¹ Also known as On the First Principles (Περὶ ἀρχῶν), or perhaps On Basic Problems (Περὶ τῶν ἁπλῶν διαπορημάτων). For a good discussion of the problems involved in recovering a title for this text, see especially Laks, A. and Most, G., Théophraste: Métaphysique (Paris, 1993), ix–xviiiGoogle Scholar. My choice to employ a system of organization according to aporiae follows Gutas, D., Theophrastus: On First Principles (known as his Metaphysics) (Leiden, 2010), 38–43CrossRefGoogle Scholar, who argues persuasively that the study of each aporia ‘on its own merit’ allows us to ‘better perceive the significance of each detail for Theophrastus's immediate milieu and thus better gauge its historical moment’. Following convention, I will also supply Usener's page numbering when citing the text.

² The phrase is Dillon's (Dillon, J., ‘Theophrastus’ critique of the Old Academy in the Metaphysics’, in Fortenbaugh, W.W. and Wöhrle, G. [edd.], On the Opuscula of Theophrastus [Stuttgart, 2002], 175–87Google Scholar, at 177) with reference to Theophrastus' attack on the Platonists at 5a23–8. By ‘Platonism’ I refer to the attempts to systematize Plato's thought in the Early Academy following his death in 347 b.c.e. By ‘Platonic’ I refer to concepts that can be derived directly from Plato's dialogues but are not explicitly present in the writings or thoughts of the Platonists.

³ Burkert, W., Lore and Science in Ancient Pythagoreanism, tr. Minar, E.L. Jr. (Cambridge, MA, 1972)Google Scholar, at 62 with n. 57, posits that Theophrastus is contrasting the Good (τὸ ἀγαθόν at 11a19), (in Burkert's words) the ‘model of everything real’ (sc. τὰ ὄντα at 11a25), with everything else. This reading has the advantage of drawing from the terms employed in the previous paragraph, where Theophrastus was discussing Speusippus' doctrine of the Good. Raalte, M. Van, Theophrastus' Metaphysics (Leiden, 1993), 566Google Scholar, in contrast, will only commit to the claim that ‘the term here apparently refers to the distance between two provinces of being, one endowed with a value which is lacking in the other’. Yet, as is clear from the context of the argument (on which, see the illuminating discussion of Gutas [n. 1], 384–6), what Theophrastus is contrasting is the opinion of Speusippus, who holds that the Good is at the centre of the universe, with Plato and the ‘Pythagoreans’, who hold that the first principles, which are of highest value, are far away from the sensible world. Moreover, Gutas's interpretation has the advantage of reflecting what Theophrastus says earlier on (Metaph. 6a14–7a6) about derivation from the first principles as a sort of ‘imitation’. See below.

⁴ I follow Ross–Fobes, Philip and Gutas in maintaining the manuscript readings of ἐπιμιμεῖσθαι, which is a hapax legomenon. For a persuasive defence of the manuscript rendering, see Gutas (n. 1), 384–5. The other option, preferred by Laks–Most and Van Raalte would be to emend the text to ἐπεὶ μιμεῖσθαι, which would produce a reading something like ‘seeing that all things wish to imitate’ (Van Raalte) or ‘s'il est vrai que tout a la volonté d'imiter’ (Laks–Most). Either way, however, the point stands: Plato and the ‘Pythagoreans’ believe that things other than the first principles desire to imitate them.

⁵ I understand ἄγειν as ἀνάγειν, given that the prefix ἀν- should be understood as transferable from the previous verb ἀνάπτουσιν. Theophrastus had used the technical term ἀνάγειν with reference to ἀνάπτων when describing Plato's ontological hierarchy earlier at Metaph. 6b11–13, and reduction to the first principles is the point in both passages. I will tend to refer to ‘reduction’ rather than something like ‘reference to’ (which is also a meaning that ἀνάγειν carries) because of the ontological-logical force that this concept carries in the writings under discussion. For useful general studies of reduction from opposites in the thought of Aristotle, see especially Merlan, P., From Platonism to Neoplatonism (The Hague, 1975 ³), ch. 7CrossRefGoogle Scholar (but also see the correctives of Leszl, W., ‘Philip Merlan e la metafisica aristotelica’, RSF 25 [1970], 3–24 and 227–49Google Scholar, and Berti, E., ‘La “riduzione dei contrari” in Aristotele’, in Zetesis: Album amicorum [Antwerp/Utrecht], 122–46Google Scholar).

