How many gods and how many spheres? Aristotle misunderstood as a monotheist and an astronomer in Metaphysics Λ 8

1 Introduction

Both as a piece of metaphysics and as a piece of the history of astronomical science, Chapter 8 of Metaphysics Lambda (= Λ 8)^[1] was, until fairly recently,^[2] under two spells. A late spell was cast by Werner Jaeger, who in the early twentieth century assessed Λ 8 as interrupting a continuous train of thought between chapters 7 and 9: whereas those two chapters set out Aristotle’s conception of God as “immaterial mind,” Λ 8 intervenes, according to Jaeger, only to postulate a “grotesque multiplication of the prime mover, this army of 47 or 55 movents, [which] inevitably damages the divine position of the prime mover and makes the whole theology a matter of mere celestial mechanics.”^[3] As a result, the ‘polytheistic’ Λ 8 was seen by Jaeger as a late piece in Aristotle’s Entwicklung and as a later insertion, exemplifying Aristotle’s degradation of theology into an adjunct of astronomy.^[4] Aristotelian scholars and philosophers became rather uninterested in Λ 8, but historians of astronomical science continued to read it; they were nonetheless under a much earlier spell.

The Peripatetic exegete Sosigenes of Rhegium published in the second century A.D. an influential work, Περὶ τῶν ἀνελιττουσῶν,^[5] in which he presented Aristotle as an accomplished astronomer, who made an important contribution to the theory of concentric celestial spheres primarily conceived by Eudoxus of Cnidus and subsequently improved by Callippus of Cyzicus.^[6] In their efforts to “account for the phenomena,”^[7] that is, to explain the apparent irregular orbits of the planets by preserving the primitive explanatory principle of circular, uniform and ordered motion (τὸ ἐγκύκλιον καὶ ὁμαλὲς καὶ τεταγμένον), the two astronomers conceived, according to Sosigenes, only of the sets of spheres that move each planet separately, as if the rotation of the spheres of a lower planet were not influenced by the rotation of the spheres of a higher planet; and while Callippus disagreed with Eudoxus as to the exact number of those ‘moving’ (φέρουσαι) spheres – they should not be twenty-six, as Eudoxus claimed, but thirty-three – Aristotle was thought to have completed the Callippean astronomical system by reasoning within a unified celestial scheme and therefore seeing the necessity of adding a number of supplementary ‘reversing’ or ‘back-turning’ (ἀνελίττουσαι) spheres. These spheres move at the same speed as the moving spheres, but in a direction opposite to them and therefore counteract their motion. As a result, the final number of the concentric spheres should be fifty-five or, alternatively, forty-nine, if one, following Eudoxus, reduced the five moving spheres of the moon and the sun to three respectively, so that the counteracting spheres that exist for the sake of the moon would not be four but two. This number, i. e., forty-nine, is not attested in the manuscript tradition of the Metaphysics, which reads forty-seven, but is an emendation proposed by Sosigenes and largely accepted by subsequent readers of the Metaphysics.

Both interpretations, I will argue in this paper, are erroneous. Aristotle was naturally a polytheist – no Hellene before Christianity would ever see a plurality of separate immaterial divine substances, such as the unmoved movers, as “grotesque”^[8] – and had no pretension of being an astronomer; it was enough for his purposes to consult with astronomers. I hope that a close look at Λ 8 will show: (a) that this chapter is an integral part of the first philosophy project that Aristotle had in mind while composing his Metaphysics, since it is in this chapter that the central question of the treatise (are there any self-existent immaterial substances as first principles and causes of all things, and if yes, how many are they?) is fully answered; and (b) that there is no compelling textual evidence for taking Aristotle to be making a contribution to astronomy. Once the structure and the language of Λ 8 are properly understood, it will become, I hope, obvious that Aristotle had no aspiration of improving the astronomical theory of his peer(s).

I will first discuss (in section 2) the place of Λ 8 in book Lambda and, more generally, in the Metaphysics, in order to show that it is by no means an insertion.^[9] I will then proceed (in section 3) to elucidate its structure; Aristotle carefully explains why an astronomical discussion is present in an otherwise philosophical chapter and marks it off as a derivative, albeit necessary, excursus. Once this is clarified, I will argue (in section 4) that Sosigenes’ emendation of forty-seven (μζ΄ or, rather, ), which is the number preserved by the manuscript tradition for the reduced number of concentric spheres, to forty-nine () has to be rejected; this issue may seem unimportant, but making sense of the reading of the manuscript tradition is important for settling the major issue of whether or not Aristotle made a contribution to the theory of concentric celestial spheres.

