the wandering stars have been stated adequately by the astronomers up to and during his time. At any rate, he speaks in the following manner: “We will now say what some of the mathematicians say for the sake of our thinking, so that we may have some definite number [of motions] to grasp in thought. But, as for the rest, we must speak in part having inquired ourselves, in part having learned from the inquirers, if something different from what is now said appears to those who deal with those matters; and we must welcome both but believe the more accurate”. But, also in the same book, once he has enumerated all the motions together, he adds: “Let the number of the motions be this many, so that we may probably think that there are just as many substances and unmoved and perceptible principles;ὥστε καὶ τὰς οὐσίας καὶ τὰς ἀρχὰς τὰς ἀκινήτους καὶ τὰς αἰσθητὰς [: παρὰ τὰς αἰσθητὰς scripsi] τοσαύτας εὔλογον ὑπολαβεῖν: Sosigenes apparently took the “perceptible principles” to be the heavenly spheres. for let [demonstrative] necessity be left for more powerful [astronomers] to speak of”. His ‘let … be’, ‘reasonable’ and leave for others ‘more powerful’, show his uncertainty about these [matters].Simplicius, In De caelo, 505.23–506.8: Δηλοῖ δὲ καὶ Ἀριστοτέλης ἐν τοῖς Φυσικοῖς προβλήμασι προσαπορῶν ταῖς τῶν ἀστρολόγων ὑποθέσεσιν ἐκ τοῦ μηδὲ ἴσα τὰ μεγέθη τῶν πλανήτων φαίνεσθαι. οὕτως οὐ παντάπασιν ἠρέσκετο ταῖς ἀνελιττούσαις, κἂν τὸ ὁμοκέντρους οὔσας τῷ παντὶ περὶ τὸ μέσον αὐτοῦ κινεῖσθαι ἐπηγάγετο αὐτόν. καὶ μέντοι καὶ ἐξ ὧν ἐν τῷ Λ τῶν Μετὰ τὰ φυσικά φησι, φανερός ἐστιν οὐχ ἡγούμενος αὐτάρκως ὑπὸ τῶν μέχρι καὶ καθ’ αὑτὸν ἀστρολόγων εἰρῆσθαι τὰ περὶ τὰς κινήσεις τῶν πλανωμένων. λέγει γοῦν ὧδέ πως· “νῦν μὲν οὖν ἡμεῖς, ἃ λέγουσι τῶν μαθηματικῶν τινες, ἐννοίας χάριν λέγομεν, ὅπως ᾖ τι τῇ διανοίᾳ πλῆθος ὡρισμένον ὑπολαμβάνειν, τὸ δὲ λοιπὸν τὰ μὲν ζητοῦντας αὐτοὺς δεῖ, τὰ δὲ πυνθανομένους <παρὰ> [addidi cum Metaph.] τῶν ζητούντων, ἐάν τι φαίνηται παρὰ τὰ νῦν εἰρημένα τοῖς ταῦτα πραγματευομένοις, φιλεῖν μὲν ἀμφοτέρους, πείθεσθαι δὲ τοῖς ἀκριβεστέροις.” ἀλλὰ καὶ καταριθμησάμενος ἐν τῷ αὐτῷ βιβλίῳ τὰς συμπάσας φορὰς ἐπάγει “τὸ μὲν πλῆθος τῶν φορῶν [: σφαιρῶν Metaph.] ἔστω τοσοῦτον, ὥστε καὶ τὰς οὐσίας καὶ τὰς ἀρχὰς τὰς ἀκινήτους καὶ τὰς αἰσθητὰς τοσαύτας εὔλογον ὑπολαβεῖν· τὸ γὰρ ἀναγκαῖον ἀφείσθω τοῖς ἰσχυροτέροις λέγειν.” τό τε οὖν ‘ἔστω’ καὶ τὸ ‘εὔλογον’ καὶ τὸ ἄλλοις ‘ἰσχυροτέροις’ καταλείπειν τὸν περὶ αὐτὰ ἐνδοιασμὸν ἐνδείκνυται.According to this account, Aristotle refrained from laying too much value on the theory of the ἀνελίττουσαι. Although Sosigenes rectified Adrastus’ account and showed that Aristotle did not really know about eccentric circles and epicycles in his theory of planetary motion, he was at the same time trying to “save” the Master, as any genuine Peripatetic philosopher would do, against later developments of astronomical science. Aristotle did not use epicycles, accepted the concentric spheres but was nevertheless ultimately unsatisfied with Eudoxus’ theory; he expressed his reservations and knew that more accurate theories of planetary motion were to come. It would be unfair to accuse him of provisorily adopting the only available theory that accounted for the apparent orbits of the planets by preserving the primitive explanatory principle of uniform motion. Since it fitted the spirit of sumphonia, in this particular case the sumphonia of Aristotle with future astronomical theory, Simplicius wholeheartedly espoused Sosigenes’ interpretation.Cf. Simplicius, In De caelo, 506.8–16: “Thus, giving credence to Aristotle, we must follow more those who came later, on the grounds that they save the phenomena more effectively, even if they do not save them completely, since neither did [the Eudoxans] know so many phenomena – on account of the fact that the observations sent by Callisthenes from Babylon, when Aristotle required this of him, had not yet arrived in Greece (Porphyry reports that these [observations] were preserved for 31,000 years up to the times of Alexander of Macedon) – nor were they able to demonstrate by means of their hypotheses all [the phenomena] which they did know” (τῷ οὖν Ἀριστοτέλει πειθομένους ἀκολουθεῖν χρὴ μᾶλλον τοῖς μεταγενεστέροις ὡς μᾶλλον σώζουσι τὰ φαινόμενα, κἂν εἰ μηδὲ οὗτοι τελέως διασώζωσιν, ἐκείνων μήτε τοσαῦτα ἐπισταμένων φαινόμενα διὰ τὸ μήπω τὰς ὑπὸ Καλλισθένους ἐκ Βαβυλῶνος ἐκπεμφθείσας τηρήσεις ἥκειν εἰς τὴν Ἑλλάδα Ἀριστοτέλους τοῦτο ἐπισκήψαντος αὐτῷ, ἃς ἱστορεῖ Πορφύριος ἐτῶν εἶναι χιλίων καὶ μυριάδων τριῶν ἕως τῶν Ἀλεξάνδρου τοῦ Μακεδόνος σωζομένας χρόνων, μήτε, ὁπόσα ἠπίσταντο, διὰ τῶν ὑποθέσεων ἐπιδεικνύναι δυναμένων). Translation by Bowen (2013), modified. Unlike Mueller (2005), Bowen takes the first sentence as concessive (“Thus, while we give credence to Aristotle, we must follow …”) and thus bypasses the spirit of sumphōnia. Simplicius here takes over what Sosigenes said in the beginning of the quotation (cf. 504.17–20: “The [hypotheses] of the Eudoxans do not in fact save the phenomena, not as they have been recorded later, nor even as they had been known before and accepted by those same people”); this indicates that the quotation has just ended.Although Sosigenes criticized Adrastus’ account of the ἀνελίττουσαι, he ultimately had a similar objective. For he could have criticized Adrastus’ account (or, for that matter, any ahistorical exposition of Λ.8) without bothering to attribute to Aristotle the introduction of the counteracting spheres. It seems, however, that, just as Adrastus was trying to save the ancient authorities of Eudoxus, Callippus and Aristotle, Sosigenes was trying to save the authority of Aristotle alone. But he used