⁶ Arist. Metaph. 1.6, 987a29–988a2.

⁷ For a balanced discussion of the problems involving the title and location of the work vis-à-vis Aristotle's Metaphysics, see esp. Laks–Most (n. 1), ix–xviii.

⁸ Burkert (n. 3), 62–3. For my criticism of Burkert's hypothesis that Aporia 24 refers to Speusippus, see below.

⁹ Huffman, C.A., Philolaus of Croton: Pythagorean and Presocratic (Cambridge, 1993), 22–5Google Scholar; Philip, J.A., Pythagoras and Early Pythagoreanism (Toronto, 1966), 11–12 and 96Google Scholar. In a more recent article, ‘Two problems in Pythagoreanism’, in Curd, P. and Graham, D.W. (edd.), The Oxford Handbook of Presocratic Philosophy (Oxford, 2008), 284–304Google Scholar, at 284–91, Huffman argues against the traditional interpretation of Metaph. 987a29–31 by suggesting that Aristotle sees Plato's pragmateia as ‘agreeing with the Presocratic tradition as a whole’ rather than following the ‘Pythagoreans’ in particular, but he does not take into account Theophrastus' evidence at all.

¹⁰ Cherniss, H., Aristotle's Criticism of Plato and the Academy (Baltimore, 1944), 246–8Google Scholar.

¹¹ Ibid. 95–7 with n. 62.

¹² Reale, G., The Concept of First Philosophy and the Unity of the Metaphysics of Aristotle, tr. Catan, J.R. (Albany, NY, 1980), 422Google Scholar.

¹³ Kahn, C., ‘Pythagorean philosophy before Plato’, in Mourelatos, A.P.D. (ed.), The Pre-Socratics (Garden City, 1974), 174Google Scholar. Nor does he account for this passage in his more comprehensive study of Pythagoreanism, Pythagoras and the Pythagoreans (Indianapolis and Cambridge, 2002)Google Scholar, although he does there cite (p. 62) an earlier passage of Theophrastus' text (Metaph. 6b11).

¹⁴ Fine, G., On Ideas: Aristotle's Criticism of Plato's Theory of the Forms (Oxford, 1993)Google Scholar.

¹⁵ Pradeau, J.-F., Platon, l'imitation de la philosophie (Paris, 2009)Google Scholar.

¹⁶ Laks and Most (n. 1), 86 speculate without comparative evidence that ‘l'existence même du désir d'imitation est prise comme un signe de la distance qui sépare le monte naturel de l'Un-bien’ (italics original). To my knowledge, Theophrastus nowhere speaks of distinguishing a metaphysical operation from a ‘sign’ in the Metaphysics.

¹⁷ Dillon (n. 2), 185–6.

¹⁸ Van Raalte (n. 3), 185.

¹⁹ She simply closes by quoting Ross and Taylor, whose comments on this passage are not particularly helpful for our study.

²⁰ This, of course, assumes that Aristotle's Metaphysics Α was written before Theophrastus' Metaphysics or, perhaps, that the question was more generally in the air. On the chronology of the works, see the useful discussion of Gutas (n. 1), 3–9.

²¹ I will discuss my criticisms further below.

²² That is, he is ‘systematic’ in his historiography in the sense that he (a) attempts to maintain a consistent set of objective interpretive paradigms and terminology for the various types of philosophers who are antecedent to and contemporary with him and (b) gestures in the direction of creating lineages of thought based in temporal progression up to his own philosophy. One could thus see Aristotle as providing a historiographical method that attempts to reconcile, in the words of Nightingale, A.W., ‘Historiography and cosmology in Plato's Laws’, AncPhil 19 (1999), 299–326, at 324Google Scholar, the ‘objective and atemporal’ aspects of first philosophy with an account that recognizes mutability over time. Moreover, countless attempts to identify Aristotle's interpretive paradigms arise in scholarship because of the difficulty in grasping Aristotle's larger system of ‘first philosophy’, which is reflected in his historiographical material as well. On this subject, see especially Barney, R., ‘History and dialectic (Metaphysics A.3, 983a24–984b8)’, in Steel, C. (ed.), Aristotle's Metaphysics Alpha (Oxford, 2012), 69–104Google Scholar; Frede, M., ‘Aristotle's account of the history of philosophy’, Rhizai 1 (2004), 9–44Google Scholar; and Schofield, M., ‘ARXH’, Hyperboreus 3 (1997), 218–35Google Scholar.

²³ Cf. Schofield (n. 22), at 222.