2 The place of Λ 8 in book Lambda and in the Metaphysics

At least prima facie, the Metaphysics is a treatise about wisdom (σοφία), which Aristotle describes as the science that knows the first principles and causes.^[10] While setting out in book Beta the numerous difficulties involved in the quest for wisdom, Aristotle assigns a prominent place to the following joint questions:

Above all (μάλιστα), we must investigate and discuss whether there is something [i. e., the form], besides the matter, which is a cause in itself or not, and whether this exists separately or not, and whether it is one or more in number.^[11]

At this stage of the investigation, Aristotle links those questions to the difficulties involved in the immaterial causes, Forms or Mathematicals, proposed by the Academics.^[12] Immaterial causes are eternally unchanging and as such must be prior to material and changing effects; if the Forms or Mathematicals exist, as the Academics claim, the first among them will be the first principles and causes – which is what wisdom is about. Aristotle will progressively show (especially in books Zeta, Mu and Nu) that the immaterial principles proposed by the Academics are beaten by the difficulties that they involve; they do not exist separately and thus cannot be the first principles. This rejection, however, does not imply that separately existing and eternally unchanging things do not exist.

In book Gamma, Aristotle starts answering the difficulties exposed in Beta by further determining σοφία as φιλοσοφία, which is primarily opposed to (Platonic) dialectic and (Megarian or Protagorean) sophistic, but also to (pre-Platonic) physics.^[13] ‘Philosophy’ is now described as a discipline that studies being qua being and its essential attributes.^[14] This means that philosophy aspires to know the first principles as causes to the things that are of the fact that they are, that they are one and many, same and different, similar and dissimilar etc., as well as of the universal truths – the principles of non-contradiction and of the excluded middle – that pertain to being qua being and are like its essential attributes.^[15] Aristotle will do this by acknowledging the priority of substance (οὐσία) with regard to being (ὄν) as said in the other categories.^[16] Thus, in searching for the first principles, the philosopher, as distinguished from the dialectician and the sophist,^[17] will look for the causes of substances, which in causing being are also causes of unity and the other essential attributes of being.

Aristotle will issue reminders both at the beginning of book Eta and at the beginning of book Lambda that the investigation of the Metaphysics primarily concerns substance.^[18] In the first two chapters of book Zeta, he resumes some topics from the previous books and announces programmatically what is to be expected in the subsequent books:

Regarding these matters, then, we must inquire which of the common statements are right and which are not right, that is, (1) what substances there are, and (a) whether there are or are not any beside sensible substances, and (b) how sensible substances exist, and (c) whether there is a substance capable of separate existence (and if so why and how) or no such substance, apart from sensible substances; but we must first sketch (2) what substance is.^[19]

Since substance is said in many senses, the central books of the Metaphysics will primarily address question (2). They will sort out what sense of substance (books Zeta and Eta) and what sense of unity (book Iota) philosophy is knowledge of, and whether it primarily studies being in actuality or being in potentiality (book Theta). (1a), (1b) and (1c) are all answered in book Lambda. But the question whether there is a separately existing and eternally unchanging substance permeates the entire treatise.

In book Gamma Aristotle demands that, against those who deny the principle of non-contradiction, “we shall ask them to believe that among existing things there is also a certain (τινὰ) substance to which neither movement nor destruction nor generation at all belongs.”^[20] At the end of the same book, he alludes to (a) “something that always moves the things that are moved,” that is, the heaven that causes the alternation of sublunary things between coming-to-be and passing-away, and to (b) “the first mover that is itself unmoved,”^[21] that is, the unmoved mover of the heaven. In book Epsilon he further determines ‘philosophy’ as ‘first philosophy.’ The existence of philosophy thus specified explicitly depends on a separately existing unmoved substance. If there is such a substance, it will be causally prior to all other substances; and the philosophy that studies this substance will be first among other branches of philosophy:

If there is not a certain (τις) substance different from those constituted by nature, physics would be the first science; but if there is a certain unmoved substance, the science that studies it [i. e., theology] will be prior and first philosophy, and universal in this way, because it is first. And it will belong to this [science] to consider being qua being, both what it is and the attributes that belong to it qua being.^[22]

But surely it is not enough to know that there is a certain such substance. The first philosopher should also be able to say what this substance precisely is and whether there is only one such substance or many, and if there are many, how many they are – as already asked in book Beta. These related questions are answered in book Lambda and, more specifically, in Λ 7 and in Λ 8.