a different and much more subtle strategy to accomplish his aim. His insistence upon making Aristotle, in the absence of any authoritative report and contrary to Adrastus’ and Theon’s accounts, the sole inventor of the counteracting spheres, which were necessary for the whole system of concentric spheres to work, was part of Sosigenes’ strategy: by conceiving of the ἀνελίττουσαι stricto sensu in order to complete the theory of his peer astronomers, Aristotle would show himself to be an able astronomer by the standards of his own time; by taking guard against the hypothesis of the ἀνελίττουσαι lato sensu, Aristotle would deserve the respect of philosophers of all times. For, the more accurate theories of planetary motion were yet to come. And just like the Master with regard to the astronomical “hypothesis” of his own time, the Exegete was ultimately to show himself critical of the alternative hypotheses of eccentric spheres and epicycles:Sosigenes cleverly raises no small number of other astronomical problems for these [i. e. the eccentric and the epicyclic] hypotheses too, problems which would belong to another leisure to examine.Simplicius, In De caelo, 510.24–26: Καὶ ἄλλας δὲ ἀστρονομικὰς ἀπορίας οὐκ ὀλίγας ὁ Σωσιγένης ἀπορεῖ καὶ πρὸς ταύτας τὰς ὑποθέσεις εὐφυῶς, ἃς ἄλλης ἂν εἴη σχολῆς ἐπισκέπτεσθαι. For Sosigenes’ critical attitude towards the eccentric and the epicyclic hypotheses, see characteristically 509.26–28: “Sosigenes brings these absurdities against these hypotheses; but he is also not satisfied with the hypothesis of the anelittousai for the reasons stated above” (καὶ ταῦτα τὰ ἄτοπα ἐπάγει ταύταις ταῖς ὑποθέσεσιν ὁ Σωσιγένης οὐδὲ τῇ τῶν ἀνελιττουσῶν ἀρεσκόμενος διὰ τὰς εἰρημένας ἔμπροσθεν αἰτίας). Translations by Bowen (2013), slightly modified. Sosigenes’ explanation of the eccentric and the epicyclic hypotheses is reproduced in Simplicius, In De caelo, 507.18–510.26. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Rhizomata de Gruyter

Aristotle as an Astronomer? Sosigenes’ Account of Metaphysics Λ.8

Golitsis, Pantelis
Rhizomata , Volume 11 (1): 12 – Aug 30, 2023
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de Gruyter
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© 2023 the author(s), published by De Gruyter.
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2196-5110
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DOI
10.1515/rhiz-2023-0006
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Abstract

Ever since the detailed discussion in the (lost) Περὶ τῶν ἀνελιττουσῶν of the Peripatetic exegete Sosigenes (second century CE),On Sosigenes, see Kupreeva (2018). Simplicius, In De caelo, 492.31–510.35 Heiberg extensively paraphrases and quotes Sosigenes’ Περὶ τῶν ἀνελιττουσῶν, as Moraux (1984), pp. 344–358, very well saw. it has been received wisdom that Aristotle was responsible for adding ‘counteracting’ spheres to Callippus’ system of planetary motions in order to construct an integrated account of the celestial domain from Callippus’ allegedly piecemeal account of the motion of the individual planets. I have argued elsewhere that there is no solid indication in Metaphysics Λ.8 for ascribing to Aristotle this contribution.See Golitsis (in press). Here I argue that the major aim of the discussion in Metaphysics Λ.8 is to grasp a precise number of self-existent immaterial substances (with which first philosophy is concerned) that provoke as final causes the rotation of the celestial spheres; and since Aristotle believed that, in all cases of natural motion, there is a one-to-one correspondence between a mover and a moved (or a mover and a motion), he needed to know how many celestial spheres there are. Such use of celestial theory for specific philosophical purposes is also present elsewhere, namely in On the Heavens II.12, where Aristotle points out that the fact that the sun and the moon move with fewer motions than the higher planets (whereas one would expect them to move with more motions) is due to their being unable, unlike the higher planets, to fully attain the Good, as they are farther removed from the sphere of the fixed stars. Sosigenes’ account has its very specific context – and setting out this context in sharp relief may help us understand what was at stake when Sosigenes made his ‘historical’ claims about Aristotle.One or two generations earlier than Sosigenes, the Peripatetic exegete Adrastus of Aphrodisias, whose concise exposition of the astronomical excursus in Λ.8 is integrated into Theon of Smyrna’s On Mathematics Useful for Understanding Plato, was ready to attribute the conception of the counteracting spheres to Aristotle or Eudoxus and Callippus:After this, [Aristotle] concludes that, if [the spheres] put together were going to account for the phenomena, there should be for each of the wandering [stars] other spheres too, less in number by one with regard to the moving [spheres], [that is,] the counteracting [spheres], proclaiming this opinion either as his own or as theirs [i. e. Eudoxus’ or Callippus].Theon, Expositio rerum mathematicarum ad legendum Platonem utilium, 180.8–12 Hiller (reproducing Adrastus’ account): Eἶτα δὲ ἐπιλογίζεται, εἰ μέλλοιεν συντεθεῖσαι σώζειν τὰ φαινόμενα, καθ’ ἕκαστον τῶν πλανωμένων καὶ ἑτέρας εἶναι σφαίρας μιᾷ ἐλάττονας τῶν φερουσῶν τὰς ἀνελιττούσας, εἴτε ἑαυτοῦ δόξαν ταύτην, εἴτε ἐκείνων ἀποφαινόμενος.It was Sosigenes who ascribed this conception to Aristotle with no hesitation.Cf. Simplicius, In De caelo, 498.1–4: “Aristotle having said these things in such a concise and clear way, Sosigenes praised his acumen and tried to find the use of the [counteracting] spheres added by him” (ταῦτα