²⁴ I omit the description of how Plato first adopted Heraclitean doctrines through his contacts with Cratylus, next adapted Socratic approaches to definition and then developed a theory of the Forms.

²⁵ Retaining with Ross the MSS reading τῶν εἰδῶν.

²⁶ This phrase is important, because it clarifies that the ‘Pythagoreans’ about whom Aristotle is speaking cannot be the Platonists Philip of Opus, Speusippus or Xenocrates, as is argued by Zhmud, L., ‘Some notes on Philolaus and the Pythagoreans’, Hyperboreus 4 (1998), 243–70Google Scholar, at 265.

²⁷ On this passage, see more below.

²⁸ Pl. Ti. 50c6–e1. Luc Brisson reminds me that the overall inheritance of this passage goes back to Plato's Phaedo (esp. 101b10–102a1), but I might emphasize that there we see a focus on ‘participation’ (μετασχεῖν) of things in ‘Oneness’ or ‘Twoness’, rather than the language of being ‘in’, as we find in the account of Timaeus and in Theophrastus' summary.

²⁹ Note that Theophrastus emphasizes the importance of being ‘in’ for his Metaphysics by concluding it (11b27–12a2) with the statement that ‘this is the ἀρχή of the study of the whole, in what the things that are real exist (ἐν τίσιν τὰ ὄντα) and how they relate to one another (πῶς ἔχει πρὸς ἄλληλα)’. Cf. Theophr. Metaph. 4a17ff. and 4b8–11: ‘Therefore, it is in accordance with better reason that, having the nature of a principle [a prior and more powerful substance (τις οὐσία προτέρα καὶ κρείττων) than mathematicals] be in a few, unordinary things – that is, if not in things primary, then in the first thing’.

³⁰ For an informative study of ‘Form’ terminology in antecedent Greek literature and in Plato's dialogues (up to the Phaedo), see Herrmann, F.-G., Words & Ideas: The Roots of Plato's Philosophy (Swansea, 2007), chh. 5 and 9CrossRefGoogle Scholar.

³¹ Pl. Phd. 65b8–66a5. Cf. Ross, W.D., Plato's Theory of Ideas (Oxford, 1951), at 22Google Scholar. Note the epistemological compatibility, as ‘thinking itself by itself’ might discover ‘reality itself by itself’: ‘Then he will do this [grasp that thing itself] most perfectly who approaches the object with thought alone, without associating any sight with his thought, or dragging in any sense perception with his reasoning, but how, using pure thought alone (ἀυτῇ καθ’ αὑτὴν εἰλικρινεῖ τῇ διανοίᾳ χρώμενος), tries to track down each reality pure and by itself (αὐτὸ καθ' αὑτό), freeing himself as far as possible from eyes and ears, and in a word, from the whole body …' (tr. after Grube). Of course, Plato inherited what was a relatively common phrase from earlier writers (cf. Herrmann [n. 30], 14–20) and modified its semantic potential, in such a way that it could be appropriated in a new technical sense. Cf. Herrmann (n. 30), 19: ‘In the case of καθ’ αὑτό, the phrase did establish itself as part of Plato's technical terminology and was as such received and adapted by Aristotle and subsequent philosophers.'

³² See Merlan (n. 5), 195–7 for a helpful discussion of the tendency of Plato to suggest something like reduction to ‘non-being’ in Plato's Sophist, a tendency that the Platonists developed into systems.

³³ It is debatable to what extent we can follow the late antique sources that suggest a Categories had been written by Theophrastus (cf. Gottschalk, H.B., ‘Did Theophrastus write a Categories?’, Philologus 181 [1987], 245–53Google Scholar). There is one clear example of Theophrastus having knowledge of Aristotle's Categories and criticizing it (F 153a FHSG = Simpl. in Cat. 435.27–31 Kalbfleisch).

³⁴ A question of concern especially to Philip (n. 9), 11–12, who allows for the possibility that Speusippus and Xenocrates, whom he takes to be the sources for Theophrastus' descriptions here, were ‘right’ and Aristotle ‘wrong’. But the pursuit of ‘right’ and ‘wrong’ understandings of Pythagoreanism/s obscures the path to understanding both (a) how each group, the Peripatetics and the Platonists, presented various accounts of the Pythagoreanizing of Plato and (b) how each philosopher's system tried to represent Platonic and/or ‘Pythagorean’ doctrine in its own terms.