Most scholars have been interpreting book Lambda as an independent treatise, thus pursuing a line of thought that was inaugurated in the nineteenth century by Hermann Bonitz.^[23] Yet Lambda seems, in fact, to culminate the argument of the Metaphysics.^[24] Not only does Lambda establish the existence of a separate and eternally unchanging substance,^[25] thereby yielding a first philosophy (as described in book Epsilon). The book also shows that this substance is an activity per se and a god,^[26] and in this way it yields a theological philosophy (θεολογικὴ φιλοσοφία).^[27] This satisfies what the reader has been expecting since book Epsilon, as well as the promise for a divine science (θεία τῶν ἐπιστημῶν) that Aristotle made in book Alpha:

For the most divine [science] is also most honorable; and this science can be alone [μόνη, that is, preeminent] in two ways; for the science which it would be most meet for god to have is divine among the sciences, and so is a certain science that knows the divine things.^[28]

Now, if book Lambda culminates the Metaphysics, then Λ 7 and Λ 8 culminate Lambda (and a fortiori the Metaphysics). As already said, the first branch of the program announced in the beginning of book Zeta, that is, questions (1a), (1b) and (1c),^[29] is altogether answered in book Lambda. Its first part (chapters 1–5) answers (1a) and (1b). It says, with respect to (1a), that there are two natural and one intelligible substances (‘two’ and ‘one’ are meant collectively), i. e., the sensible perishable substance, the sensible eternal substance, and the unchanging substance whose existence is disputed,^[30] and shows, with respect to (1b), that the sensible substances exist through numerically six causes, namely the three constituent causes (matter, privation, form),^[31] the conspecific efficient cause,^[32] the non-conspecific efficient cause, namely the sun and its orbit around the ecliptic,^[33] and the first mover.^[34] Its second part (chapters 6–10) answers the last and most important question, namely (1c). This is done through a fresh start, which recalls what has been said in the beginning of the book,^[35] and takes a causal path to the discovery of the first principles, which is different from the paths explored until now.^[36] It now starts from the non-conspecific efficient cause, which by including potentiality both in motion and substance cannot guarantee by itself its eternal motion (as shown in Physics VIII 1). Through Λ 6 and Λ 7 Aristotle moves from the eternal motion of the heavenly bodies to their movers, i. e. their souls, and from the eternally moved movers, i. e. the souls of the heavenly bodies, to an eternally unmoved mover,^[37] which is substantially activity.^[38] But Λ 7 only establishes that there is at least one such substance,^[39] namely the principle on which “the heavens and the nature depend.”^[40] This is rather too vague a conclusion for the discipline of wisdom newly determined as first philosophy, which has promised to deliver the first principles and causes. In the very beginning of Λ 8, Aristotle underscores the superiority of his approach for determining the number of the immaterial substances or principles. For previous Platonists and contemporary Academics have not considered this important question “separately” (οὐδεμίαν ἔχει σκέψιν ἰδίαν), which is why they do not have a consistent theory on this matter:

The question whether we suppose one substance of this kind (τὴν τοιαύτην οὐσίαν) or more than one – and how many – must not be overlooked. And we must also recall, in respect of the statements of the others,^[41] that they have said nothing which can even be clearly stated concerning the number [of such substances]. For the theory of the Ideas has no special examination of this question; for those who say that there are Ideas say that the Ideas are numbers but concerning the numbers they sometimes speak of them as infinite and sometimes as limited by the decad; but as to the reason why this is the number of the numbers, nothing is said with demonstrative seriousness.^[42] We, however, must speak on the basis of the things which we have laid down and the distinctions which we have made.^[43]

Aristotle consistently refers to the first principles (in plural) in Alpha meizon and asks in book Beta whether the separately existing immaterial principles are one or more in number. He switches to the singular by book Gamma but he always adds a τις.^[44] This seems to suggest that he is consistently thinking of a certain separately existing and immaterial substance, namely the unmoved mover that moves the outermost celestial sphere of the unwandering stars. This is made clear in Λ 7 and, in addition to its intrinsic value, functions as a bridge to Λ 8,^[45] which will determine whether there are one or many – and how many – such substances. The plural (τὰς οὐσίας) that occurs once in Λ 6 actually anticipates what will be established in Λ 8.^[46]

