I. INTRODUCTION
In the twenty-fourth aporia of Theophrastus' Metaphysics,Footnote 1 there appears an important, if ‘bafflingly elliptical’,Footnote 2 ascription to Plato and the ‘Pythagoreans’ of a theory of reduction to the first principles via ‘imitation’ (μίμησις):
Πλάτων δὲ καὶ οἱ Πυθαγόρειοι μακρὰν τὴν ἀπόστασιν, ἐπιμιμεῖσθαι τ' ἐθέλειν ἅπαντα· καίτοι καθάπερ ἀντίθεσιν τινα ποιοῦσιν τῆς ἀορίστου δυάδος καὶ τοῦ ἑνός, ἐν ᾗ καὶ τὸ ἄπειρον καὶ τὸ ἄτακτον καὶ ὡς εἰπεῖν πᾶσα ἀμορφία καθ' αὑτήν, ὅλως δ' οὐχ οἷον τ' ἄνευ ταύτης τὴν τοὺ ὅλου φύσιν, ἀλλ' οἷον ἰσομοιρεῖν ἢ καὶ ὑπερέχειν τῆς ἐτέρας, ᾗ καὶ τὰς ἀρχὰς ἐναντίας. Διὸ καὶ οὐδὲ τὸν θεόν, ὅσοι τῷ θεῷ τὴν αἰτίαν ἀνάπτουσιν, δύνασθαι πάντ' εἰς τὸ ἄριστον ἄγειν, ἀλλ' εἴπερ, ἐφ' ὅσον ἐνδέχεται· τάχα δ' οὐδ' ἂν προέλοιτ', εἴπερ ἀναιρεῖσθαι συμβήσεται τὴν ὅλην οὐσίαν ἐξ ἐναντίων γε καὶ ἐν ἐναντίοις οὖσαν.
(Theophrastus, Metaphysics, 11a26–b12)Plato and the Pythagoreans make the distance [between the first principles and everything else]Footnote 3 a great one, and they make all things desire to imitate fully;Footnote 4 and yet, they set up a certain opposition, as it were, between the Indefinite Dyad and the One. In the former [resides] the Unlimited and the Unordered and, as it were, all Shapelessness as such; and they make it altogether impossible for the nature of the universe to exist without this [that is, the Indefinite Dyad] – it [that is, the Indefinite Dyad] could only have an equal share in things, or even exceed the other [first principle, that is, the One] – whereby they also make their first principles contrary [to one another]. Therefore, those who ascribe causation to the god claim that not even the god is able to reduce all thingsFootnote 5 to the best, but, even if at all, only in so far as is possible. And perhaps he wouldn't even choose to, if indeed it were to result in the destruction of all existence, given that it [that is, existence] is constituted from contraries and consists of contraries.
One can imagine the excitement that might accompany such a complex description of and challenge to the metaphysics ascribed to Plato and the ‘Pythagoreans’. After all, Aristotle's summary of Plato's adoption of the Pythagorean philosophical system (pragmateia) in Metaphysics Α assumes strong relationships between their metaphysics, especially their employment of the coextensive operations of ‘participation’ (μέθεξις) and ‘imitation’ (μίμησις), but it is cryptic and inconclusive.Footnote 6 Naturally, Aporia 24 in Theophrastus' Metaphysics, a text which might have been an appendix placed before Metaphysics Α in the Corpus,Footnote 7 should have stirred up excitement among scholars who are interested in two controversial topics, (1) Plato's unwritten dialogues (and the first principles of Plato's philosophy) and (2) the relationship between Plato and the ‘Pythagoreans’ (and the curious interposition of ‘participation’ and ‘imitation’). On the former, there have been many commentators. Burkert, who thought that a Platonist of the Early Academy (most likely Speusippus)Footnote 8 was the source for Theophrastus' description in Aporia 24, focusses on the meaning of the ‘distance’ (ἀπόστασις) apparently posited between the One and the Indefinite Dyad – itself a debatable inference into the text; on ‘imitation’ of the first principles he has little to say. The same goes for Huffman and Philip, who follow Burkert's interpretation closely and emphasize the interweaving of ‘Pythagorean’ with Platonist first principles in the Early Academy.Footnote 9 Cherniss, who did indeed spend a great deal of energy trying to unpack the relationship of production to ‘imitation’ in Plato's metaphysics,Footnote 10 nevertheless used this passage primarily to make sense of the various aspects of the Indefinite Dyad.Footnote 11 Reale brought some colour to the debate by arguing that Theophrastus places the thought of Plato and the ‘Pythagoreans’ in an intermediary position within a larger dialectic between those who posit evil and disorder as a ruling element in the universe (that is, Speusippus, on Theophrastus' count) and those who postulate good and order as predominant.Footnote 12
Concerning the ascription to Plato and the ‘Pythagoreans’ of a theory of reduction by means of the obscure operation called ‘imitation’, however, little ink has been spilled. In his discussion of ‘imitation’ in Aristotle's famous passage from Metaphysics Α, Kahn, for example, does not take into account Theophrastus' testimony.Footnote 13 Fine, in her analysis of Aristotle's criticism of Platonic metaphysics, doesn't even mention Theophrastus;Footnote 14 neither does Pradeau, whose comprehensive new monograph sets the tone for the future of studies on Platonic ‘imitation’ without reference to Aristotle's student.Footnote 15 In a more helpful light, Laks and Most, in their critical edition of Theophrastus' Metaphysics, explain how the operation of ‘imitation’ ascribed to Platonic and ‘Pythagorean’ metaphysics is meant to be distinguished from the aforementioned position ascribed to Speusippus, but their exegesis of this passage cannot be said to follow in any obvious way from the textual evidence.Footnote 16 Dillon, who also discusses this passage in detail, uncharacteristically does not put to the test the relationship of Plato to the ‘Pythagoreans’ or the details of the first principles, but instead provides a general analysis of how it reiterates earlier arguments made by Theophrastus.Footnote 17 In this way, he follows Van Raalte, who, in her commentary on the Greek text, relates Aporia 24 to the larger issues of ‘imitation’ in Plato's writings as well as Theophrastus' and Aristotle's Metaphysics. In her analysis of Aporia 8 (Theophr. Metaph. 5a25–8) she usefully contextualizes this passage with the larger philosophical approach in Theophrastus' work:
It is to be noted that in the present discussion the theory of μίμησις is in contrast to the Aristotelian doctrine of cosmic ἔφεσις/ὄρεξις, whereas elsewhere these notions are associated with it, μίμησις featuring in the context of cosmic ὄρεξις, 7b 23ff. … ὄρεξις/ ἔφεσις in that of cosmic μίμησις, 11a 27 f.: Πλάτων δὲ καὶ οἱ Πυθαγόρειοι μακρὰν τὴν ἀπόστασιν, ἐπεὶ μιμεῖσθαι γ' ἐθέλειν ἅπαντα. All this seems to indicate that, although he takes as his point of departure here the Aristotelian doctrine, to [Theophrastus] himself cosmic ὄρεξις and cosmic μίμησις are cognate notions – which, incidentally, may be precisely why the discussion of ὄρεξις here provokes his comments on the notion of μίμησις.Footnote 18
Van Raalte's interpretation improves our understanding of the passage by placing it within the larger context of Theophrastus' thought. But it does not sufficiently address the concerns I have raised about what (if anything) could be understood by Theophrastus' attribution to Plato and the ‘Pythagoreans’ of reduction to the first principles via ‘imitation’. Moreover, while she is correct to note that Aristotelian ‘tendency toward’ (ἔφεσις) and Platonic/‘Pythagorean’ ‘imitation’ (μίμησις) are ‘cognate notions’ for Theophrastus in Aporia 24, Van Raalte assumes that the arguments concerning the ‘Pythagoreans’ agree with and substantiate Aristotle's claim that, for the ‘Pythagoreans’, sensibles imitate numbers.Footnote 19 Unfortunately, she goes no further in making sense of how Theophrastus – whose treatment of these issues, as I will show, diverges in notable ways from his teacher's – modifies, appropriates or responds to the Aristotelian claim.Footnote 20
What is apparent from this brief discussion of the secondary literature is that – with the exception of Van Raalte, whose account, while valuable as an impetus, is both problematic and incompleteFootnote 21 – very little attention has been paid to the idea of Platonic and ‘Pythagorean’ reduction through the operation of ‘imitation’ as presented by Theophrastus in his Metaphysics. This article will proceed by interrogation of the concepts of ‘reduction’ and ‘imitation’ as described in the extant fragments of Theophrastus' writings – with special attention to his Metaphysics – in an attempt to make sense of how, precisely, Theophrastus characterizes the metaphysical systems of Plato and the ‘Pythagoreans’. The goal here is to provide greater insight into Aristotle's claims concerning the intellectual legacy of Plato and the ‘Pythagoreans’ in Metaphysics Α by contextualizing his account with that of Theophrastus. A fuller examination of Aporia 24 produces important new understandings of the nature of the Early Academy in the mid fourth century b.c.e. Specifically, what I will argue is that by ascribing the concept of reduction via ‘imitation’ to Plato and the ‘Pythagoreans’, Theophrastus is actually describing theories about the structure of the universe held by an important Platonist competitor and the contemporary head of the Academy in Athens, Xenocrates of Chalcedon (396/5–314/13 b.c.e.), who (a) took it upon himself to establish a Platonic doctrine that could be associated with his master's writings and (b) coordinated that doctrine with the philosophical precepts of the Pythagoreans. As a consequence of our study, we are prompted to question Aristotle's famous ascription of a theory of ‘imitation’ to the metaphysics of the genuine contemporary or recently deceased Pythagoreans (such as Philolaus of Croton or Archytas of Tarentum) and consider how Xenocrates' writings on Plato and the ‘Pythagoreans’ might be informing both Theophrastus' and Aristotle's descriptions of the Platonic and Pythagorean philosophical system(s). Investigation of such matters might have the potential to enlighten us about how Plato's students in the Early Academy were engaged both in the project of assimilating specific aspects of Plato's philosophy to that of the Pythagoreans and in the codification of the central tenets of Plato's metaphysics.