τοίνυν τοῦ Ἀριστοτέλους συντόμως οὕτω καὶ [D E F : οὕτως Heiberg cum Ab] σαφῶς εἰρηκότος ὁ Σωσιγένης ἐγκωμιάσας τὴν ἀγχίνοιαν αὐτοῦ ἐπεχείρησεν εὑρεῖν τὴν χρείαν τῶν ὑπ’ αὐτοῦ προστιθεμένων σφαιρῶν). In what follows, I would like to explain why he did so.According to Simplicius’ testimony, Sosigenes tried to explain by himself the position and function of the counteracting spheres as rotational components of the concentric planetary motions. This was not just a standard and expected endeavour by a Peripatetic exegete but also an important rectification of previous accounts of the planetary theory espoused by the Master. Eudemus’ Astronomical History, on which Sosigenes otherwise relied for his knowledge of ancient astronomical theories, especially of Eudoxus’, may have included a quite succinct and insufficient account of the counteracting spheres. At any rate, the absence of an authoritative account was probably the reason why Aristotle’s ἀνελίττουσαι were seriously distorted in the course of history. The very title of Sosigenes’ work Περὶ τῶν ἀνελιττουσῶν also reflects this distortion.The explanation of Aristotle’s counteracting spheres, as they are presented in Λ.8, was, as it can be deduced with certainty from Simplicius’ commentary on On the Heavens, an important part of Sosigenes’ work. The title of a work, however, reflects the whole: the ἀνελίττουσαι that Sosigenes primarily had in mind are not the counteracting spheres, as in Aristotle, but all concentric spheres. This is why his treatise began with a detailed exposition of the theory of Eudoxus, the first mathematician who allegedly responded to “Plato’s problem”, namely how the apparent orbits of the planets can be accounted for through the primitive explanatory principle of circular, uniform and ordered motion:Eudoxus of Cnidus is said to be the first among the Hellenes to have made use of such hypotheses – as Eudemus recorded in the second book of his Astronomical History and Sosigenes [recorded too] taking this over from Eudemus – after Plato, as Sosigenes says, put the following problem to those who were dealing with those issues, namely ‘given what circular, uniform and ordered motions will the phenomena of the wandering [stars] be preserved?’.Simplicius, In De caelo, 488.18–24: Καὶ πρῶτος τῶν Ἑλλήνων Εὔδοξος ὁ Κνίδιος, ὡς Εὔδημός τε ἐν τῷ δευτέρῳ τῆς Ἀστρολογικῆς ἱστορίας ἀπεμνημόνευσε καὶ Σωσιγένης παρὰ Εὐδήμου τοῦτο λαβών, ἅψασθαι λέγεται τῶν τοιούτων ὑποθέσεων Πλάτωνος, ὥς φησι Σωσιγένης, πρόβλημα τοῦτο ποιησαμένου τοῖς περὶ ταῦτα ἐσπουδακόσι, τίνων ὑποτεθεισῶν ὁμαλῶν καὶ <ἐγκυκλίων καὶ> [addidi] τεταγμένων κινήσεων διασωθῇ τὰ περὶ τὰς κινήσεις τῶν πλανωμένων φαινόμενα. See Zhmud (1998) for a critical discussion of whether the report about the problem set by Plato was present in Eudemus or rather only in Sosigenes.And further:We have said also earlier that Plato assigned without hesitation to the heavenly motions circularity, uniformity and order and put forward to the mathematicians the following problem: given what hypotheses will it be possible that the phenomena of the wandering [stars] be preserved by means of uniform, circular and ordered motions? And [we said following Sosigenes] that Eudoxus of Cnidus was the first to conceive of the hypotheses that use the so-called anelittousai spheres.Simplicius, In De caelo, 492.31–493.5: Kαὶ εἴρηται καὶ πρότερον, ὅτι ὁ Πλάτων ταῖς οὐρανίαις κινήσεσι τὸ ἐγκύκλιον καὶ ὁμαλὲς καὶ τεταγμένον ἀνενδοιάστως ἀποδιδοὺς πρόβλημα τοῖς μαθηματικοῖς προὔτεινε, τίνων ὑποτεθέντων δι’ ὁμαλῶν καὶ ἐγκυκλίων καὶ τεταγμένων κινήσεων δυνήσεται διασωθῆναι τὰ περὶ τοὺς πλανωμένους φαινόμενα, καὶ ὅτι πρῶτος Εὔδοξος ὁ Κνίδιος ἐπέβαλε ταῖς διὰ τῶν ἀνελιττουσῶν καλουμένων σφαιρῶν ὑποθέσεσι. Translation by Mueller (2005), modified. As it is unlikely that Eudemus used the word ὑπόθεσις for qualifying Eudoxus’ theory, we may surmise that Simplicius is here wholly relying on Sosigenes.The ἀνελίττουσαι are not only the name of a class of spheres, as in Aristotle, but have also evolved to become the name of a hypothesis. By the time of Sosigenes, this hypothesis had become an obsolete one, since it could not account for the planetary motions as accurately and as simply as the posterior hypotheses of the eccentric circles and the epicycles.Cf. Simplicius, In De caelo, 507.9–12: “Thus, in giving judgment against the hypothesis of turning [spheres] especially because it does not preserve the difference in depth, that is, the anomaly of the [planetary] motions, those who came later rejected the homocentric [turning] spheres and hypothesized eccentric and epicyclic ones” (κατεγνωκότες οὖν τῆς τῶν ἀνελιττουσῶν ὑποθέσεως οἱ μεταγενέστεροι μάλιστα διὰ τὸ τὴν κατὰ βάθος διαφορὰν καὶ τὴν ἀνωμαλίαν τῶν κινήσεων μὴ ἀποσώζειν τὰς μὲν ὁμοκέντρους ἀνελιττούσας παρῃτήσαντο, ἐκκέντρους δὲ καὶ ἐπικύκλους ὑπέθεντο). Translation by Bowen (2013). As Bowen explains, the term ἀνωμαλία is used here to signify the mean motion of a planet on its epicycle: the difference “in depth” is accounted for by the epicyclic anomaly, which is measured from the apogee of the epicycle.Simplicius himself takes ἀνελίττουσας lato sensu as equivalent to ὁμοκέντρους, as his expression ἡ διὰ τῶν ἀνελιττουσῶν σφαιροποιία readily makes clear.Simplicius, In De caelo, 504.16–17: “The spherical construction by means of the anelittousai, which [actually] cannot preserve the phenomena, is somewhat like this [i. e. as described]” (τοιαύτη τίς ἐστιν ἡ διὰ τῶν ἀνελιττουσῶν σφαιροποιία μὴ δυνηθεῖσα διασῶσαι τὰ φαινόμενα). Cf. also 488.7–9: “Those who hypothesize eccentric and epicyclic [motions], as well as those who hypothesize concentric [motions] (the ones