Aristotle’s philosophical argument for settling the issue of the number of the immaterial substances is an argument by analogy. Granted that the outermost celestial sphere depends for its motion on a separately existing and unmoved substance, there will be further such substances, if there exist further celestial spheres. Now, all stars, both the unwandering and the wandering, are by themselves in the same condition, that is, unmoved.^[47] They are moved by the celestial spheres that act for their sake and explain their motions.^[48] Nonetheless, while the large number of the unwandering stars is moved only by one sphere, i. e., the outermost celestial sphere, the wandering stars, i. e., the seven planets (Saturn, Jupiter, Mars, Venus, Mercury, sun, moon), are moved in accordance with more than one motion, that is, by more than one celestial sphere. This, Aristotle contends, is obvious even to those who are moderately familiar with astronomy.^[49] But how many are these motions is a question that can be answered only by professional astronomers; hence the necessary excursus in Λ 8 (1073b17–1074a14) about the astronomical theory of the concentric spheres.^[50]

Thus, Λ 8 is launched as an integral part of the project that Aristotle pursues in his Metaphysics; it does not interrupt but completes Λ 7. Indeed, one may argue that it is in this chapter that the aim of Aristotle’s Metaphysics is fully attained, whereas Λ 9 is subsequently introduced more or less as an appendix to Λ 7.^[51] Separating Λ 8 from Λ 7 and interpreting it as an insertion downgrades its contribution to first philosophy; it is Λ 8 which shows that there is a first separately existing and eternally unmoved substance but also that there are many such substances (a provisional but precise number for these substances is fifty-five or forty-seven), which are equally important for the world to exist. The souls of the celestial spheres do not transform matter into material form, as is the case with the souls of the sublunary realm, but actualize infinitely, constantly and uniformly, that is, rationally and in the best possible way, the orbits of the divine bodies. Aristotle has explained in Λ 7 that this rational stability is achieved first of all thanks to a first principle, an unmoved final causality, which the soul of the sphere of the unwandering stars cognizes and therefore desires.^[52] This is “the Principle and First of beings that is unmoved both per se and per accidens,” which is spoken of in Λ 8,^[53] the Good-itself^[54] that will be ultimately called the “one ruler.”^[55] This in its turn implies that the rest of the unmoved movers, which are the causes of each one of the circular motions that explain the apparent orbits of the planets against the background of the unwandering stars, move per accidens. Given that they are moved per accidens not by themselves but by something else,^[56] they are within the sphere of the fixed stars and are moved with it. Just like the absolute immobility of the “First of beings,” their motion per accidens is necessary for the world to exist. If they were not moved per accidens, they, too, would cause motion around a stationary axis, as is the case of the motion of the unwandering stars caused by the First of beings. The world, however, exists because the axes of the other celestial spheres are not stationary but move in accordance with the sphere of the unwandering stars.^[57] And they are not stationary because they are in constant intelligible contact with intelligible substances that are moved per accidens.

Jaeger’s downgrading of Λ 8 has ultimately no foundation and is explained by an unfounded eagerness to “save” Aristotle as a monotheist. Aristotle, however, is happy to praise at the end of Λ 8 the most ancient tradition, which was naturally polytheistic:

Those of long ago and of the most ancient times handed down to their posterity things that have survived in the form of a myth^[58] – that these (οὗτοι) are gods, and that the divine encloses the whole of nature. Now the rest has been added [by posterity] mythically for the persuasion of the many and for the benefit of the laws and the common advantage; for they [i. e., posterity] say that these have human form and are like some of the other animals, and they say other things which follow from or are similar to what has been said. But if one were to separate the primary thing from these and take it alone – that [those of the most ancient times] thought that the primary substances were gods – one would think that they had spoken divinely, and that while, in all likelihood, each craft and [branch of] philosophy has been many times discovered as far as possible and again lost, these beliefs too of those people have survived destruction, like ruins, down to the present time. Only to this extent are our ancestral beliefs and those from the first people evident to us.^[59]

This passage, which was considered as a late intrusion by Blass,^[60] ends Λ 8 purposefully. Aristotle links his own first philosophy project, which has just identified the First principles and causes with the divine intelligible substances that move the heavenly spheres, to the views of the most ancient sages, which survive the recurring cataclysms. Several scholars have been puzzled by the lack of referent of οὗτοι (an argument adduced by Blass) but it is not hard to see that οὗτοι is attracted by the word θεοί that precedes it.^[61] The gods of the ancient sages, Aristotle says, “enclose the whole of nature,” and in the whole of nature the heavenly spheres are also included. Aristotle actually venerates the ancient polytheistic tradition for having identified as gods not the divine bodies of the heavens but the first substances (τὰς πρώτας οὐσίας). We cannot exactly know, he says, what the ancient sages conceived of as first substances but we may guess; for the anthropomorphic or zoomorphic immobile causes of the names of the planets and the constellations (say, the castrating Kronos or the punished Cassiopeia or the Little Bear) are the mythical remnants of an ancient tradition, which had recognized numerous invisible and immaterial substances that enclose the heavenly spheres; these substances, he takes it, were akin to his unmoved movers.