³⁵ Dillon, J., The Heirs of Plato: A Study of the Old Academy (347–274 bc) (Oxford, 2003)CrossRefGoogle Scholar, especially ch. 3 on Xenocrates and the article cited at n. 2, which remains the best overall assessment of this topic.

³⁶ Cf. Halliwell, S., The Aesthetics of Mimesis: Ancient Texts and Modern Problems (Princeton, 2002), 287Google Scholar; Janko, R., Aristotle on Comedy: Towards a Reconstruction of Poetics II (Berkeley, 1984), 48–52Google Scholar with n. 111; and Gray, V., ‘Mimesis in Greek historical theory’, AJPh 108.3 (1987), 467–86Google Scholar, at 484–5.

³⁷ Theophrastus F 184.105–21 FHSG = Philo, De aeternitate mundi 25.134–36.

³⁸ For Democritus, see Sharples, R. W., Theophrastus of Eresus: Sources for his Life, Writings, Thought and Influence, Commentary Volume 3.1: Sources on Physics (Texts 137–223) (Leiden, 1998), 139–40Google Scholar. Heraclitus and Hippasus, however (cf. F 225.15–28 FHSG = Simpl. in Phys. pp. 23.33–24.12 Diels), were the figures associated with fire as the first principle that was ‘One’, ‘in motion’ and ‘limited’. Theophrastus himself, in On Fire (F 4 Coutant), criticizes those who believe that fire is the first principle on the grounds that fire cannot subsist ‘without matter’ (ἄνευ τῆς ὕλης).

³⁹ Theophr. Metaph. 4b22. Cf. Aristotle's description of the prime mover at Metaph. 12.7, 1072a19–27 as ‘something which moves although it is not moved’ (τι ὃ οὐ κινούμενον κινεῖ). It should be noted that the difference between Aristotle's unmoved mover and the first principle described by Theophrastus is precisely the Platonic per se language.

⁴⁰ Theophr. Metaph. 5a1–5. Theophrastus' use of these terms indicates a strong affinity with Aristotle's accounts of cosmic will – if we can call it that – at both the levels of the heavenly and the individual human. Cf. Arist. Metaph. 12.7, 1072a26–30 (τὸ ὀρεκτόν described); De motu an. 6, 700b35–701a2 (τὸ μὲν οὖν πρῶτον οὐ κινούμενον κινεῖ, ἡ δ' ὄρεξις καὶ ὀρεκτικὸν κινούμενον κινεῖ), where motion of animals is compared and contrasted with the motion of the heavens; De an. 3.10, 433a31 (ὄρεξις, considered the ‘power in the soul’ that originates movement). On ἔφεσις as a ‘neutral term’ related to ὄρεξις but ‘apposite in physical contexts’ specifically, see Van Raalte (n. 3), 165.

⁴¹ Skemp, J.B., ‘The Metaphysics of Theophrastus in relation to the doctrine of κίνησις in Plato's later dialogues’, in Düring, I. (ed.), Naturphilosophie bei Aristoteles und Theophrast (Heidelberg, 1969), 217–23Google Scholar, at 218 with n. 3.

⁴² At Theophr. Metaph. 4a20 and 4b1. Cf. Skemp (n. 41), 219 but, other than identifying the significance of συνάπτειν and its cognates for Theophrastus' criticism of Aristotle, he does not go into detail about this concept. Van Raalte (n. 3), 86 simply notes, vis-à-vis Theophrastus' project, that συναφή is ‘obviously relevant’.

⁴³ e.g. Pl. Resp. 588d7–e1; Soph. 253d5–e2.

⁴⁴ Aristotle may be said to present his most metaphysical version of this concept in (possibly) On Philosophy (F 17 Rose = Schol. in Proverbia Salomonis), in a passage worth quoting at length (because of its relevance for Theophrastus' Metaphysics): ‘The first principle is either one or many. If it is one, we have what we're looking for. But if there are many, they are either arranged or unarranged. And if they are unarranged, the things that come from them are more unarranged, and the ordered world is not ordered (ὁ κόσμος) but chaos (ἀκοσμία), and that which is contrary to nature exists since what is in accordance with nature does not exist. But if they are arranged, either the things were ordered by themselves or by some outside cause. But if they were ordered by themselves, they have something in common, a connection (τι κοινὸν τὸ συνάπτον), and that is the first principle’. Also cf. Arist. Cat. 4b26–5a1, on which see the next note.