II. ARISTOTLE'S ACCOUNT IN METAPHYSICS Α vs. THEOPHRASTUS' ACCOUNT IN HIS METAPHYSICS
Few passages in Aristotle's Metaphysics Α have catalysed such confusion among historians of ancient philosophy as his description of Plato's inheritance of Pythagorean philosophy. After all, Aristotle, as Plato's student, is a reliable witness of Plato's philosophy – at least in so far as he reads Plato through his own philosophical assumptions and technical terminology – and, more importantly, he is the first systematic historian of philosophy whose work survives.Footnote 22 The pursuit of first principles for philosophy, a project that Aristotle in some ways inherited from Plato (and, I might add, the Pythagorean Philolaus),Footnote 23 naturally brings in tow a flurry of problems, questions and concerns that themselves informed both Aristotle's composition of the Metaphysics and Theophrastus' approximation to Aristotle's effort. Things are made more complicated, and friction arises, when we seek the first principles of (historical) existence, things that are meant to function on the one hand as logically prior principles of knowledge (such as hypotheses assumed for a proof) and temporally prior origins of a phenomenon that we can trace up to the present moment – such as philosophy which, in Aristotle's opinion anyway, has a traceable history. Throughout the Metaphysics, Aristotle exhausts himself with the first of these questions, whereas (for the most part) the second he relegates to a sketch in Book Α. Consequently, when he attempts to present a diachronic historical ‘lineage’ for the development of philosophy in Metaphysics Α, he sometimes complicates this ‘lineage’ with a comparative or dialectical study of principles. One possible result of the tension that arises is that such an exercise in dialectic might force Aristotle into believing that the terms of the comparison employed are unclear, or perhaps even ill-equipped for the subject at hand, as we see in his analysis of Plato and the ‘Pythagoreans’:
After the aforementioned philosophies [of the ‘Pythagoreans’] came the system (πραγματεία) of Plato, which followed them in most respects, but his philosophy had peculiar features that went beyond theirs …Footnote 24 With regard to participation (μέθεξις), it was only the name that he changed; for the ‘Pythagoreans’ say that things exist by ‘imitation’ (μίμησις) of numbers, whereas Plato says that they exist by ‘participation’ – changing the name. But what ‘imitation’ or ‘participation of the Forms’Footnote 25 could be, they left an open question.
(Aristotle, Metaph. 1.6, 987a29–31, b11–15)In the larger scheme of Aristotle's project, this passage is effectively transitional, that is, it marks the point in the narrative where Aristotle shifts from describing the historical development of Plato's thought – both in terms of the larger scope of the history of philosophy and in terms of the idiomatic development of Plato's thinking throughout his lifetime – to a discussion of Plato's ontology, with special attention paid to the three types of entities (Forms, intermediary objects of mathematics, sensibles) and the chain of causation that leads from first principles. Aristotle pays special attention to the first principles of Plato and the ‘Pythagoreans’, that is, the ‘One’ and the ‘Unlimited’: in the passage that follows (1.6, 987b14–988a2), he emphasizes that Plato ‘spoke’ (ἔλεγε) in a way very close to the ‘Pythagoreans’, with the characteristic differences in their philosophical systems being (a) Plato considered the Unlimited not to be one thing, but two (that is, the ‘Great and the Small’); (b) that Plato treated the ‘One’ as a substance (οὐσία) and not a predicate; (c) that he regarded numbers (including the ‘One’?) and sensibles as distinct; (d) that he posited an intermediary group (that is, the objects of mathematics) between the ‘One’ and sensible objects; and (e) that he introduced the Forms. The reason, so Aristotle claims, for (c) and (e) is that Plato employed dialectical arguments, to which the ‘earlier (οἱ πρότεροι) Pythagoreans’ did not have access.Footnote 26 This is the extent to which Aristotle draws comparisons between Plato and the ‘Pythagoreans’ in this important but frustratingly compact summary.
Now we can use Aristotle's account as a test for that of Theophrastus (and vice versa) since, apparently, Theophrastus has taken up the open question concerning what Plato meant by ‘participation in the Forms’, as well as what the ‘Pythagoreans’ meant by ‘imitation’, by investigating the latter. Theophrastus' examination of ‘imitation’ takes up from where Aristotle had left off and, although Aporia 24 itself cannot count as a comprehensive analysis of this problem (its focus, after all, is on explaining the ‘distance’ between the first principles and everything else), examination of the problem of ‘imitation’ in Theophrastus' Metaphysics as a whole yields valuable results. Still, with regard to each author's treatment of the relationship between Plato and the ‘Pythagoreans’, I would argue that there is significant divergence of opinion.
It will be of value to start by examining what is similar in these accounts. On two issues Aristotle and Theophrastus can be said to agree: first, they agree that, for Plato and the ‘Pythagoreans’, some sort of ‘imitation’ is the vehicle for relationships between the first principles and sensible objects; and, second, they both present the essential first principle as the ‘One’.