Aristotle begins his Metaphysics by appealing to common truths about human beings (“All men by nature desire to know”) and by reviewing in the first two chapters of Alpha meizon the common opinions about who the sage is and what wisdom is. He concludes on the basis of these preliminary considerations that wisdom is the science that knows the first principles and causes. It is perhaps not without significance for the place of Λ 8 that, once these principles and causes have finally come to be known, he validates this knowledge by appealing not to the common opinions but to the divine beliefs of the most ancient sages.

3 The structure of Λ 8 and the astronomical excursus

To know that there exists a separately existing and unmoved immaterial substance is a thesis established through (first) philosophy, and to know, moreover, that there are more than one such substances is a thesis established through observation and natural philosophy.^[62] But to arrive at a precise number of these substances is something that can be tackled only through astronomy.^[63] While rejecting the Speusippean choice of arithmetic as supportive of the quest for the first principles, Aristotle turns to the mathematical science that is, as he says, “most akin to philosophy.” In opposition to arithmetic or geometry, which investigate accidents of substances, astronomy deals with a substance; and because the substance that astronomy investigates is eternal, it is most akin to first philosophy.^[64]

Thus, the astronomical excursus is fully justified, and Aristotle states indeed that he will now reproduce what the astronomers actually know. There is, however, some ambiguity in the words with which he introduces this excursus:

But as to how many these [motions]^[65] actually are, we will now (νῦν μὲν) say what some of the mathematicians [i. e., the astronomers] 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 (τὸ δὲ λοιπόν), 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.^[66]

Most scholars believe that Aristotle intends to say that he will contribute by himself to astronomical theory. They interpret this passage as announcing three different steps to be taken in the excursus: Aristotle will first (νῦν) recount the theories of Eudoxus and Callippus and then (τὸ δὲ λοιπόν) turn to his own views by introducing the counteracting spheres.^[67] But this reading presupposes that Aristotle actually made a contribution to astronomical theory (which, as we shall see, is by no means as evident as it is taken to be) and, most importantly, does not fully account for what is actually said in the passage. It is obvious that the νῦν introduces the astronomical theories of Eudoxus and Callippus (“we will say what some of the mathematicians say”), as it is also obvious that we will go through these very theories in order to arrive at some definite number regarding the motions of the planets. It will turn out that the definite number of these motions, which we will “grasp in thought,”^[68] is actually two numbers – fifty-five or forty-seven – and these numbers already include the counteracting spheres,^[69] which are allegedly Aristotle’s own contribution to astronomical theory. Thus, it is unlikely that τὸ δὲ λοιπόν, which comes after our grasping in thought a definite number of motions, announces the addition of the counteracting spheres. Rather, it refers to what remains to be investigated once a definite number of the motions of the planets has been suggested: on the one hand, (first) philosophy will go on investigating (τὰ μὲν ζητοῦντας αὐτοὺς) the causes of the planetary motions, namely the immaterial substances – and this actually happens after 1074a14 – on the other hand it will continue to rely on astronomy for knowing what it cannot know by itself (τὰ δὲ πυνθανομένους παρὰ τῶν ζητούντων), namely the number of the planetary motions, which is likely to be modified.^[70] When Aristotle says that “if something different from what is now said (τὰ νῦν εἰρημένα) appears to those who deal with those matters,” he cannot be referring to Eudoxus and Callippus, whose astronomical theories are now presented (νῦν μὲν ἡμεῖς ἃ λέγουσι τῶν μαθηματικῶν […] λέγομεν), but to astronomers who may present in the future a more accurate theory of planetary motions. Aristotle seems aware of the fact that the existent theories do not fully account for the apparent motions of the planets.^[71] We, philosophers, he says, welcome ex prooemio both astronomers (φιλεῖν μὲν ἀμφοτέρους),^[72] that is, both Eudoxus and Callippus, as will become clear throughout the excursus. But we also hope for further astronomers who, while preserving the primitive explanatory principle of circular and uniform motion, will develop even better mathematical models that will account for the planetary motions more accurately (πείθεσθαι δὲ τοῖς ἀκριβεστέροις). This is why, when resuming his first philosophy project after the astronomical excursus, Aristotle expresses his wish for a demonstration in planetary theory:

Let the number of the spheres, then, be this many, so that we may think with good cause that there are just as many substances and principles which are unmoved and <different from> the sensible [substances]; for let [demonstrative] necessity be left for more powerful [astronomers] to speak of.^[73]

The probability of thought concerns, of course, the number (primarily of the heavenly spheres and, consequently, of their immaterial movers) and not the existence of the immaterial substance, which has been established in Λ 6–7 through first philosophy.