⁴⁵ ‘Connection’ is an activity associated with the activity of mental combination, and contrasted with separation, in Aristotle's analysis of dialectic in Metaphysics Ε (6.4, 1027b23–34; cf. 13.4, 1078b9–12, where he warns against ‘connecting’ (σύναπτοντας) the Forms with numbers. The classic example of Aristotle's discussion of ‘connection’ as a mathematical term would be his treatment of quantity in ch. 6 of the Categories (4b20–6a36). There, Aristotle identifies two types of quantity, namely, the discrete (τὸ διωρισμένον) and the continuous (τὸ συνεχές). He classifies number and speech as discrete, as well as line, superficies, solid, time (cf. Phys. 4.11, 218b25–7), and place as continuous. Aristotle demonstrates that number is discrete by arguing that ‘there is no common boundary (κοινὸς ὅρος) among the parts of number towards which its parts connect’ (πρὸς ὃν συνάπτει τὰ μόρια αὐτοῦ). Further development of this usage occurs in Books 5–6 of the Physics, especially in Aristotle's definition of ‘continuity’ (τὸ συνεχές), where he claims it is due to something's natural constitution vis-à-vis ‘connection’ (ἡ σύναψις) that it is able to be continuous (cf. Phys. 5.3, 227a15). In this section of the Physics, however, Aristotle prefers to speak more simply of ‘touching’ (τὸ ἅπτεσθαι θιγγάνον) rather than ‘connection’, which he associates with people who confuse universality and separate existence (Metaph. 13.9, 1086a35–7, but there is a problem with the text, on which see Ross' note ad loc.; also cf. De motu an. 3, 699a15, with Nussbaum's note ad loc.). For a useful discussion of the shift in Aristotle's position regarding the ontology of mathematical objects, see Cleary, J., Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics (Leiden, 1995), 143–8CrossRefGoogle Scholar.

⁴⁶ Note e.g. Aristotle's criticism of Xenocrates' Form-Numbers in Metaphysics Μ (13.4, 1078b9–11, not in Isnardi Parente's or Heinze's editions): ‘But with regard to the Ideas we should first examine the actual theory in relation to the Idea, without connecting it with the nature of number (μηδὲν συνάπτοντας πρὸς τὴν τῶν ἀριθμῶν φύσιν), but as the first people who posited Ideas originally propounded it.’ For an elegant but not uncontroversial narrative of the development of Aristotle's Metaphysics vis-à-vis Xenocrates, see Jaeger, W., Aristotle: Fundamentals of the History of his Development, tr. Robinson, R. (Oxford, 1948 ²), ch. 7.3Google Scholar.

⁴⁷ A remarkable treatment of the problem of ‘contact’ (figured variously as συναφή, σύναψις, ἐπαφή and related cognates) among circles, lines and points occupies a sustained criticism of some anonymous mathematicians in the Pseudo-Aristotelian On Indivisible Lines (970a27–971b31). One of the figures being criticized in this text, as Dillon (n. 2), 113–17 has discussed in detail, is Xenocrates, on whom see below.

⁴⁸ See e.g. Dillon (n. 2), 183 who prophetically comments: ‘Presumably lying behind this theological exposition there was a more “physical” account, involving something like the basic triangles of the Timaeus.’ I have not found that any of the major studies of Xenocrates or, for that matter, of Theophrastus have taken this passage sufficiently into account.

⁴⁹ So speculates Festugière, A.J., Proclus: Commentaire sur la Republique (Paris, 1970), 156Google Scholar, but the issue of who is doing this activity must be kept open especially if Proclus is following Xenocrates' text closely.

⁵⁰ It is easy to underestimate the significance of this point. We will recall that Aristotle (Metaph. 1.6, 987b11–15) characterizes Plato as understanding ‘participation’ (μέθεξις) as the vehicle for bridging separation between the Forms and sensibles, and the ‘Pythagoreans’ as understanding the same operation to be ‘imitation’ (μίμησις). Apparently, Xenocrates combines Platonic and ‘Pythagorean’ metaphysics (in Aristotle's description) by setting up ‘participation’ and ‘imitation’ as operations that catalyse relations between particular strata of the entire cosmos. Thanks to George Boys-Stones for pressing me on this.