Beyond that, their accounts surprisingly diverge in many ways. The closest point of comparison is their treatment of the Platonic and ‘Pythagorean’ principle of duality, which Aristotle calls the ‘Unlimited’ (as a general term that refers to the first principles of both Plato and the ‘Pythagoreans’) and Theophrastus the ‘Indefinite Dyad’. At first glance, this might seem to be splitting hairs, except for the fact that Theophrastus immediately goes on to explain that, for Plato and the ‘Pythagoreans’, the Unlimited resides (or is) ‘in’ the Indefinite Dyad, just like the qualities of being without order or shape (ἐν ᾗ καὶ τὸ ἄπειρον καὶ τὸ ἄτακτον καὶ ὡς εἰπεῖν πᾶσα ἀμορφία καθ' αὑτήν). As a fundamental term in Aristotle's classification of beings, to be ‘in’ something must be understood as vastly different from being identical to it. For the Aristotle of the Categories (1a24–b9), anything that is ‘in’ a subject is a quality that cannot exist independently of that subject; this is perhaps something like what Theophrastus means when he claims that the ‘Unlimited’ (τὸ ἄπειρον), the ‘Unordered’ (τὸ ἄτακτον) and ‘all Shapelessness as such’ (πᾶσα ἀμορφία καθ' αὑτήν)Footnote 27 are ‘in’ the Indefinite Dyad. It is likely that the terminology for ‘in’ employed by Theophrastus is in dialogue with Aristotle's and Plato's usages, although a lack of corroborating evidence from his Metaphysics complicates any understanding on our part of Theophrastean ‘inherence’. It should also be noted that Plato's Timaeus, which exercised a great deal of influence over Platonist metaphysics, describes the Receptacle in similar terms, calling it essentially ‘shapeless’ (ἄμορφον) and describing it as the matter ‘in’ which (ἐν ῷ) the Demiurge creates imitations of the Forms to which he is looking.Footnote 28 The fact that ‘in’ features prominently in both Aristotelian and Platonist systems of language and metaphysics suggests that the question of the logical and ontological values of ‘in’ was up for grabs among the successors of Aristotle and Plato.Footnote 29
Related to the issue of the Unlimited, the Unordered and Shapelessness ‘as such’ (καθ' αὑτήν) is the question of the Forms. Now Aristotle clearly speaks about the Forms in his discussion of Plato's pragmateia, and there has been a long debate about whether numbers played the same role in ontology of the ‘Pythagoreans’ as the Forms did in Plato's. It is notable that numbers (οἱ ἀριθμοί) do not appear in Theophrastus' account of the Platonic and ‘Pythagorean’ ontology in Aporia 24 of his Metaphysics, although there was a fierce and sustained debate about whether the One and the Indefinite Dyad were actually numbers in the Early Academy and Lyceum. Neither do the Forms, at least explicitly: a survey of occurrences of the ‘Form’ terminology in Theophrastus' Metaphysics suggests that the terms εἶδος and γένος are used taxonomically, as ‘species’ and ‘genus’, in accordance with Aristotelian usage; the only term that apparently means something like ‘Form’ in Theophrastus' Metaphysics is ἰδέα, which he uses twice, once to refer to something like the Forms of Plato's middle dialogues (6b13) and once to refer to outward shape (10b28), as was relatively more common in the Greek language.Footnote 30 But by referring to the Unlimited, Unordered and Shapelessness ‘as such’ (καθ' αὑτήν) Theophrastus is probably speaking about Forms (in a Platonic and/or Platonist sense) of the qualities of being limitless or lacking order and shape. This is the language Plato himself uses to describe the Forms in the Phaedo, in what we might consider, with Ross, their definitive appearance in Plato's oeuvre.Footnote 31 On this reading, Theophrastus does address the problem of the Forms as Aristotle had done, but only in an oblique way: the attributes or qualities of being shapeless, and their attendant Forms (if that is how we are to read them), are ontologically dependent on the Indefinite Dyad as a first principle.Footnote 32
It is only in the aforementioned sense, that is, ontologically, that one might understand any possible reference to predication, which is expressly discussed in Aristotle's account. In general, Theophrastus does not treat predication of the Aristotelian type in his Metaphysics, despite its central importance to both of Aristotle's major works on first philosophy, the Categories and Metaphysics.Footnote 33 Nor does Theophrastus attribute any sort of ‘definition’ that might lead to predication, thus removing entirely the Socratic element that Aristotle emphasized as a distinguishing factor between the philosophies of Plato and the ‘Pythagoreans’. Finally, and most conspicuously, Aporia 24 makes no explicit reference to anything like the ‘objects of mathematics’ with which Aristotle famously associated Plato's philosophy. We might be surprised to find that, in many aspects of his philosophy (notwithstanding the history of philosophy), Theophrastus does not simply adopt Aristotelian assumptions about language and logic.
What is the result of such a comparison between the accounts of Aristotle and his student? What becomes quickly apparent is that Theophrastus' account, while it takes up the question of ‘imitation’ raised by Aristotle, represents a distinct treatment of the relationship between Plato and the ‘Pythagoreans’. We are thus prompted to ask ourselves whether Aristotle's and Theophrastus' accounts of this relationship (a) are informed by different sources on this relationshipFootnote 34 or (b) focus on different aspects of the relationship. The picture that begins to develop is one of divergent ways of linking Plato with Pythagoreanism, with Aristotle on one side, and his student Theophrastus on the other. Does this divergence occur because Theophrastus is expanding upon Aristotle's characterizations of Platonic and Pythagorean thought (perhaps in a lost work?), because both are independently deriving their propositions from the same source/s, or perhaps both? Are the ‘unwritten’ doctrines lurking in the background? Multiple attempts to make better sense of Aristotle's claim (Metaph. 987b11–14) that ‘the “Pythagoreans” say that things exist by “imitation” of numbers, whereas Plato says that they exist by “participation” in the Forms – changing the name' have produced little if any agreement among scholars, even going as far back as Zeller in the late nineteenth century. I suggest that we might gain traction on the problem of ‘imitation’ by appeal to a closer examination of Theophrastus' Aporia 24, directing our attention to how Theophrastus understands ‘imitation’ throughout his philosophical writings and how this might be derived from what are likely to have been his immediate sources in the Early Academy.
III. THEOPHRASTUS ON XENOCRATEAN REDUCTION VIA ‘IMITATION’
Theophrastus and the doxographical tradition that follows from his fragmentary and lost writings constitute some of the most important sources for our knowledge of the Early Academy after Plato's death. The other major early source is Aristotle. But, as we have already seen, it is relatively common for Theophrastus and Aristotle to disagree about attribution of philosophical doctrine to various competitors and predecessors, as well as to clash about how to challenge those figures. Theophrastus' treatment of the major Platonists Speusippus and Xenocrates, as well as less notable figures like Hestiaeus, Philip of Opus and Hermodorus, comes out of the perspective of his own philosophical system, as Dillon has argued in recent work.Footnote 35 This means that we are able to approach the problem of Platonic/‘Pythagorean’ ‘imitation’ by way of (a) Theophrastus' employment of this concept in his own philosophical systems and (b) the Platonists' application of the same concept to their own philosophical systems.
In the most general sense, ‘imitation’ (μίμησις) is an activity or, perhaps better, a metaphysical operation that is associated with various topics in Theophrastus' writings. It is possible that, like Aristotle, he had a theory of literary ‘imitation’, or at least used the term and its cognates in reference to comedy, drama and historiography, although the evidence is meagre and circumstantial.Footnote 36 With regard to Theophrastus' writings on plants and other natural objects, there is no evidence for any peculiar notion of ‘imitation’. There is, however, one example where Theophrastus describes ‘imitation’ as an operation that mediates between entities. While defending the idea that mountains grow in his writings on physics, Theophrastus ascribes to ‘wise men of old’ the idea that the upward force of fire from deep inside the earth brings with it earth that, once it reaches a certain peak, ‘imitates’ the shape of fire (τὸ πυρὸς σχῆμα μιμουμένη).Footnote 37 Precisely who the ‘wise men of old’ might be is under dispute, with plausible candidates including Democritus, Heraclitus, and the Pythagorean Hippasus of Metapontum.Footnote 38 Regardless of the referent for this testimony, a brief survey of Theophrastus' surviving fragments reveals no unique theory of ‘imitation’ that we should ascribe to him; on the contrary, the only outstanding example of ‘imitation’ as an operation in the other fragments of Theophrastus' writings attributes it to another intellectual.