called anelittousai), admit a greater number of motions [than one] for each [planet] in order that these [apparent motions] be saved” (διὰ γὰρ τὸ ταύτας σώζεσθαι πλείονας καθ’ ἕκαστον κινήσεις παραλαμβάνουσιν, οἱ μὲν ἐκκέντρους καὶ ἐπικύκλους, οἱ δὲ ὁμοκέντρους τὰς ἀνελιττούσας καλουμένας ὑποτιθέμενοι) and 493.8–11: “The hypothesis of anelittousai, which hypothesizes the anelittousai as concentric with the universe and not eccentric, as later [astronomers suppose], was pleasing to Aristotle, who thought that all heavenly [bodies] must move about the centre of the universe” (τῷ γὰρ Ἀριστοτέλει νομίζοντι δεῖν τὰ οὐράνια πάντα περὶ τὸ μέσον τοῦ παντὸς κινεῖσθαι ἤρεσκεν ἡ τῶν ἀνελιττουσῶν ὑπόθεσις ὡς ὁμοκέντρους τῷ παντὶ τὰς ἀνελιττούσας ὑποτιθεμένη καὶ οὐκ ἐκκέντρους, ὥσπερ οἱ ὕστερον). Translations by Bowen (2013), slightly modified. The loose sense of the term ἀνελίττουσαι has been put into light and explained through pars pro toto synecdoche by Mendell (2000), p. 92 nn. 40 and 41. Stricto sensu, however, the ἀνελίττουσαι were the spheres that Theophrastus had previously called ἄναστροι, namely the spheres that move for the sake of the star but do not themselves have the star:Thus, [Aristotle] says that the sphere having the single star said to wander moves by virtue of being fastened in many spheres called anelittousai or, as Theophrastus calls them, starless [spheres], being the last of the entire system of spheres.Simplicius, In De caelo, 491.17–20: Λέγει οὖν ὅτι ἡ σφαῖρα ἡ τὸ ἓν ἄστρον ἔχουσα τὸ πλανᾶσθαι λεγόμενον ἐν πολλαῖς σφαίραις ταῖς ἀνελιττούσαις καλουμέναις ἤ, ὡς ὁ Θεόφραστος αὐτὰς καλεῖ, ταῖς ἀνάστροις ἐνδεδεμένη φέρεται τελευταία οὖσα τῆς ὅλης αὐτῶν συντάξεως.Such are three of the four spheres of Saturn and Jupiter according to the system of Eudoxus, which of course did not include ἀνελίττουσαι strictiore sensu, that is, counteracting spheres. It is in virtue of the loose sense of ἀνελίττουσαι that Simplicius, obviously following Sosigenes, is justified in saying “The first who conceived of the hypotheses [that preserve the phenomena] through the so-called ἀνελίττουσαι spheres was Eudoxus of Cnidus”. Of course, the use of the term in the loose sense does not imply that Theophrastus himself identified the ἀνελίττουσαι of Λ.8 with all the spheres that move for the sake of a planet but do not contain the planet. It does show, however, that at some point the need was felt to distinguish between the ἀνελίττουσαι of Λ.8, the counteracting spheres which constitute only a subset of Theophrastus’ ἄναστροι, and the ἀνελίττουσαι as applying to all the spheres of a by then obsolete astronomical theory. Labelling all of them as ἀνελίττουσαι accentuated the contrast between that old account and the modern accounts, which do not posit counteracting spheres at all but deploy eccentric or epicyclic spheres. Sosigenes seems aware of this semantic development when he speaks of “the spheres which Aristotle calls counteracting” (ἃς ἀνελιττούσας καλεῖ).Simplicius, In De caelo, 498.3. When Alexander of Aphrodisias, who was a disciple of Sosigenes, says, in his commentary on the Metaphysics, that Aristotle will discuss how many immaterial forms there are in “the theory about the ἀνελίττουσαι”,Cf. Alexander of Aphrodisias, In Metaphysica, 146.8–9 Golitsis (= 179.1–2 Hayduck): Καὶ εἰ ἔστιν ὅλως ἄυλά τινα εἴδη, ὁπόσα ταῦτά ἐστι […] ποιήσεται λόγον ἐν τῇ περὶ τῶν ἀνελιττουσῶν θεωρίᾳ (“And if there are any immaterial forms at all, he will discuss how many these are in the theory about the ἀνελίττουσαι”). i. e. in Λ.8, he certainly does not mean the term in the Aristotelian sense; for to arrive at a definite number of immaterial forms, one needs, in addition to the spheres in which the planets are fastened, not only the counteracting spheres but also the moving ones.The identification of the ἀνελίττουσαι with all the spheres that do not have a star – and, thus, their parallelism with Theophrastus’ ἄναστροι – was probably intended as a rectification by Sosigenes of a previous account.Simplicius, In De caelo, 493.17–20, says that the three spheres posited by Eudoxus for the sun were called starless by Theophrastus, as well as “bringing back in turn” (ἀνταναφέρουσαι), i. e. the lower spheres, and “reversing” (ἀνελίττουσαι), i. e. the higher spheres (διὰ τοῦτο οὖν ἐν τρισὶν αὐτὸν φέρεσθαι ἔλεγον σφαίραις, ἃς ὁ Θεόφραστος ἀνάστρους ἐκάλει ὡς μηδὲν ἐχούσας ἄστρον καὶ ἀνταναφερούσας μὲν πρὸς τὰς κατωτέρω, ἀνελισσούσας δὲ πρὸς τὰς ἀνωτέρω). The information that Theophrastus called those spheres ἀνταναφέρουσαι that Aristotle called ἀνελίττουσαι comes from Sosigenes, as is made clear by the quotation at 504.4–9: “Sosigenes also adds the following when he says that ‘it is clear from what has been said that Aristotle calls [the spheres] reversing [anelittousai] in one sense, whereas Theophrastus calls them bringing back in turn [antanapherousai] in another. Indeed, both [designations] apply to them. That is to say, [these spheres] reverse the upper motions and bring back in turn the poles of the spheres beneath by removing the former [motions] and bringing the latter to what is required” (προστίθησι δὲ καὶ τοῦτο ὁ Σωσιγένης δῆλον εἶναι λέγων ἐκ τῶν εἰρημένων, ὅτι κατ’ ἄλλο μὲν ἀνελιττούσας αὐτὰς ὁ Ἀριστοτέλης προσαγορεύει, κατ’ ἄλλο δὲ Θεόφραστος ἀνταναφερούσας· ἔστι γὰρ ἄμφω περὶ αὐτάς· ἀνελίττουσι γὰρ τὰς τῶν ὑπεράνω κινήσεις καὶ ἀνταναφέρουσι τοὺς τῶν ὑπ’ αὐτοὺς σφαιρῶν πόλους, τὰς μὲν ἀφαιροῦσαι, τοὺς [scripsi: τὰς codd.] δὲ εἰς τὸ δέον καθιστῶσαι). Translation by Bowen (2013), adapted. Of course, the claim that all three Eudoxean spheres of the sun are starless is wrong. I find it difficult to explain this as