The astronomical excursus itself offers no real indication that Aristotle contributed to astronomical theory.^[74] Translations of the excursus either do not render at all or quickly abandon the oratio obliqua, which Aristotle quite naturally uses for recounting the theories of the “mathematicians,” and at any rate switch with no real justification to oratio directa, when it comes to the addition of the counteracting spheres.^[75] Had Aristotle believed that he was making an original contribution to the moving spheres of Eudoxus and Callippus by adding the counteracting spheres, he would have likely introduced his novelty with a particle stronger than the (transitive) δέ (ἀναγκαῖον δέ …) and would have naturally used a verb in the indicative. But such a verb can only be supposed to be implied, whereas we would expect it to be actually there.^[76] Note also that ἀναγκαῖον δέ is parallel to εἶναι δέ at 1073b30, which closes Aristotle’s account of Eudoxus’ theory of the concentric spheres; one would naturally read ἀναγκαῖον δέ as introducing the last clause of Aristotle’s account of Callippus’ theory. I hope that the reader will excuse a literal translation of the excursus:

One the one side, then, Eudoxus posited (ἐτίθετο)^[77] that the motion of the sun and moon each happens in three spheres, of which the first is that of the unwandering stars, the second [is the sphere that moves] along the [circle] through the middle of the constellations of the zodiac, and the third [is the sphere that moves] along the [circle] slanted across the breadth of the constellations of the zodiac ([he posited that the circle] along which the moon is carried is slanted across a greater breadth than that along which the sun is carried), whereas [he posited] that the motion of each of the wandering stars happens in four spheres, of which the first and second are the same as those mentioned above (for [he posited] that the sphere of the unwandering stars is the one which carries all the spheres,^[78] and that the one which is set under this one and whose motion is along the [circle] through the middle of the constellations of the zodiac is common to all [spheres]^[79]) but the poles of the third sphere of all [planets]^[80] are on the [circle] which goes through the middle of the constellations of the zodiac, and the motion of the fourth sphere is along the circle which is slanted in relation to the middle [circle] of this [i. e., the third sphere]; and [he posited] that (εἶναι δὲ) the poles of the third sphere are different for the rest of the planets, but the same for Venus and Mercury. On the other side, Callippus posited (ἐτίθετο) the same setting of the spheres as Eudoxus, but as for their number, while he gave the same number [of spheres] as him to the star of Jupiter and to the star of Saturn, he believed (ᾤετο) that two more spheres had to be added (προσθετέας εἶναι) to the sun and to the moon if one were going to account for the phenomena, and to the rest of the planets one more each; and [he believed that] it is necessary (ἀναγκαῖον δέ, sc. εἶναι), if all the spheres put together are going to account for the phenomena, that for each of the wandering [stars] there exist other spheres, less in number by one, which counteract [the moving spheres]^[81] and in every case restore to the same setting the first sphere of the star which is arranged below. For only in this way is it possible (ἐνδέχεται) for all [wandering stars] (ἅπαντα) to make for themselves (ποιεῖσθαι) the motion of the unwandering stars.^[82] Since, then, the spheres in which the planets are moved are eight and twenty-five,^[83] and of these only those in which the [star] arranged lowest^[84] is moved do not need to be counteracted, those which counteract the spheres of the first two [stars]^[85] will be six, while those for the subsequent four will be sixteen. Hence the number of all [the spheres], both the moving and the counteracting, will be fifty-five.^[86] But if one were not to add to the moon and the sun the motions which I have mentioned, all the spheres will be forty-seven.^[87]

The indicative mood used in “For only in this way is it possible (ἐνδέχεται) for all [wandering stars] to make for themselves (i. e., reproduce) the motion of the unwandering stars” need not distract us: in order to account for the phenomena, Aristotle espouses Callippus’ theory of planetary motions, which seems to include both the moving and the counteracting spheres, while at the same time he makes the necessary reservation vis-à-vis a theory that is not a proof. Aristotle thinks that Callippus’ theory is not absolutely true due to the very features of the science of astronomy (at least in its state at the time), but he is convinced that it is closer to the truth than Eudoxus’ theory. This is why he counts at first fifty-five spheres as explanatory of the totality of planetary motions (whereas he does not even mention the number twenty-six, to which Eudoxus’ spheres amount). But Aristotle also proposes an alternative number, i. e., forty-seven, which at first seems problematic. In fact, however, this number suggests the view that Aristotle did not actually interfere with the theory of the concentric spheres that was primarily elaborated by Eudoxus and later developed by Callippus.

4 The reduced number of the concentric spheres and the role of Sosigenes

In the alternative version, Aristotle reduces the five moving spheres of the sun to three, so that the counteracting spheres that exist for the sake of the moon should not be (five minus one equals) four but (three minus one equals) two; then, Aristotle also subtracts two moving spheres from the moon, so that the total reduced number of the concentric spheres should be (fifty-five minus six equals) forty-nine. In his treatise Περὶ τῶν ἀνελιττουσῶν, Sosigenes rejected some tentative accounts of the number forty-seven and ultimately concluded that it is a scribal error; the true (that is, according to Aristotle) number should be forty-nine.^[88] Indeed, such an astronomical error would not be expected from the person who conceived of the counteracting spheres. But, as a number, it is justifiable, if it was written by a person who did not conceive of the counteracting spheres but was merely thinking about the validity of two complementary but different theories of planetary motion.^[89]

Aristotle does not explain why the two extra motions should be removed from the system of the sun and the system of the moon,^[90] but we may plausibly argue that the reason was their proximity to earth. In On the Heavens II 12, Aristotle explains why the sun and the moon move with less motions than the higher planets, even though one would expect that the inverse should be the case, since if the first heaven attains its perfection and the good with only one motion, the higher planets, which are nearer to it, should logically move with fewer motions than the sun and the moon. Aristotle argues that, despite this plausible line of thought, the sun and moon, like the earth but unlike the higher planets, do not really attain the most divine principle, as the other planets do, but come as near to it as they can:

It is for this reason that the earth moves not at all and the [stars] near to it [i. e., the moon and the sun] with few motions. For they do not attain the final end, but only come as near to it as their share in the most divine principle permits. But the first heaven finds it immediately with a single motion, and the [stars] intermediate between the first [heaven] and the last [stars] attain it indeed, but with multiple motions.^[91]

According to the Callippean model, however, the sun and the moon are carried each in five spheres, that is, in as many spheres as those in which Mars, Venus, and Mercury are carried. If the counteracting spheres are added, the sun and the moon will move with (five + four =) nine motions, that is, with as many as those with which Venus and Mercury will move. In both cases, the sun and the moon lose their special, lower, status. Accepting the Eudoxean model as partially valid provided Aristotle a way out of ascribing to the sun and moon the same status as other, “intermediate,” planets: Saturn would attain the Good with four motions, Jupiter with (four + three =) seven motions, Mars with (five + three =) eight motions, Venus and Mercury with (five + four =) nine motions; by moving respectively with (three + four =) seven and three motions, the sun and moon would not attain the Good but would come as near to it as they could.

Thus, Aristotle had a philosophical reason – the lower status of the moon and sun with regard to the higher planets – to retain a part of the Eudoxean model and to combine it (not compose it) with the Callippean model. Although this combination was probably unacceptable to Callippus (the subtraction of the two extra spheres of the sun and moon would leave the anomalies observed in their speed without explanation and, even if Callippus had accepted in this case the Eudoxean system, he would have found Aristotle’s calculation mistaken: the combined system still is a unified scheme, and the two lower spheres of the sun would still need to be counteracted for the sake of the moon), Aristotle was not wholly unjustified in considering, on philosophical grounds, the partial validity of the Eudoxean model. He was aware of the fact that the available theories did not fully account for the apparent motions of the planets and, as he himself was not an astronomer, he explicitly hoped for astronomers who, while preserving the primitive explanatory principle of circular and uniform motion, would develop in the future better mathematical models that would account for the planetary motions more accurately. In a definite account, it was to be expected, the sun and the moon would move with fewer motions than the rest of the planets. Since this account was not provided by Callippus, Aristotle considered, for the time being, combining with the Callippean model the model of Eudoxus in order to satisfy his philosophical assumptions. He thus removed the two moving spheres of the sun, added by Callippus, and the two moving spheres of the moon, also added by Callippus. Of course, despite his not being an astronomer, Aristotle could not simply ignore the rationale behind the addition of the counteracting spheres. Unless one is likely to have recourse with Sosigenes to the unlikely explanation of scribal error, Aristotle must have had his reasons for discarding not two but all four spheres which, according to the Callippean setup, counteract the moving spheres of the sun for the sake of the moon. Perhaps he was aware of an astronomical endeavor which promised to account for the rotational components of the apparent motions of the sun and the moon jointly, that is, without interference of counteracting spheres. Or at least he hoped for such a theory on philosophical grounds: the counteracting spheres would be operative in, and distinctive of, the intermediate heaven, cancelling all moving spheres from Saturn down to Mercury, so that the unitary motion of the first heaven is transmitted to the first sphere of all planets down to the first of “the last stars”; on the contrary, there would be no counteracting spheres operative in the last heaven, but the last star, the moon, would reproduce the motion of the first heaven only thanks to the respective motion of the sun.