The most compelling descriptions of ‘imitation’ in Theophrastus' surviving writings, to be sure, come in other aporiae of his Metaphysics. In these passages, we discover that Theophrastus inscribes the unique problem of ‘imitation’ into the more universal problems of cosmic desire and motion. In search of what is most prior, one must seek, Theophrastus claims, the principle that is prior to movement. This principle cannot be moved, and it must exist only ‘as such’ (καθ' αὑτήν).Footnote 39 Theophrastus, following Aristotle, commits himself to the argument that the power which fulfils these requirements is a cosmic version of ‘desire’ (ὄρεξις) or, perhaps, ‘tendency’ (ἔφεσις).Footnote 40 The special relationship between Aristotelian ‘desire’ and ‘tendency’, on the one hand, and the Platonic/‘Pythagorean’ ‘imitation’, on the other, has been a noted subject for discussion among scholars since J.B. Skemp, whose contribution to the Symposium Aristotelicum of 1966 generated a debate among the participants about how Theophrastus' account of first principles challenges Aristotle's theories of cosmic motion, especially the unmoved mover.Footnote 41 Still, what Skemp and those who have followed him took for granted was the nature of reduction through the operation ‘imitation’, despite the lack of a clear definition of this concept for both Aristotle and Theophrastus.
‘Imitation’ plays a role in Theophrastus' metaphysics at several key points, a fact that is surprising given the infrequency of occurrences of terms relating to μίμησις in the corpus of his fragments. Before we can understand more precisely what Theophrastus means by ‘imitation’, we will be required to take a short detour from this idea in order to see the contexts for its development in his Metaphysics. A brief digression on the general description of Theophrastus' first principles in Aporia 5.1 allows us to see how Theophrastus conceives of ‘imitation’ as somehow related to how sensibles ‘connect’ with the first principles:
Such is the first principle [i.e. divine (θεία)], and since it is connected with the sensibles (συνάπτει τοῖς αἰσθητοῖς) – and nature is, to put it simply, in motion, and this is the property unique to it – it is clear that we must posit that principle as a cause of movement. And since it is as such unmoved (ἀκίνητος καθ' ἀυτήν), it is evident that it could not by being in motion serve as a cause of the things of nature. Rather, the only alternative is that it could do so by some other power superior and prior [to this]. And such is the nature of the object of desire (ἡ τοῦ ὀρεκτοῦ φύσις), from which comes the circular [motion] which is continuous and unceasing. Therefore, on this basis, [the objection] that there could not be any origin of motion except one that has been moved by means of a motion could be resolved.
(Theophrastus, Metaphysics 4b19–5a5)As is clear from this passage as well as earlier ones,Footnote 42 what is being examined throughout Theophrastus' doxography of other intellectuals' metaphysical systems (especially, for our purposes, those of Plato and the ‘Pythagoreans’) is the nature of the ‘connection’ (ἡ συναφή) between the first principle/s and sensibles. Theophrastus is not fully innovating here, as investigation into the precise nature of the ‘connection’ between metaphysical and physical objects had been a concern of Plato in his various accounts of the Forms and dialectic.Footnote 43 Moreover, Theophrastus' pursuit of the ‘connection’ between first principle/s and the phenomena reflects a Platonic and likely Platonist heritage, and it provides Theophrastus with a way to interrogate the anonymous proposal that ‘number itself’ (αὐτὸς ὁ ἀριθμός) could be a first principle. Aristotle, for his part, declares (Metaph. 987b22–988a2) that Plato ‘spoke’ in a way very similar to the ‘Pythagoreans’, by which Aristotle means that each held that ‘numbers are the causes of Being for everything else’ (τοὺς ἀριθμοὺς αἰτίους εἶναι τοῖς ἄλλοις τῆς οὐσίας). As I discussed earlier, Aristotle goes on to describe the distinctions between their systems, but at this point we might focus on one aspect that was of great concern to Theophrastus, namely the relationship of ‘connection’ between causes (or, in some cases, first principles) and sensibles. Aristotle claims in arguments (c) and (d) cited above that Plato did not conflate causes with sensibles, as the ‘Pythagoreans’ had done, but instead separated them out and provided as an intermediary the mathematical objects. Nowhere in this account does Aristotle refer to a ‘connection’ per se, but instead he concerns himself with relationships of ‘participation’ and ‘imitation’. In certain places of his earlier works On Philosophy and Categories, Aristotle figures problems of general ontology in terms of ‘connection’, and this is especially the case with mathematics.Footnote 44 Still, it should be noted that crucial passages of import in the Physics and Metaphysics refrain from using ‘connection’ as an operational term and might suggest some uneasiness about using it in reference to Aristotle's own ideas about physics and metaphysics, at least in his later writings.Footnote 45
The shift away from using ‘connection’ as a way of describing ontological relationships in Aristotle's philosophy might be thought to signal Aristotle's increased criticism of Platonist doctrines, especially the influence of Xenocrates on the question of the Forms.Footnote 46 Of particular concern to Aristotle as well as Theophrastus, I would argue, is the ‘mathematical’ status of the Form-Numbers. Theophrastus examines this problem with consideration of the semantics of ‘connection’ and related terms, which were important in theoretical mathematics as discussed in the Lyceum and the Academy.Footnote 47 While, among surviving fragments of Speusippus, the term ‘connection’ (ἡ συναφή) and its cognates do not appear, it features prominently in an important and understudiedFootnote 48 summary of Xenocrates' ontology of beings that bears import on Theophrastus' account:
Of the three types of triangular entities, the equilateral, so Xenocrates claimed, devotes itself to all the divine souls in so far as they are controlled by the One. For Equality is Unity. Thus they are also called divine, for the One is the unique property of the divine. But since the one that is in souls is not [the One] by itself, but it participates (μετεχόμενον) in the Multiplicity that is in them, Unity becomes Equality in the souls devoted to the divine on all sides and generates in all living beings a triangle equal on all sides. Thereby, they [wise men of old?]Footnote 49 also devote the entirety [of the triangle to the divine], both the motions in straight lines and the conjunctions of motions in angles.
The isosceles triangle is consecrated to those souls that come after the divine souls and are daemonic. In these souls, which are intermediary, are both Equality and Inequality, Unification and Diversity of powers, since their bases are unequal to the lines above them. Consequently, then, the daimones attach themselves (ἐφάπτονται) to the inferior entities at their [lower] extremities, as well as to the superior entities at their higher extremities; and attachment assimilates them (ἡ ἐπαφή … ἐξομοιοῖ) to the [superior entities] in virtue of Equality, whereas it connects them (συνάπτει) to the [inferior entities] in virtue of Inequality.
And, in fact, the third type of souls, the scalene, which is unequal in every way, is the image (εἰκών) of those that ascend and descend, the ones which are unequal to the superior and the inferior entities – for, indeed, they [the isosceles souls?], once put into motion, touch upon [the superior entities] now more, and now less; and the same with regard to the inferior entities; and, most incredible, the same with regard to one another as well. Thus, to those which are unequal in every way, that which is Unequal in all aspects is assigned.
