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),^[1] 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.^[2] 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].^[3]

It was Sosigenes who ascribed this conception to Aristotle with no hesitation.^[4] 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?’.^[5]

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.^[6]

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.^[7]

Simplicius himself takes ἀνελίττουσας lato sensu as equivalent to ὁμοκέντρους, as his expression ἡ διὰ τῶν ἀνελιττουσῶν σφαιροποιία readily makes clear.^[8] 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.^[9]

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).^[10] 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”,^[11] 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.^[12] Before Sosigenes, Adrastus of Aphrodisias (or, at any rate, his contemporary Theon of Smyrna)^[13] 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].^[14]

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.^[15] 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.^[16]

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 1074^a1–3 (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.^[17] 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]?”^[18]

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.^[19] 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.^[20] 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.^[21] 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.^[22] 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;^[23] 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].^[24]

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.^[25]

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.^[26]