a misleading account by Simplicius. Rather, ἃς ὁ Θεόφραστος … ἀνωτέρω looks like an erroneous gloss based on a parallel reading of 491.17–20 (λέγει οὖν ὅτι ἡ σφαῖρα ἡ τὸ ἓν ἄστρον ἔχουσα τὸ πλανᾶσθαι λεγόμενον ἐν πολλαῖς σφαίραις ταῖς ἀνελιττούσαις καλουμέναις ἤ, ὡς ὁ Θεόφραστος αὐτὰς καλεῖ, ταῖς ἀνάστροις ἐνδεδεμένη φέρεται τελευταία οὖσα τῆς ὅλης αὐτῶν συντάξεως) and 504.4–9, since it reproduces the erroneous τὰς instead of τοὺς (sc. πόλους). Before Sosigenes, Adrastus of Aphrodisias (or, at any rate, his contemporary Theon of Smyrna)As said earlier, Adrastus’ concise exposition of the astronomical excursus in Λ.8 is integrated into Theon’s On Mathematics Useful for Understanding Plato. There is some discussion as to how much Theon draws from Adrastus for describing the concentric planetary theory. See lately Petrucci (2012), who maximizes Adrastus’ presence in Theon’s exposition. identified as ἀνελίττουσαι a class of spheres more restricted than Aristotle’s and, what is more, a class of spheres that he took to be non-concentric and to “move according to a certain proper motion about their own centres” (i. e. epicycles). Once his concise exposition of the astronomical excursus of Λ.8 has been completed, Adrastus goes on to explain:Since they [i. e. Eudoxus, Callippus and Aristotle] thought that it is natural that everything should move in the same direction [i. e. westward] but observed that the planets move also in the opposite direction too, they assumed that among the moving [spheres] there must be some other spheres, obviously solid, which by their motion will reverse the moving [spheres] in the opposite direction, since they touch them, in the way the so-called rollers [touch larger whoops] in the spherical machines: while they move according to a certain proper motion about their [own] centres, they move in the opposite direction and reverse what are underneath them and are attached to them beneath because of the entanglement of their cogs. It is indeed natural for all the spheres to move in the same direction, as they are carried around by the outermost [sphere], but because of the ordering of their positions, of their places and their sizes, they move, some slower, some faster, in the opposite direction according to their own motion and about their own axes that are oblique to the sphere of the fixed [stars]. The result is that, although the stars [i. e. the planets] that are fastened in them are carried in accordance with the simple and uniform motion [of the spheres], they seem to perform per accidens some composite, non-uniform and intricate motions. And they describe [against the background of the fixed stars] circles of various sorts, some being concentric [i. e. they account for their diurnal motion], some eccentric [i. e. they account for their latitudinal motion along the ecliptic], and some epicyclic [i. e. they account for their motion in depth].Theon, Expositio rerum mathematicarum …, 180.13–181.9: Ἐπεὶ γὰρ ᾤοντο κατὰ φύσιν μὲν εἶναι τὸ ἐπὶ τὸ αὐτὸ φέρεσθαι πάντα, ἑώρων δὲ τὰ πλανώμενα καὶ ἐπὶ τοὐναντίον μεταβαίνοντα, ὑπέλαβον δεῖν εἶναι μεταξὺ φερουσῶν ἑτέρας τινάς, στερεὰς δηλονότι, σφαίρας, αἳ τῇ ἑαυτῶν κινήσει ἀνελίξουσι τὰς φερούσας ἐπὶ τοὐναντίον, ἐφαπτομένας αὐτῶν, ὥσπερ ἐν ταῖς μηχανοσφαιροποιίαις τὰ λεγόμενα τυμπάνια, κινούμενα περὶ τὸ κέντρον ἰδίαν τινὰ κίνησιν, τῇ παρεμπλοκῇ τῶν ὀδόντων εἰς τοὐναντίον κινεῖν καὶ ἀνελίττειν τὰ ὑποκείμενα καὶ προσυφαπτόμενα. ἔστι δὲ τὸ μὲν φυσικὸν ὄντως, πάσας τὰς σφαίρας φέρεσθαι μὲν ἐπὶ τὸ αὐτό, περιαγομένας ὑπὸ τῆς ἐξωτάτω, κατὰ δὲ τὴν ἰδίαν κίνησιν διὰ τὴν τάξιν τῆς θέσεως καὶ τοὺς τόπους καὶ τὰ μεγέθη τὰς μὲν θᾶττον, τὰς δὲ βραδύτερον ἐπὶ τὰ ἐναντία φέρεσθαι περὶ ἄξονας ἰδίους καὶ λελοξωμένους πρὸς τὴν τῶν ἀπλανῶν σφαῖραν· ὥστε τὰ ἐν αὐταῖς ἄστρα τῇ τούτων ἁπλῇ καὶ ὁμαλῇ κινήσει φερόμενα κατὰ συμβεβηκὸς αὐτὰ δοκεῖν συνθέτους καὶ ἀνωμάλους καὶ ποικίλας τινὰς ποιεῖσθαι φοράς. καὶ γράφουσί τινας κύκλους διαφόρους, τοὺς μὲν ἐγκέντρους, τοὺς δὲ ἐκκέντρους, τοὺς δὲ ἐπικύκλους. What comes next (181.9–11: ἕνεκα δὲ τῆς ἐννοίας τῶν λεγομένων ἐπὶ βραχὺ καὶ περὶ τούτων ἐκθετέον, κατὰ τὸ δοκοῦν ἡμῖν ἀναγκαῖον εἰς τὰς σφαιροποιίας διάγραμμα) suggests that up to that point Theon was quoting from a source that, pace Petrucci, did not provide geometrical illustrations. Theon’s diagram (see Petrucci [2015], p. 179 for a helpful reconstruction) clearly identifies the epicycle as the proper motion of the planet.According to this account, the ἀνελίττουσαι are spheres that accomplish the epicyclic motion, which is per se uniform and in the same direction as the natural motion of the outermost sphere (i. e. westward), but at the same time move in the opposite direction (i. e. eastward) the two moving spheres between which they are placed (the lower one belongs to the next planet); the result for the observer of the wandering star is its intricate (ποικίλη) and per accidens non-uniform motion.