(Xenocrates F 223 Isnardi Parente = Procl. In Remp. 2.48.4ff. Kroll)I suggest that Proclus' presentation of Xenocrates' fragment helps us to understand more precisely what Theophrastus means when he discusses ‘connection’ between sensibles and first principles in his Metaphysics. In order to make sense of this claim, however, it will be necessary to discuss in some detail what Proclus is saying about Xenocrates' so-called ‘intermediary’ type of souls, since the ‘intermediary’ realm is the place where ‘imitation’ of some sort apparently occurs. Xenocrates associates the ‘daemonic’ souls, which are not the same as the ‘divine’ souls, with isosceles triangles, on the grounds that ‘daemonic’ souls are (a) intermediary between the superior (that is, the equilateral) and the most inferior (that is, the scalene) entities and (b) have ‘in’ them contrary Forms, such as Equality and Inequality or Unification and Diversity. They are unlike the superior entities apparently by virtue of their being at a distance from the first principles, namely the One and Multiplicity, which are the Forms in which only the highest type of triangle (that is, the equilateral) participates (μετεχόμενον). Note that participation is an operation that only occurs between the very highest orders of being, whereas everything below employs different operations related to what we might consider types of ‘attachment’.Footnote 50 The intermediary entities are ‘assimilated’ (ἐξομοιοῖ) to the highest type of entities, which is evident, so Xenocrates argues, in the fact that two of their three sides (that is, the two that are distinct from the base) are equal. Contrastively, their base is unequal to the other two sides; by virtue of the Inequality ‘in’ them, the isosceles entities are said to be ‘attached’ (συνάπτει) to the lower entities, the scalene triangles, which possess sides that are all unequal. It is difficult to know with precision what terminology can be traced directly back to Xenocrates,Footnote 51 but the text is pretty clear in distinguishing two species of ‘attachment’ (ἡ ἐπαφή) for the daemonic types of souls, namely, attachment to the superior parts of the cosmos, which is the activity of upwards ‘assimilation’ (ἡ ἐξομοίωσις), and attachment to the inferior parts of the cosmos, which is activity of downwards ‘connection’ (ἡ συναφή).Footnote 52 Importantly, the attachment of the daemonic souls that leads upwards, namely ‘assimilation’, might be a concept coextensive with the concept of reduction through ‘imitation’ that Theophrastus attributes to Plato and the ‘Pythagoreans’ in Aporia 24 of his Metaphysics.Footnote 53
Indeed, if we return to the basic notion under scrutiny in Theophrastus' discussion of first principles and of the nature of the ‘connection’ between superior and inferior entities, namely, whether ‘number itself’ (αὐτὸς ὁ ἀριθμός) could be a first principle, we are struck by quite specifically Xenocratean-sounding language.Footnote 54 ‘Number itself’ as described here suggests the absolute Form-Number that is associated with Xenocrates' philosophy by Aristotle and others.Footnote 55 Moreover, when Theophrastus explicitly describes Xenocrates' ontological system – under the general heading of those who posit the first principles as the One and the Indefinite DyadFootnote 56 – he praises Xenocrates and distinguishes him from the other Platonists for ‘somehow assign[ing] everything a place in the universe, alike objects of sense, objects of intellection, mathematical objects and, furthermore, divine things’ (ὁμοίως αἰσθητὰ καὶ νοητὰ καὶ μαθηματικὰ καὶ ἔτι δὴ τὰ θεῖα). Comparison between this tripartite scheme and that outlined by Sextus Empiricus – which posits three realms of being, namely the ‘sensible’, the ‘intelligible’ and the ‘opinable’ – has led to confusion for Dillon, who unnecessarily assumes that the ‘divine things’ that Theophrastus apparently tacks on to (ἔτι δή) his tripartite levels of reality are heavenly bodies, which, one might imagine, should occupy an intermediary position between intelligibles and sensibles.Footnote 57 But if we compare these accounts with that of Proclus quoted above, we see that in mentioning the ‘divine things’ Theophrastus is not referring to the heavenly bodies, which would be on the same level as the daemonic (and not the divine) souls.Footnote 58 A diagram comparing these relationships might be appropriate here:
Such a diagram is potentially obfuscating, in the sense that it draws explicit connections between realms of being that are not expressly analogized in any one given text. It is also the case that we should be careful not to read the ‘Types of Attachment’ as Xenocratean doctrine, since we cannot be sure that he employed the very same terms (especially in their nominal form) that Proclus implies. But, if scholars such as Dillon and Merlan are right, Xenocrates represents the first Neoplatonist in the sense that he pursued a doctrinal codification of Plato's philosophy.Footnote 61 The reception of Xenocrates' philosophy by figures such as Sextus Empiricus also testifies to the antiquity of the Xenocratean ‘realms of being’. Of course, what is of interest to our investigation into ‘connection’ is the intermediary level, called the ‘opinable’ by Sextus and understanding daemonic souls – which might be analogous to the heavenly bodies – as mathematical objects. The status of such mathematical objects is a cause for confusion for modern scholars, but it is comforting to know that such confusion can be traced back to the commentators of Aristotle.Footnote 62 The confusion might lie with Xenocrates himself, however. Aristotle, for his part, complained of Xenocrates that his system collapsed eidetic into arithmetical number, effectively eliding out the application of mathematics.Footnote 63
In the absence of a precise understanding of how to parse out the differences between the Formal and mathematical in Xenocrates, we can be confident that he (a) posited at least – but probably not more than – three realms of being and that he (b) conceived of them as being related to one another by means of an intermediary mathematical and ‘opinable’ realm which was in contact with both the superior and inferior realms of being. The nature of Xenocrates' ‘connection’ was of concern primarily to Theophrastus and, to a lesser extent, to Aristotle. The testimony of Proclus confirms our suspicions that Theophrastus is referring to Xenocrates when he considers ‘number itself’ as an unmoved mover against Aristotle's ‘object of desire’. Indeed, in anticipation of his criticism of Aristotle's principle of impulse (ἡ ἕφεσις), he returns to the problem of ‘imitation’ at Aporia 8, with, I would argue, Xenocrates chiefly in mind:
Also a matter of aporia is how in the world they [rotating bodies], although they have a natural desire, pursue not rest but motion. Why is it, then, that both those who posit the One and those who posit the numbers alike make that claim [that is, that rotating bodies pursue motion] along with imitation? For the latter claim that numbers <imitate>Footnote 64 the One.
(Theophrastus, Metaphysics, 5a23–8)As Ross and Fobes note, the point of comparing Aristotle's with the Academic explanations of the movements in the universe is that ‘whether we say that the sensible world “desires” or that it “imitates” the first principle, we should expect to find it in that case having the same characteristics as the first principle – not movement but rest’.Footnote 65 The challenge Theophrastus poses to the Platonists in particular is to explain how things that seek to be like (that is, to imitate) the first principle, which is at rest, pursue motion in order to achieve that quality. This is an apparent absurdity: how can something that aims to have the quality of being at rest go into motion in order to pursue that quality? Implicit here is that the operations of ‘impulse’ and ‘imitation’ are compatible, at least for Theophrastus' purposes.
Such, indeed, is the problem to which Theophrastus returns when he attempts to define the relationship between the first principles and sensibles in Aporia 16 (Metaph. 7b9–8a7). Initially (7b9–23), he proposes to revise the theory by describing ‘actualization’ rather than ‘motion’ as a criterion for first principles, on the grounds that the latter should only be reserved for sensibles, which cannot be prior ontologically. He then shifts the discussion back to the problem of desire and ‘imitation’:
Absurd, too, is the other claim that has been made, that the things that desire what is at rest do not imitate [it]. For why would the [imitation] of the things other [than the first principles] not accompany those [things that desire?]?Footnote 66 Except that, perhaps, we should not understand <the universe>Footnote 67 in the same way as (1) reducing it to the partless (εἰς τὸ ἀμερὲς ἄγοντας), but rather [to understand it] as (2) something in concord with itself and well fitted together so far as it can be (ὅτι μάλιστα σύμφωνον ἑαυτῷ ἀπηρτισμένον) – indeed, they claim that ‘the entire heaven is most perfect’ – as though it were a city or an animal or something else that has parts.
(Theophrastus, Metaphysics, 7b23–8a7)The key to understanding this extremely terse passage – and, to my mind, understanding the metaphysics ascribed to Plato and the ‘Pythagoreans’ in Aporia 24 – is making sense of what imitation has to do with reducing all things ‘to the partless’ (εἰς τὸ ἀμερὲς ἄγοντας).
The problem of ‘desire’ and ‘imitation’ prompts Theophrastus to juxtapose two claims about the structure of the universe and the relationship between its elements: first (1) the complex claim that (a) things that desire the first principle do so by imitating it, and (b) such an activity of imitation is a type of reduction to ‘the partless’; and second (2) that the universe is not an indivisible unity but rather a well-fitted (ἀπηρτισμένον) harmony of its disparate parts, like a city or a human being. Note that ‘desire’ and ‘imitation’ play no explicit role in the characterization of the second (2) claim; moreover, it would not be easy to make sense of how ‘desire’ and ‘imitation’ factor in harmonization of, for example, body parts.