⁵¹ Speusippus may have used comparable terminology, which makes it possible that the language itself goes back to the Early Academy. Tarán, L., Speusippus of Athens (Leiden, 1981), 430–1CrossRefGoogle Scholar speculates about Speusippus' use of the term ἐπαφή for mental ‘apprehension’ (F 74 Tarán = Procl. In Euc. p. 179.12–22), which he compares (following Stenzel) with similar usages of ἐφάπτεσθαι in passages of Plato's dialogues (Symp. 212a4 and Ti. 37a5–6). Indeed, it is possible that the Peripatetic author of On Indivisible Lines is referring to Speusippus when (969a32–b2) he criticizes the proposition, attributed to people who might think that the mind's ‘apprehending of infinite things’ (ἐφάπτεσθαι τῶν ἀπείρων) is ‘counting’ (ἀριθμεῖν). Xenocrates' use (if it is indeed his) of the term ἐπαφή, to be sure, does not demonstrate applicability to cognition in the same way as Speusippus', in part because Xenocrates accepts the Forms and the attendant per se ontology. For example, Xenocrates' use accords more fully (in an epistemological context) with Plato's working definition of φρόνησις (Phd. 79d1–9) as the soul's activity of ‘ceas[ing] to stray and remain[ing] in the same state, since it is in touch with things of the same kind’ (ἀεὶ κατὰ ταὐτὰ ὡσαύτως ἔχει, ἅτε τοιούτων ἐφαπτομένη). According to Cherniss (n. 10), 407 and 394 with n. 316, Aristotle takes the notion of attachment as described in Plato's Timaeus (37a2–b3) too literally because he assumes that the soul's activity of ἐφάπτεσθαι with the objects of thinking is a physical contact of two divisible magnitudes.

⁵² Parente, M. Isnardi, Senocrate – Hermodoro: Frammenti (Naples, 1982)Google Scholar, at 414 follows Heinze in suggesting that it is more likely that Proclus has derived some information here from Plutarch, rather than directly from Xenocrates. There is reason to doubt this. Of the nine occurrences of ἐπαφή in Plutarch's works (outside of quotations of Greek tragedians), only one (Adv. Col. 1109d4) evinces philosophical application, and there it is employed in an epistemological context that resembles (to some degree) the usage of Plato and Speusippus. Importantly, there is no mathematical or ontological context for this term in Plutarch's works; likewise, it never occurs in the surviving fragments of Nicomachus. It is also doubtful that the language of ‘attachment’, especially the nominal concept of ἐπαφή, is uniquely Proclean: outside of Xenocrates F 223 IP and Speusippus F 73 Tarán (cited above), we should note, the term does occur eighteen times in Proclus' corpus. Of those occurrences, twice (In Ti. 2.296.28 Diehl and Mal. Sub. 51.3) does ἐπαφή refer to an explicitly epistemological context (developing Plato's and Speusippus' usage of ἐφάπτεσθαι); and twice (In Prm. p. 871.24 Stallbaum and In Ti. 1.349.30 Diehl) does it refer to an expressly mathematical context, following a standard usage in Euclid, Archimedes and Apollonius of Perga, who wrote two books On Tangents. We cannot be absolutely sure when the language of tangents/attachment became associated with Platonism, but we cannot discount Xenocrates himself, who undertook the project of geometricizing Plato's metaphysics in several works.

⁵³ Of course, Plato closes description of the history of the universe in the Timaeus (90d1–7) by suggesting that humans should learn the harmonies and revolutions of the universe in order to ‘assimilate’ (ἐξομοιῶσαι) the activity of contemplation to the objects of said contemplation. Such assimilation produces the best life possible for humans.

⁵⁴ Plutarch (Quaest. Plat. 1007c = F 171 IP), Alexander of Aphrodisias (In Top. 493.21 Wallies = F 173 IP), Philoponus (In An. post. p. 348.2 Wallies = F 185 IP) and others formulate Xenocrates' famous definition of the soul as ‘number itself moving itself’ (ἀριθμὸς αὐτὸς ἑαυτὸν κινῶν), apparently following Aristotle's description at Top. 6.3, 140b2 (= F 168 IP). Cf. Dillon (n. 2), 177. It is true, as Mariska Leunissen points out to me, that Aristotle too employs the term ‘number itself’ (ἀριθμὸς αὐτὸς) when giving an explanation for how things could have essential attributes (i.e. exist καθ' αὑτά) in the Posterior Analytics (1.22, 84a12–18). But, within the context of discussing ontological ‘connection’, and given the significance of number to the entire metaphysical system being described by Theophrastus, it becomes unlikely that Aristotle is the target here.