ποικίλη (φορά) is reminiscent of Plato’s Timaeus, 39d2: ὡς ἔπος εἰπεῖν οὐκ ἴσασιν χρόνον ὄντα τὰς τούτων (sc. τῶν ἄστρων [without the moon and the sun]) πλάνας, πλήθει μὲν ἀμηχάνῳ χρωμένας, πεποικιλμένας δὲ θαυμαστῶς. The ἀνελίττουσαι are the last spheres of each planetary system and are obviously not hollow, like the moving spheres, but solid in order that they can bear the heavenly body of the wandering stars.Cf. also Theon, Expositio rerum mathematicarum …, 178.17–179.1: “How can it indeed be possible that bodies of such size are fastened in bodiless circles? It is appropriate that there are some spheres constituted of the fifth body which are placed and move across the depth of the whole heaven; some of them are higher, whereas others are arranged below them, and some are bigger, whereas others are smaller, and moreover some are hollow, whereas the ones in their depth are in turn solid; the planets are fixed in these [latter] spheres, like fixed stars” (πῶς γὰρ καὶ δυνατὸν ἐν κύκλοις ἀσωμάτοις τηλικαῦτα σώματα δεδέσθαι; σφαίρας δέ τινας εἶναι τοῦ πέμπτου σώματος οἰκεῖον ἐν τῷ βάθει τοῦ παντὸς οὐρανοῦ κειμένας τε καὶ φερομένας, τὰς μὲν ὑψηλοτέρας, τὰς δὲ ὑπ’ αὐτὰς τεταγμένας, καὶ τὰς μὲν μείζονας, τὰς δὲ ἐλάττονας, ἔτι δὲ τὰς μὲν κοίλας, τὰς δ’ ἐν τῷ βάθει τούτων πάλιν στερεάς, ἐν αἷς ἀπλανῶν δίκην ἐνεστηριγμένα τὰ πλανητά …).It is obvious that Adrastus tried to adjust the ἀνελίττουσαι of Λ.8 to the epicycles explaining the retrograde and prograde motions of the planets, as well as their apogees and perigees, which were first conceived of in the second century B. C. by Hipparchus of Nicaea and were dominant in the theory of planetary motion in Adrastus’ time. Such an adjustment was possible only through an obvious misinterpretation of Aristotle’s statement at 1074a1–3 (καθ᾽ ἕκαστον τῶν πλανωμένων ἑτέρας σφαίρας μιᾷ ἐλάττονας εἶναι τὰς ἀνελιττούσας), as if it read “there should be for each of the wandering stars other spheres too, one in number [and] lesser [in size than its moving spheres], that is, the counteracting spheres”. The result was that there should be one ἀνελίττουσα in each planetary system, namely the sphere in which the star is fastened. This far-fetched interpretation is the exact opposite of the interpretation of Sosigenes, who, by appealing to the authority of Theophrastus, identified the ἀνελίττουσαι with the starless spheres.Adrastus was a Platonizing Aristotelian and was apparently interested in presenting the theory of planetary motion of the ancient Platonist astronomers and Aristotle as more “accurate” than it actually was. But his interpretation could not be retained as valid by any diligent reader of Λ.8 – e. g. it cannot possibly provide the Aristotelian tallies of celestial spheres. Sosigenes probably conceived of his work Περὶ τῶν ἀνελιττουσῶν also as a response to any account which tried to make sense of the astronomical excursus of Λ.8 by combining concentric, eccentric and epicyclic spheres and motions. Sosigenes endeavoured to show what the ἀνελίττουσαι (stricto sensu) really are according to Aristotle by providing thanks to his own ingenuity a solid physical interpretation of the Eudoxean scheme of concentric spheres and a geometrical reconstruction that proved the necessity of adding the counteracting spheres.Sosigenes believed that Aristotle used two different words, namely ἀνελίττουσας and ἀποκαθιστώσας, in order to capture two different functions performed by the counteracting spheres: the rectilinearization of the axis of the first moving sphere of the lower planet with the axis of the sphere of the fixed stars (ἀποκαθιστᾶν) and subsequently the restoration of the diurnal speed to this and the rest of its moving spheres (ἀνελίττειν); cf. Simplicius, On Aristotle’s On the Heavens, 498.4–10 (quoting Sosigenes): “It is necessary for these spheres, which Aristotle calls counteracting, to be added to the hypotheses for two reasons: so that there will be the proper position for both the fixed sphere for each planet and for the spheres under it; and so that the proper speed will be present in all the spheres. For it was necessary both that a sphere move in the same way as the sphere of the fixed around the same axis as it and that it rotate in an equal time, but neither [property] could possibly belong to it without the addition of the spheres mentioned by Aristotle” (δυοῖν ἕνεκα ταύτας, ἃς ἀνελιττούσας καλεῖ, φησὶν ἀναγκαῖον εἶναι προσγενέσθαι ταῖς ὑποθέσεσιν, ἵνα τε θέσις ἡ οἰκεία εἴη τῇ τε καθ’ ἕκαστον ἀπλανεῖ καὶ ταῖς ὑπ’ αὐτῇ, καὶ ὅπως τάχος τὸ οἰκεῖον ἐν πάσαις ὑπάρχοι· ἔδει γὰρ τήν γε ὁμοίαν τῇ τῶν ἀπλανῶν [ἢ ἄλλῃ τινὶ σφαίρᾳ delevi cum Bowen] περί τε τὸν αὐτὸν ἄξονα ἐκείνῃ φέρεσθαι καὶ χρόνῳ ἴσῳ αὐτὴν περιστρέφεσθαι, ὧν οὐδὲν ἄνευ τῆς προσθέσεως τῶν ὑπὸ Ἀριστοτέλους λεγομένων σφαιρῶν ὑπάρξαι δυνατόν). Translation by Mueller (2005). At first glance, this was a mere exegetical task. For Sosigenes followed the astronomical science of his day and had no other verdict to pronounce than this: the model that tried to account for the phenomenal planetary motions by means of the ἀνελίττουσαι (now meant lato sensu) had failed:The spherical construction by means of the ἀνελίττουσαι is approximately as described. It cannot preserve the phenomena, as Sosigenes also remarks critically when he says: “Nevertheless, the [hypotheses] of the Eudoxans do not in fact save the phenomena, not as they have been recorded later, nor even as they had been known before and accepted by those same people. And what necessity is there to speak about the other [phenomena], some of which even Callippus of Cyzicus tried to preserve when Eudoxus was not successful, whether or not [Callippus] did preserve [them]?”Simplicius, In De caelo, 504.16–22: Τοιαύτη τίς ἐστιν ἡ διὰ τῶν ἀνελιττουσῶν σφαιροποιία μὴ δυνηθεῖσα διασῶσαι τὰ φαινόμενα, ὡς καὶ ὁ Σωσιγένης ἐπισκήπτει λέγων· “οὐ μὴν αἵ γε τῶν περὶ Εὔδοξον σώζουσι τὰ φαινόμενα, οὐχ ὅπως τὰ ὕστερον καταληφθέντα, ἀλλ’ οὐδὲ τὰ πρότερον γνωσθέντα καὶ ὑπ’ αὐτῶν ἐκείνων πιστευθέντα. καὶ τί δεῖ περὶ τῶν ἄλλων λέγειν, ὧν ἔνια καὶ Κάλλιππος ὁ Κυζικηνὸς Εὐδόξου μὴ δυνηθέντος ἐπειράθη διασῶσαι, εἴπερ ἄρα καὶ διέσωσεν;”. Translation by Bowen (2013), modified. Bowen supplies ‘spheres’ (αἵ γε, sc. σφαῖραι) instead of ‘hypotheses’ (αἴ γε, sc. ὑποθέσεις) supplied by Mueller (2005). He also takes the quote from Sosigenes to be ending with πιστευθέντα on the grounds that “its syntax does not require such