What positions is Theophrastus contrasting here? One scholarFootnote 68 makes sense of the argument by suggesting that if imitation follows desire universally, the consequence would be a universe fully undifferentiated and, what is more, fully without motion. This creates a contradiction, since the Platonists who hold that the things that imitate the One (cf. Aporia 8, discussed above) are in motion in order to do so. Thus claim (2), which postulates a universe with parts that are differentiated but work in harmony with one another, is being solicited to answer the objections to claim (1). But the question of what claims are being contrasted here might be further enlightened if we can figure out who the authorities behind claims (1) and (2) are.
Van Raalte has implied that Aristotle is behind the claim (1) that things which desire and imitate the first principle do so by reduction to ‘the partless’ (τὸ ἀμερὲς). This would make good sense if there were any clear evidence in Aristotle's corpus that desiderative imitation were the vehicle for imperishable sensibles – especially the heavenly bodies – to reduce to the unmoved mover, which indeed is described as ‘partless’ twice in Aristotle's texts (Metaph. 7.7, 1073a6 and Phys. 8.10, 267b27). But the evidence she cites from Aristotle's texts for ascription to imitation of the ‘partless’ in reduction is circumstantial and exhibits Platonic qualities,Footnote 69 and internal comparanda from Theophrastus' Metaphysics associate both imitation and reduction centrally with Plato and the ‘Pythagoreans’.Footnote 70 On the other hand, it is perhaps more likely that a Platonist is the object of Theophrastus' criticism of the proposal that imitation of the first principle is a type of reduction to ‘the partless’.Footnote 71 Now none of the fragments of the Platonists of the Early Academy Speusippus, Philip of Opus, Hermodorus and Hestiaeus claims that the first principle is ‘partless’.Footnote 72 This fact alone makes it unlikely that any of these Platonists are the intended target of Theophrastus' objection. But we know of one Platonist who did indeed posit a ‘partless’ first principle, namely Xenocrates of Chalcedon. The relevant source for much of this information is the Peripatetic treatise On Indivisible Lines, which, it has been suggested, might be attributed to Theophrastus himself.Footnote 73 There, the author first presents a summary of five arguments attributed to someone who posits a ‘Form of Line’ (ἰδέα γραμμῆς), the first of which constitutes a proof that a certain ‘partless’ unit is prior to all other mathematical objects:
If ‘much’ and ‘big’, and their opposites ‘few’ and ‘little’, are similarly constituted, and if it is ‘much’ that has nearly infinite divisions, and not ‘few’, it is evident that ‘few’ and ‘little’ will have a finite number of divisions; if, then, the divisions are finite, there must be a partless magnitude, with the result that in all magnitudes there will be some partless thing (τι ἀμερές), since in all of them there is a ‘few’ and a ‘little’.
(On Indivisible Lines, 968a1–9)The argument, which is meant as a response to one of Zeno's paradoxes that stipulated ‘if things are many, they must be both small and large: so small as not to have magnitude, but so large as to be infinite’ (DK 29B1), operates on the assumption that the arithmetical (that is, of a discrete quantity) terms ‘much’ and ‘few’, as well as the geometrical (that is, of a continuous quantity) terms ‘big’ and ‘little’, are opposites. The argument runs something like this:
(i) If we accept that these pairs of terms are oppositional, then the characteristics of the ‘much’ and the ‘big’ must be opposite to the characteristics of the ‘few’ and the ‘little’;
(ii) The ‘much’ and ‘big’ admit of a nearly infinite number of divisions, and not ‘few’;
(iii) Therefore, ‘few’ and ‘little’ must admit of the opposite, namely, a finite number of divisions;
(iv) If the number of divisions for the ‘few’ and ‘little’ is finite, then there must be a minimum-sized (most ‘small’) magnitude that is the most finite (most ‘few’);
(v) If a thing is minimum-sized and of the most finite quality, it must have no parts;
(vi) Therefore, there is a certain minimum-sized thing that has no parts (τι ἀμερές).
Now given that Xenocrates assumes the existence of a thing totally partless, one would want to understand its relationship to things, for example, constituted of parts or, moreover, to wholes. Perhaps surprisingly for a Platonist, Xenocrates appears to believe that parts are prior (ontologically) to the whole, on the grounds that whenever a part is taken away from a whole, the whole is destroyed, whereas when a whole is destroyed, the part is not necessarily destroyed thereby.Footnote 74 From this alone, it becomes likely that, just as things constituted of parts are prior to wholes, so too what is partless is prior to things constituted of parts. Indeed, the universal theory of Xenocratean reduction to the partless described here also applies to the Form-Line as well as geometrical shapes constructed out of the Form-Line, such as squares, triangles and planes, which are constitutive of elemental bodies that have volume.Footnote 75 Furthermore, as the author of On Indivisible Lines attests explicitly, Xenocrates believed that, by virtue of the priority of the part over the whole, the ‘partless thing’ (τι ἀμερές) exists not only in the intelligible realm (with Form-Lines) but also the sensible realm, where the elemental bodies, such as fire, can be perceived:
Moreover, if there are elements of a body, and nothing is prior to the elements, and if parts are prior to the whole, then fire and, generally speaking, each of the elements of the body would be indivisible, with the result that some partless thing exists not only among the intelligibles, but also among the sensibles.
(On Indivisible Lines, 968a15–18)So much makes sense enough for Xenocrates' philosophy, even if a complete account of Xenocratean ontology and the role of mathematics in it cannot be undertaken here.Footnote 76 Serious questions, however, accompany Theophrastus' comparison of Xenocrates' operation of reduction to a ‘partless thing’ with ‘imitation’.Footnote 77 Of utmost importance for our study of Aporia 24 is how, in Aporia 16, Theophrastus is distinguishing Xenocrates' position (1) – in which all things can be reduced to a ‘partless’ thing – from that which he apparently prefers, namely the position of those who (2) ‘claim that the entire heaven is most perfect’ (ὁ ὅλος οὐρανός … φασιν εἶναι τελεώτατον) and posit a universe that is ‘in concord with itself and well fitted together so far as it can be’ (ὅτι μάλιστα σύμφωνον ἑαυτῷ ἀπηρτισμένον), like a city or an animal or something else that has parts (8a3–7). Who might the figures who espouse claim (2) be?
The description of the universe (2) as ‘in concord with itself’ carries with it Pythagorean and Platonic overtones, in the sense that it associates the cosmos with music. At first glance, we might imagine that Theophrastus is referring to the popular description of the design of the sensible World-Soul by the Demiurge in the Timaeus (35a1–36d7), which emphasizes the mixture (συνεκεράσατο) of the indivisible (ἀμερίστος) reality that is eternally existent and the divisible (μεριστή) into a combined ‘type’ (εἶδος) by ‘fitting together’ (συναρμόττων) these contrary qualities in accordance with musical intervals.Footnote 78 The likelihood of this being a reference to Plato is strengthened by the description of the ‘entire heaven’ as ‘most perfect’, a phrase that echoes the last line of the Timaeus.Footnote 79 It is certainly possible that Theophrastus is referring to Plato as the authority behind this claim. But there are problems with this hypothesis. Theophrastus is contrasting one position, namely that (1) of Xenocrates, which emphasizes the reduction of the universe, with a theory (2) which emphasizes the divisibility of the universe into disparate parts that, when taken together, create a ‘concord’. Plato here is not describing the reconstruction through a type of combination, but rather the opposite, the separation and ordering of parts of the universe. Moreover, the use of the terms ‘concord’ and ‘fitting together’ does not signal uniquely Platonic ideas about the structure of the cosmos.
The terms ‘concord’ and ‘fitting together’ and their cognates do not appear together anywhere else in Greek philosophy, but ‘fitting together’ does appear alongside ‘perfect’ in the contexts of music and epistemology in a fragment of Speusippus (Sext. Emp. Math. 8.145–6 = F 75 Tarán).Footnote 80 Still, Speusippus' text offers no close thematic or argumentative comparandum here other than in vocabulary. Aristotle indeed does use the term ‘fitting together’ in mathematical contexts, but he cannot be assumed to have advocated a universe organized according to the principles of ‘concord’.Footnote 81 None of the other Platonists, to our knowledge, imagined that the universe was constituted of parts in ‘concord’.