⁵⁵ On Xenocrates' first principles and the role that Number plays in his metaphysics, see recently Dillon (n. 35), 99–103. An important passage that suggests how Xenocrates might have described Form-Numbers appears in the Aristotelian treatise On Indivisible Lines, a title attested for a work of Theophrastus (Diog. Laert. 5.42; see Dillon [n. 2], 113 with n. 69), although we cannot be sure the Peripatetic text in question was his (968a10–14 = F 127 IP): ‘Moreover, if there is a Form of Line (ἰδέα γραμμῆς) and the Form is primary among the entities synonymous with it, and if the parts are prior by nature to the whole, the Line Itself (αὐτὴ ἡ γραμμή) would be indivisible, and in the same way also the Square, the Triangle, and the other figures, and in general the Plane itself and Body; for the consequence will be that there will be some prior entities in their case also’ (tr. Dillon). For the ascription of the theory that the Dyad as the ‘Line Itself’ (αὐτογραμμή) as described elsewhere by Aristotle (Metaph. 7.11, 1036b12–15 [= F 105 IP] and 14.3, 1090b20–32 [= F 117–18 IP]) should be attributed to Xenocrates, see Cherniss (n. 10), 567–9 and Isnardi Parente (n. 52), 338–9.

⁵⁶ Dillon (n. 2), 181 assumes that Speusippus and Xenocrates are being ‘distinguished from “those who postulate the One and the Indefinite Dyad”’, but there is no clear evidence in the text that Speusippus and Xenocrates are not being considered under the larger umbrella grouping of those who employ the One and the Indefinite Dyad as first principles. We are better served to read the text with Cherniss, H., ‘Some war-time publications concerning Plato’, in Tarán, L. (ed.), Harold Cherniss: Selected Papers (Leiden, 1977), 142–216Google Scholar, at 188 with n. 78, as distinguishing, from among all those who posit the One and the Indefinite Dyad as first principles, two groups: (a) Speusippus and the ‘others’ who do not give a full account of the derivatives and (b) Xenocrates and Hestiaeus, and Plato, who do provide some sort of account of reduction. Van Raalte (n. 3), 259 and 264, argues that Speusippus is not intended to be included here because he did not posit ‘as second principle the indefinite dyad (but posited “multiplicity” (πλῆθος) instead)’; but this is not persuasive, since it relies on the assumption that Theophrastus followed Aristotle in specifically ascribing multiplicity to Speusippus (cf. Tarán [n. 51], 324–6), which we have already shown to be a problematic assumption, and that Aristotle's version preserves the correct terminology. If anything, it is Aristotle who is more likely to be modifying the original terminology of the Platonists. As Tarán (n. 51), 326 n. 133, himself points out, ‘since Xenocrates’ system was an attempt to bridge the gap between Plato and Speusippus, it is possible that [Aristotle] indicated that Speusippus' τὸ πλῆθος was merely a more general term than Indefinite Dyad to designate the material principle'. See Dillon (n. 2), 100–1 for a plausible interpretation that Xenocrates used several terms to describe the second principle depending on the context (and, I might add, the aspect or quality being solicited).

⁵⁷ Dillon (n. 2), 181. Merlan (n. 5), 44 misinterprets the point of Theophrastus' text – that Xenocrates is unlike the other Platonists by determining relationships of derivation based on the notion of the divine (καὶ ἔτι δὴ τὰ θεῖα) – in interpreting Theophrastus' text as positing four ‘spheres of being’. So too Van Raalte (n. 3), 269–70, although she does not cite him. Zeller, E., Plato and the Older Academy, tr. Alleyne, S.A. and Goodwin, A. (London, 1876)Google Scholar, 583 n. 11 was closer to the mark when he suggested that τὰ θεῖα, ‘only added incidentally by Theophrastus, form no separate class’ but ‘are found in the three others, so far as they are treated from a theological point of view’. I would speculate, following Zeller, that it is intelligible objects that are most fully divine (and thus called ‘divine’), but that mathematical and sensible objects partake of divinity to an extent reversely commensurate with their distance from the supercelestial realm.

⁵⁸ It remains not fully clear whether, for Xenocrates, Soul belongs centrally (has a home?) in one of these realms of being, e.g. in the ‘middle’, as Merlan (n. 5), 48 suggests, whether it is able to change places, or whether – in some form – it extends throughout the whole of being, but to various degrees, as plausibly suggested by Zeller (n. 57), 592.

⁵⁹ See Schibli, H., ‘Xenocrates’ Daemons and the Irrational Soul’, CQ NS 43.1 (1993), 143–67CrossRefGoogle Scholar, at 146–7.