an attribution [i. e. to Sosigenes]” (p. 165); but it does not require either that the rest of the passage be attributed to Simplicius. Until 506.8sqq., where the testimony of Porphyry is adduced, there is no real indication that Simplicius is commenting by himself (even if he does not always “quote” Sosigenes).Callippus’ rectifications were only the beginning of a critical distance vis-à-vis the theory of Eudoxus. Sosigenes insists on the failure of this theory to account for the most important empirical observation that needed to be “saved”, namely the variation of planets in distance, which is particularly evident in the cases of Mars and Venus. We are told that a younger contemporary of Callippus, namely Autolycus of Pitane, undertook to provide a rectification that would be explanatory also of this phenomenon but with no satisfying results.Cf. Simplicius, In De caelo, 504.22–26: “But this very thing, which is also manifest to the eye, none of them until Autolycus of Pitane conceived of showing it by means of hypotheses, although not even Autolycus himself was able to establish it […]. What I mean is that there are times when the planets appear near, but there are times when they appear to have moved away from us” (ἀλλ’ αὐτό γε τοῦτο, ὅπερ καὶ τῇ ὄψει πρόδηλόν ἐστιν, οὐδεὶς αὐτῶν μέχρι καὶ Αὐτολύκου τοῦ Πιταναίου ἐπεβάλετο διὰ τῶν ὑποθέσεων ἐπιδεῖξαι, καίτοι οὐδὲ αὐτὸς Αὐτόλυκος ἠδυνήθη […]. ἔστι δέ, ὃ λέγω, τὸ ποτὲ μὲν πλησίον, ἔστι δὲ ὅτε ἀποκεχωρηκότας ἡμῶν αὐτοὺς φαντάζεσθαι). Translation by Mueller (2005), modified. We are also told that Callippus’ fellow countryman and master, namely Polemarchus, was aware of the inequality of distances of each planet in relation to itself but was completely unready to abandon the principle of concentricity of all celestial spheres.Cf. Simplicius, In De caelo, 505.19–23: “But yet it is not admissible to say that the inequality of the distances of each [planet] in relation to itself really escaped their notice. For, evidently, Polemarchus of Cyzicus recognizes it but neglects it on the grounds that it is not perceptible, because he loves more the positioning of the spheres themselves in the universe about its very centre” (ἀλλὰ μὴν οὐδὲ ὡς ἐλελήθει γε αὐτοὺς ἡ ἀνισότης τῶν ἀποστημάτων ἑκάστου πρὸς ἑαυτόν, ἐνδέχεται λέγειν. Πολέμαρχος γὰρ ὁ Κυζικηνὸς γνωρίζων μὲν αὐτὴν φαίνεται, ὀλιγωρῶν δὲ ὡς οὐκ αἰσθητῆς οὔσης διὰ τὸ ἀγαπᾶν μᾶλλον τὴν περὶ αὐτὸ τὸ μέσον ἐν τῷ παντὶ τῶν σφαιρῶν αὐτῶν θέσιν). Translation by Bowen (2013), slightly modified. Nevertheless, in this short history of the reception of the concentric theory of Eudoxus, Aristotle’s own voice is presented by Sosigenes as dissonant:Aristotle, too, is obviously aware [of this phenomenon] in his Problemata physica, when he sets forth further difficulties for the hypotheses of the astronomers, [difficulties] which derive from the fact that the sizes of the planets do not appear to be the same.The Problemata physica transmitted under Aristotle’s name do not contain such a discussion. Thus, he was not completely satisfied with the anelittousai, even if [the thesis] that they are concentric with the universe and move about its centre won him over.Heiberg ends here the quote from Sosigenes. But there is no reason to think that it was Simplicius who thought to adduce the testimony of Λ.8 ad extra, when Sosigenes had practically provided already a commentary on the astronomical excursus. And, further, from what he says in Metaphysics Lambda, he is evidently not one to think that the motions of the wandering stars have been stated adequately by the astronomers up to and during his time. At any rate, he speaks in the following manner: “We will now say what some of the mathematicians say for the sake of our thinking, so that we may have some definite number [of motions] to grasp in thought. But, as for the rest, we must speak in part having inquired ourselves, in part having learned from the inquirers, if something different from what is now said appears to those who deal with those matters; and we must welcome both but believe the more accurate”. But, also in the same book, once he has enumerated all the motions together, he adds: “Let the number of the motions be this many, so that we may probably think that there are just as many substances and unmoved and perceptible principles;ὥστε καὶ τὰς οὐσίας καὶ τὰς ἀρχὰς τὰς ἀκινήτους καὶ τὰς αἰσθητὰς [: παρὰ τὰς αἰσθητὰς scripsi] τοσαύτας εὔλογον ὑπολαβεῖν: Sosigenes apparently took the “perceptible principles” to be the heavenly spheres. for let [demonstrative] necessity be left for more powerful [astronomers] to speak of”. His ‘let … be’, ‘reasonable’ and leave for others ‘more powerful’, show his uncertainty about these [matters].Simplicius, In De caelo, 505.23–506.8: Δηλοῖ δὲ καὶ Ἀριστοτέλης ἐν τοῖς Φυσικοῖς προβλήμασι προσαπορῶν ταῖς τῶν ἀστρολόγων ὑποθέσεσιν ἐκ τοῦ μηδὲ ἴσα τὰ μεγέθη τῶν πλανήτων φαίνεσθαι. οὕτως οὐ παντάπασιν ἠρέσκετο ταῖς ἀνελιττούσαις, κἂν τὸ ὁμοκέντρους οὔσας τῷ παντὶ περὶ τὸ μέσον αὐτοῦ κινεῖσθαι ἐπηγάγετο αὐτόν. καὶ μέντοι καὶ ἐξ ὧν ἐν τῷ Λ τῶν Μετὰ τὰ φυσικά φησι, φανερός ἐστιν οὐχ ἡγούμενος αὐτάρκως ὑπὸ τῶν μέχρι καὶ καθ’ αὑτὸν ἀστρολόγων εἰρῆσθαι τὰ περὶ τὰς κινήσεις τῶν πλανωμένων. λέγει γοῦν ὧδέ πως· “νῦν μὲν οὖν ἡμεῖς, ἃ λέγουσι τῶν μαθηματικῶν τινες, ἐννοίας χάριν λέγομεν, ὅπως ᾖ τι τῇ διανοίᾳ πλῆθος ὡρισμένον ὑπολαμβάνειν, τὸ δὲ λοιπὸν τὰ μὲν ζητοῦντας αὐτοὺς δεῖ, τὰ δὲ πυνθανομένους <παρὰ> [addidi cum Metaph.] τῶν ζητούντων, ἐάν τι φαίνηται παρὰ τὰ νῦν εἰρημένα τοῖς ταῦτα πραγματευομένοις, φιλεῖν μὲν ἀμφοτέρους, πείθεσθαι δὲ τοῖς ἀκριβεστέροις.” ἀλλὰ καὶ καταριθμησάμενος ἐν τῷ αὐτῷ βιβλίῳ τὰς συμπάσας φορὰς ἐπάγει “τὸ μὲν πλῆθος τῶν φορῶν [: σφαιρῶν Metaph.] ἔστω τοσοῦτον, ὥστε καὶ τὰς οὐσίας καὶ τὰς ἀρχὰς τὰς ἀκινήτους καὶ τὰς αἰσθητὰς τοσαύτας εὔλογον ὑπολαβεῖν· τὸ γὰρ ἀναγκαῖον ἀφείσθω τοῖς ἰσχυροτέροις λέγειν.” τό τε οὖν ‘ἔστω’ καὶ τὸ ‘εὔλογον’ καὶ τὸ ἄλλοις ‘ἰσχυροτέροις’ καταλείπειν τὸν περὶ αὐτὰ ἐνδοιασμὸν ἐνδείκνυται.According to this account, Aristotle refrained from laying too much value on the theory of the ἀνελίττουσαι. Although Sosigenes rectified Adrastus’ account and showed that Aristotle did not really know about eccentric circles and epicycles in his theory of planetary motion, he was at the same time trying to “save” the Master, as any genuine Peripatetic philosopher would do, against later developments of astronomical science. Aristotle did not use epicycles, accepted the concentric spheres but was nevertheless ultimately unsatisfied with Eudoxus’ theory; he expressed his reservations and knew that more accurate theories of planetary motion were to come. It would be unfair to accuse him of provisorily adopting the only available theory that accounted for the apparent orbits of the planets by preserving the primitive explanatory principle of uniform motion. Since it fitted the spirit of sumphonia, in this particular case the sumphonia of Aristotle with future astronomical theory, Simplicius wholeheartedly espoused Sosigenes’ interpretation.Cf. Simplicius, In De caelo, 506.8–16: “Thus, giving credence to Aristotle, we must follow more those who came later, on the grounds that they save the phenomena more effectively, even if they do not save them completely, since neither did [the Eudoxans] know so many phenomena – on account of the fact that the observations sent by Callisthenes from Babylon, when Aristotle required this of him, had not yet arrived in Greece (Porphyry reports that these [observations] were preserved for 31,000 years up to the times of Alexander of Macedon) – nor were they able to demonstrate by means of their hypotheses all [the phenomena] which they did know” (τῷ οὖν Ἀριστοτέλει πειθομένους ἀκολουθεῖν χρὴ μᾶλλον τοῖς μεταγενεστέροις ὡς μᾶλλον σώζουσι τὰ φαινόμενα, κἂν εἰ μηδὲ οὗτοι τελέως διασώζωσιν, ἐκείνων μήτε τοσαῦτα ἐπισταμένων φαινόμενα διὰ τὸ μήπω τὰς ὑπὸ Καλλισθένους ἐκ Βαβυλῶνος ἐκπεμφθείσας τηρήσεις ἥκειν εἰς τὴν Ἑλλάδα Ἀριστοτέλους τοῦτο ἐπισκήψαντος αὐτῷ, ἃς ἱστορεῖ Πορφύριος ἐτῶν εἶναι χιλίων καὶ μυριάδων τριῶν ἕως τῶν Ἀλεξάνδρου τοῦ Μακεδόνος σωζομένας χρόνων, μήτε, ὁπόσα ἠπίσταντο, διὰ τῶν ὑποθέσεων ἐπιδεικνύναι δυναμένων). Translation by Bowen (2013), modified. Unlike Mueller (2005), Bowen takes the first sentence as concessive (“Thus, while we give credence to Aristotle, we must follow …”) and thus bypasses the spirit of sumphōnia. Simplicius here takes over what Sosigenes said in the beginning of the quotation (cf. 504.17–20: “The [hypotheses] of the Eudoxans do not in fact save the phenomena, not as they have been recorded later, nor even as they had been known before and accepted by those same people”); this indicates that the quotation has just ended.Although Sosigenes criticized Adrastus’ account of the ἀνελίττουσαι, he ultimately had a similar objective. For he could have criticized Adrastus’ account (or, for that matter, any ahistorical exposition of Λ.8) without bothering to attribute to Aristotle the introduction of the counteracting spheres. It seems, however, that, just as Adrastus was trying to save the ancient authorities of Eudoxus, Callippus and Aristotle, Sosigenes was trying to save the authority of Aristotle alone. But he used a different and much more subtle strategy to accomplish his aim. His insistence upon making Aristotle, in the absence of any authoritative report and contrary to Adrastus’ and Theon’s accounts, the sole inventor of the counteracting spheres, which were necessary for the whole system of concentric spheres to work, was part of Sosigenes’ strategy: by conceiving of the ἀνελίττουσαι stricto sensu in order to complete the theory of his peer astronomers, Aristotle would show himself to be an able astronomer by the standards of his own time; by taking guard against the hypothesis of the ἀνελίττουσαι lato sensu, Aristotle would deserve the respect of philosophers of all times. For, the more accurate theories of planetary motion were yet to come. And just like the Master with regard to the astronomical “hypothesis” of his own time, the Exegete was ultimately to show himself critical of the alternative hypotheses of eccentric spheres and epicycles:Sosigenes cleverly raises no small number of other astronomical problems for these [i. e. the eccentric and the epicyclic] hypotheses too, problems which would belong to another leisure to examine.Simplicius, In De caelo, 510.24–26: Καὶ ἄλλας δὲ ἀστρονομικὰς ἀπορίας οὐκ ὀλίγας ὁ Σωσιγένης ἀπορεῖ καὶ πρὸς ταύτας τὰς ὑποθέσεις εὐφυῶς, ἃς ἄλλης ἂν εἴη σχολῆς ἐπισκέπτεσθαι. For Sosigenes’ critical attitude towards the eccentric and the epicyclic hypotheses, see characteristically 509.26–28: “Sosigenes brings these absurdities against these hypotheses; but he is also not satisfied with the hypothesis of the anelittousai for the reasons stated above” (καὶ ταῦτα τὰ ἄτοπα ἐπάγει ταύταις ταῖς ὑποθέσεσιν ὁ Σωσιγένης οὐδὲ τῇ τῶν ἀνελιττουσῶν ἀρεσκόμενος διὰ τὰς εἰρημένας ἔμπροσθεν αἰτίας). Translations by Bowen (2013), slightly modified. Sosigenes’ explanation of the eccentric and the epicyclic hypotheses is reproduced in Simplicius, In De caelo, 507.18–510.26.

Journal

Rhizomata – de Gruyter

Published: Aug 30, 2023

Keywords: Aristotle; Sosigenes; Adrastus; Metaphysics; astronomy; concentric planetary motions; counteracting spheres

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