Rather, the cosmological and ontological position (2) being contrasted with Xenocrates' reduction to the ‘partless thing’ (1) in Aporia 16, I would suggest, is that of Philolaus of Croton and/or other Pythagoreans. Evidence that the Pythagoreans were interested in the relationships between the motions of music and the motions of the heavenly bodies comes as early as Plato's Republic Book 7 (530d8–531c4), where Socrates criticizes the ‘Pythagoreans’ who, like the ‘astronomers’, ‘pursue numbers in … audible consonances’ for ‘not ascend[ing] to the problems, that is, to examine which numbers are concordant and which are not, and the reasons for each’. This is a veiled but certain criticism of Archytas of Tarentum, and possibly his predecessors, who apparently investigated the properties of sound by analysis of string length.Footnote 82 Er's description of the Spindle of Necessity in Republic Book 10 (617a4–b7) illustrates eight Sirens placed at the top of eight cosmic circles, each singing a sustained note of variegated tone as the cosmic circles turn: ‘a single concord was harmonized (μίαν ἁρμονίαν συμφωνεῖν) from the eight beings’. This cosmological description, to be sure, does not clearly reflect Archytan cosmology, musicology or astronomy,Footnote 83 but most scholars have justly taken it to be generally Pythagorean in the light of Aristotle's ascription to some ‘Pythagoreans’ of a similar theory (On the Heavens 2.9, 290b12–291a10). There, Aristotle explicitly refers to the Pythagorean ‘concord of moving bodies’ (συμφωνίαν τῶν φερομένων) in reference to the theory that the speed of the moving bodies, based on the distances of the bodies from the centre, conforms to ratios of musical consonances.Footnote 84 Huffman's work on Pythagorean astronomy has concluded, with very little doubt, that this and other passages that refer to the Pythagoreans in Aristotle's writings are chiefly concerned with the cosmology of Philolaus of Croton.Footnote 85
The ascription of a theory that the universe has ‘parts’ like a ‘city or an animal’ can also be traced to the Pythagoreans more generally, and there may be good reason to see this as a reference specifically to Philolaus of Croton. The Doric Pseudo-Pythagorica preserve ‘Pythagorean’ traditions that both analogize ‘god’ with the ‘king’ and ‘city state’ and do so according to the coextensive operations (in Theophrastus' mind) of ‘imitation’ and reduction.Footnote 86 Unfortunately, we cannot be sure when or by whom these texts were composed. Their employment as evidence can only be circumstantial and might refer to traditions of Pythagoreanism, but not necessarily with unmediated reference to genuine writings of fifth- and fourth-century b.c.e. Pythagoreans like Philolaus of Croton or Archytas of Tarentum. Still, a remarkable fragment (F 17 Huffman = Stob. Ecl. 1.15.7) said to come from Philolaus' Bacchae and considered genuine by Huffman asserts that the ‘cosmos is one’ (ὁ κόσμος εἷς), that it grew ‘from the middle’ (ἀπὸ τοῦ μέσου) both upwards and downwards and that the ‘parts’ (μέρη) at the upper and lower extremities are similar. This in itself is not convincing evidence for the analogizing of the cosmos to the city state or to the body in Philolaus' thought. But a recent study by Huffman (see n. 87) has demonstrated the relationships of macrocosm to microcosm in Philolaus' overall philosophy by highlighting the analogies between cosmogony and anthropogony, specifically in his description of the birth of an infant (T A 27 Huffman = Meno Anonymi Londinensis 18.8). The central entity responsible for the symmetry that occurs following the birth of the infant as well as the birth of the cosmos is harmony (ἁρμονία), the ultimate ‘fitting together’ (συναρμόχθη) of limiting and unlimited entities (cf. F 1 Huffman = Diog. Laert. 8.85).Footnote 87 While Philolaus' fragments do not explicitly elicit the city state in this chain of analogies, it is not beyond imagination that he would have considered such relationships tenable.Footnote 88
The most likely point of reference for Theophrastus' claim that some people (2) see the universe as ‘something in concord with itself and well fitted together so far as it can be (ὅτι μάλιστα σύμφωνον ἑαυτῷ ἀπηρτισμένον) as though it were a city or an animal or something else that has parts’, then, would be those people called ‘Pythagoreans’ by Aristotle in On the Heavens, and very likely Philolaus of Croton himself.
If this speculative argument holds water, then we are presented with a problem in our understanding of ‘imitation’ as a modality of reduction to the first principles of Plato and the ‘Pythagoreans’ in Theophrastus' Metaphysics. In this text, there is no evidence that corroborates Aristotle's enigmatic claim that ‘imitation’ is a uniquely ‘Pythagorean’ metaphysical operation outside of Aporia 24. Instead, throughout the rest of Theophrastus' Metaphysics, ‘imitation’ is associated chiefly with reduction to the first principles in Plato's and Xenocrates' ontology. And in Aporia 16, the position of Xenocrates (1), which associates ‘imitation’ with the reduction to the ‘partless thing’ (τι ἀμερές), is contrasted with a genuinely Pythagorean position – that of Philolaus of Croton and demonstrated in his fragments (2) – which also corresponds directly with accounts of ‘Pythagorean’ astronomy and ontology in Aristotle's fragments on the Pythagoreans as well as in the Corpus. The metaphysical position (2) contrasted with that of Xenocrates, that of (what Aristotle calls) the Pythagoreans, makes no reference to reduction by appeal to ‘imitation’ as a vehicle.
So we are faced with another difficult interpretive question: when Theophrastus refers to the ‘Pythagoreans’ as espousing reduction to the first principles by means of ‘imitation’ in Aporia 24, is he actually referring to the thought of the genuine Pythagoreans whose writings survive (like Philolaus or Archytas), or is he referring to the thought of a Platonist such as Xenocrates or Speusippus?
The evidence presented above suggests that in the ascription of a theory of ‘imitation’ as a vehicle for reduction to the ‘Pythagoreans’, the point of reference is a Platonist, likely to be Xenocrates of Chalcedon, whose philosophy is associated with that of Plato in Theophrastus' surviving writings, including the doxography that ultimately traces back to Theophrastus.Footnote 89 It is well known that Xenocrates (apparently following Plato)Footnote 90 was deeply interested in the specific relationship between the One and the Indefinite Dyad and, moreover, that the latter may have played a significant role in the determination of subordinate ontological entities in his metaphysics.Footnote 91 Just as Theophrastus attests for Plato and the ‘Pythagoreans’ in Aporia 24, for Xenocrates the Indefinite Dyad was the principle of inequality, which made it possible for numbers to be generated.Footnote 92 This may have been the position of Speusippus too, although there are reasons to doubt that anything in Aporia 24 can be traced back specifically to him. First of all, Speusippus is likely to have preferred the term ‘multiplicity’ (πλῆθος) over ‘Indefinite Dyad’ (ἡ ἀόριστος δυάς), which is associated strongly with Plato and especially with Xenocrates.Footnote 93 Moreover, Xenocrates is considered to have attempted to save Plato's Forms as well as the language of the Forms by appeal to Form-Numbers, which are implicitly suggested by the language of Aporia 24. Finally, one would be required to explain why Theophrastus contrasts the opinions of Plato and the ‘Pythagoreans’ in Aporia 24 with those of Speusippus in the preceding paragraph, only two sentences earlier.Footnote 94 He had also done so much earlier, in Aporia 13 (Metaph. 6a23–b22), where the theories of reduction to first principles of Xenocrates, Hestiaeus and Plato are contrasted with the metaphysics of Speusippus. If he wanted to refer to Speusippus when describing the theory of reduction to first principles via ‘imitation’, why wouldn't he just have said ‘Speusippus’ in this circumstance, instead of referring to Plato and the ‘Pythagoreans’?Footnote 95
There is one other figure from the Early Academy whose philosophy shows intriguing correspondences with that ascribed to Plato and the ‘Pythagoreans’ in Aporia 24 of Theophrastus' Metaphysics, and whom we should take very seriously as a possible referent for the claims made in this passage: Hermodorus of Syracuse. Little is known about this figure, but one surviving fragment (quoted by Dercylides in Book 11 of his On the Philosophy of Plato) testifies to a fully realized theory of derivation from the first principles:Footnote 96
All the things considered to be great in relation to the small possess the More-and-the-Less; for it is more possible (?) that the More-and-the-Less is brought to the unlimited … those which are described as equal and stable and harmonized do not possess the More-and-the-Less, whereas their opposites do possess [it]. For it is possible for something to be more unequal than another unequal thing, and for something to be more activated than another activated thing, and for something to be more unharmonized than another unharmonized thing, with the result that – of each of these pairs – all except the element One are susceptible to the More-and-the-Less. The result is that such a thing may be said to be unstable and shapeless and unlimited and non-existent, by virtue of the negation of existence (ἄστατον καὶ ἄμορφον καὶ ἄπειρον καὶ οὐκ ὂν τὸ τοιοῦτον λέγεσθαι κατὰ ἀπόφασιν τοῦ ὄντος). To such a thing, neither origin (ἀρχή) nor existence (οὐσία) is befitting, but it is brought into a certain indeterminacy (ἐν ἀκρισίᾳ). For [Hermodorus] shows that in the same way that what creates is the cause in a strict and distinct sense, so too it is an origin (ἀρχή), but matter (ὕλη) is not an origin (ἀρχή). Thus it used to be said also by the followers of Plato that there is [only] one origin.