Thus, there is in the Metaphysics some real textual evidence – the reduced number of the concentric spheres – against attributing the addition of the counteracting spheres to Aristotle himself, whereas there is none for attributing this addition to him. There can be little doubt that Sosigenes lies behind this definitive attribution.^[92] 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 in Theon of Smyrna’s On Mathematics Useful for Understanding Plato,^[93] was ready to attribute the conception of the counteracting spheres alternatively to Aristotle or to 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].^[94]

Admittedly, Sosigenes was more reliable in astronomical matters than Adrastus, since he drew much of his astronomical knowledge from Eudemus’ Astronomical History, which Adrastus seems to have deliberately ignored.^[95] As Simplicius makes clear, Sosigenes’ detailed discussion of “the spherical model (reproducing the planetary motions) according to Eudoxus” (ἡ κατὰ Εὔδοξον σφαιροποιία), which occupies several pages of his Commentary on Aristotle’s On the Heavens (493.11–497.5),^[96] relied on the second book of Eudemus’ descriptive work.^[97] By contrast, Callippus’ theory is presented in Simplicius’ commentary quite succinctly (497.15–24): only the inequality of the seasons (the solar anomaly), observed by Euctemon and Meton, is quoted as the reason adduced by Eudemus for the Callippean addition of two extra spheres to the sun and moon (in the latter case, the two extra spheres would account for the anomaly in speed proper to the moon),^[98] whereas there is no proper explanation for the addition of an extra sphere to Mars, Venus, and Mercury, even though it is said that Eudemus provided such an explanation, even a succinct one.^[99] This was possibly due to Sosigenes’ haste to provide an account of the counteracting spheres, which he ascribed to Aristotle. At any rate, Simplicius makes clear that Sosigenes provided this account by himself, which implies that, like the moving spheres added by Callippus, the counteracting spheres were also quite succinctly presented in Eudemus’ Astrological History:

Aristotle having stated these things briefly and in such a clear manner, Sosigenes praised him for his acumen and tried to find the use of the spheres which he added; and he [i. e., Sosigenes] says that …^[100]

Now, if Adrastus, who was probably unable to tell from Eudemus’ report, hesitated to attribute the conception of the counteracting spheres to Aristotle, and if Sosigenes did not rely on Eudemus for attributing this conception and its details to Aristotle, Sosigenes’ account seems to lose its exegetical authority.^[101]

Scholars and historians of astronomy have uncritically followed Sosigenes. They thought that only a philosopher, not a ‘mathematician,’ would be interested in putting together all the concentric spheres to see how the whole system works in nature. They consequently ascribed the conception of the counteracting spheres to Aristotle. The application of this kind of astronomical instrumentalism has been shown to be a myth in the case of Eudoxus.^[102] Simplicius himself had no doubt that, through their astronomical theories, Eudoxus and Callippus endeavored to capture the real motions of the planets. Indeed, it is only through the progression of the astronomical science, and after other hypotheses, such as the eccentric and the epicyclic theory, which were equally, if not more, capable of accounting for the apparent orbits of the planets, had been formulated,^[103] that the concentric theory became a hypothesis among others. It was not, however, a hypothesis proper (because without any actual claim to truth) for the initiators of this theory. Except for an anachronistic projection of the value of mathematical astronomy in Late Antiquity,^[104] there is no compelling reason to think that Callippus was indifferent to making the whole system work. And even if one was to reserve such a worry to the philosopher, there is no compelling reason to think that the philosopher would not bother to ask the astronomer. Aristotle found in the concentric theory of planetary motions an important help to complete his first philosophy project, which culminates in Λ 8. Had he done this in spite of Eudoxus’ and Callippus’ (putative) warnings about the instrumentalist character of their hypotheses, he would have sabotaged his project by himself; for astronomy would then not be “more akin to philosophy” than arithmetic.