(Simplicius, On the Physics of Aristotle, p. 247.30ff. Diels = Hermodorus F 7 Isnardi Parente)We might note the similarities between the ontological systems attributed to Plato and the ‘Pythagoreans’ and to Hermodorus: both assume two principles and focus especially on the ways in which substratum entities adopt the aspects of their first principles. Moreover, both focus on the ways in which the material principle bestows its qualities on its derivatives, especially the absence of shape (ἄμορφον; recall Theophrastus' Metaphysics 11b4–5: ἀμορφία καθ' αὑτήν). In this sense, Hermodorus might be seen to fill in some of the holes that Theophrastus leaves open in his discussion of derivation from the material principle in Aporia 24. But there are two major problems with the hypothesis that Hermodorus is the source of the claims made in Aporia 24: he never (so far as we know) refers to the material principle as the ‘Indefinite Dyad’, but rather calls it the ‘More-and-the-Less’; and, in the case of Hermodorus, derivation from the material principle is established in order to prove that there is only one first principle (ἀρχή), namely the One, and that the ‘More-and-the-Less’ is indeed not a first principle. This squarely contradicts Theophrastus' attribution to Plato and the ‘Pythagoreans’ of two first principles, and while it could be very easy to confuse many things in Platonist ontologies, the number of first principles is likely not to be one of them.
IV. CONCLUSIONS
The evidence collected and analysed here suggests that the information relating to Plato and the ‘Pythagoreans’ in Aporia 24 of Theophrastus' Metaphysics is to be considered most likely derived from the writings of Xenocrates of Chalcedon. In the course of our study, we have traced the ways in which Platonist philosophy more generally, and the ontology of Xenocrates more specifically, are subjects whose ideas are worth examining constantly throughout Theophrastus' aporetic treatise. Several unexpected discoveries occurred in the process of investigating the theory of ‘imitation’ as vehicle for reduction to the first principles: Xenocrates, we have discovered, posited an ontological system that understood various modalities of ascending (from inferior to superior) and descending (from superior to inferior) ‘attachment’ between entities in the universe; the former is considered something like upwards ‘assimilation’ (ἐξομοίωσις) and the latter something like downwards ‘connection’ (συναφή) by Xenocrates. Xenocratean reduction, which is something like ‘assimilation’, is formulated by Theophrastus as a type of ‘imitation’ of the first principles, and the ultimate form of reduction via imitation is to a ‘partless’ minimum (τι ἀμερές), which is equated with the Form-Line and is said to reside (as a quality) ‘in’ mathematical objects that are located in both the intelligible and sensible realms. The Form-Line, which is ‘partless’, is prior to any of its derivatives (planes, solids, etc.) on the ground that a whole cannot preserve its identity if a part of it is destroyed, but a part can preserve its identity even when the whole of which it is a part is destroyed. Theophrastus contrasts this theory of reduction to the ‘partless’ with the Philolaic (and thus Pythagorean) conceptualization of the universe as a divisible unity that is ‘in concord with itself and well fitted together’.
The results of this study compel us to consider two theories regarding the historical relationship between the philosophical systems of the mathematicizing Platonists (such as Xenocrates) and of the genuine Pythagoreans. First, the evidence as presented allows us to raise further inquiries regarding the characterization of the metaphysics of Plato and the ‘Pythagoreans’ in Theophrastus' Metaphysics. There is a strong possibility that the information concerning the ‘Pythagoreans’ was derived from one of Xenocrates' writings on the Pythagoreans, the Pythagoreia, or was perhaps in his writings on mathematics; it is also possible, in light of the close connections established between Plato and the Pythagoreans by the Platonists, that this information might have come from Xenocrates' discussion of the first principles of Plato's philosophy in his works on metaphysics.Footnote 97 A confusion of Platonic and ‘Pythagorean’ would certainly be understandable if Xenocrates were the primary source for Theophrastus' conceptualization of ‘Pythagorean’ doctrine. Second, the observation that Xenocrates is really the source for Theophrastus' information regarding the ‘Pythagoreans’ – and not Aristotle alone – raises further questions for our understanding of Aristotle's summary of the philosophical systems of Plato and the ‘Pythagoreans’ in Metaphysics Α: is it the case that both Aristotle and Theophrastus were deriving their knowledge of ‘Pythagorean’ metaphysics from the same work of Xenocrates but interpreting basic operations (such as ‘imitation’ or ‘connection’) in different ways? Or might we speculate that, given the considerable amount of difference in focus between Aristotle's and Theophrastus' accounts of the philosophy of the ‘Pythagoreans’, that they were responding to different sources?
With regard to the theme of the work under examination, our study has concluded aporetically; but one of the important consequences is that we can better discern how Xenocrates' discussion of Plato and the ‘Pythagoreans’ played a significant role in the determination of Platonism and Pythagoreanism as philosophical systems associated with one another in the Early Academy. As Plato's students went on to adapt the central tenets of his metaphysics – especially the suggestive corollaries between ‘participation’ and ‘imitation’ of sensibles in intelligibles – they sought to clarify various aspects of Plato's thought that remain obscure in the dialogues. The testimony of Theophrastus thus provides us with an important avenue for pursuance of a better understanding of Platonic metaphysics as it was reformulated in the Academy immediately following Plato's death in 347 b.c.e. Does this account reflect Plato's own ‘unwritten’ teachings in the Academy? We cannot be sure about that, but the results presented here might be worth considering in relation to that debate. Still, Theophrastus' account of the systems of being of Plato and the ‘Pythagoreans’ has been shown to reflect rather closely what we know to have been genuinely Xenocratean – even if it cannot be considered necessarily Platonic or Pythagorean. The role that Xenocrates has played in the correlation of Platonic and Pythagorean metaphysics is central, so central that the most valuable contemporary ‘alternative perspective’ to Aristotle's account – that of Theophrastus – might be completely indebted to it. Scholars of ancient Pythagoreanism are thus faced with the impossible task, once again, of extricating genuine Pythagorean ideas from the Platonist substrate. The upshot of our study is that we can now better see how seriously Theophrastus took Xenocrates' claims in the intellectual battles over cosmology, psychology, metaphysics and logic. It has long been recognized that Aristotle saw Xenocrates as a worthy competitor; our study has shown that Theophrastus has much to say about, and in response to, Xenocrates as well, even if we must admit that Theophrastus' own knowledge about Pythagoreanism has been mediated.