⁶⁰ Of course, triadic subdivisions that follow the basic order of ‘superior’, ‘intermediary’, and ‘inferior’ include Proclus' description of the three types of triangles (equilateral, isosceles, and scalene).

⁶¹ Dillon (n. 35), 98 and Merlan (n. 5), 2 and 9.

⁶² Cf. Isnardi Parente (n. 52), 341–2.

⁶³ Arist. Metaph. 13.9, 1086a5–10 = F 110 IP. See Dillon (n. 35), 108–18 for his illuminating interpretation of Aristotle's criticism.

⁶⁴ Here I follow Ross, W.D. and Fobes, F.H., Theophrastus: Metaphysics (Oxford, 1929), 9Google Scholar and Laks and Most (n. 1), ad loc., in supplementing with the infinitive μιμεῖσθαι. Skemp (n. 41), 218 thought that διώκειν should be supplemented, but see the criticisms of Van Raalte (n. 3), 189, who unfortunately assumes (ibid. 41) that εἶναι has fallen out. She is followed by Henrich, J., Die Metaphysik Theophrasts: Edition, Kommentar, Interpretation (Leipzig, 2000), 47Google Scholar and Dillon (n. 2), 178 with n. 11. But Gutas (n. 1), 284–5 has sufficiently demonstrated that this supplement cannot be entertained especially on stylistic grounds (i.e. it would lead to excessive pleonasm).

⁶⁵ Ross and Fobes (n. 64), 44. The anonymous reader for Classical Quarterly helpfully notes that the perceived absurdity here is slightly uncharitable if one grants that circular motion is the next best thing to primal stability.

⁶⁶ The text is corrupt here, and interminably difficult to make sense of. I follow most closely the text and interpretation of Laks and Most – also followed by Gutas (n. 1), 341–2, with some reservations – by accepting Usener's conjecture τί γὰρ for the most common manuscript reading εἰ γὰρ (attested in the Arabic translation of Ishāq and, among modern commentators, accepted only by Van Raalte) and in accepting Ross' emendation to οὐ συνακολουθεῖ (as all modern commentators do) for the more common manuscript reading of οὖσιν ἀκολουθείη. The resulting text is τὶ γὰρ αὐτοῖς [sc. ὀργομέναις] οὐ συνακολουθεῖ ἡ τῶν ἄλλων [sc. μίμησις]. This interpretation has the benefit of allowing Theophrastus to restate, in roughly the same terms, the criticism he had mentioned back in Aporia 8; cf. Henrich (n. 64), 120. On this interpretation, συνακολουθεῖ roughly corresponds to a similar usage of Aristotle in Metaphysics Μ (13.9, 1085a16), where Aristotle complains of the Platonists that they imagine of their first principles that the qualities of broad and narrow are ‘associated’ (συνακολουθοῦσι) with long and short, respectively. Van Raalte (n. 3), 352 with n. 2 rejects this interpretation on the grounds that ‘οὐ συνακολουθεῖ apparently corresponds to οὐ μιμοῦνται’, but her rejection is far from decisive, despite the persuasive suggestion that there is attested a relationship (unfortunately not defined by Van Raalte) between ‘imitation’ and ‘accompaniment’ in Plato's writings (cf. Plt. 273e11–274a3, cited by Van Raalte). It might be objected, however, that earlier, at 7a1–6, Theophrastus has used συνακολουθεῖν and μιμεῖσθαι roughly analogously when he compares how the sciences that come after the first principles, such as grammar, music and mathematics, ‘accompany’ them and how the crafts ‘imitate’ nature. But it is also likely that Theophrastus, in appropriating the language of his sources (especially the Platonists), sometimes employs their language outside of their Platonist context and for the sake of the diction of his own philosophical argumentation, e.g. at 6a27 where, in discussing the first principles of the Platonists, he criticizes them for only ‘touching on’ (ἐφαπτόμενοι) the topic of the heavens. In this instance, I would argue, Theophrastus is transferring the language of Plato and the Platonists from their original context (e.g. discussions of relationships between various entities in the chain of being) to a different context, i.e. to the context of his own interpretation of the success or failure of their ideas as philosophy.

⁶⁷ I've supplemented ‘the universe’ for the sake of clarifying the argument. The grammar of this passage offers no obvious help, which could be a consequence of Theophrastus' characteristic brevity or, as Van Raalte (n. 3), 350–2 has suggested, a textual problem, marked by a loss of apodosis from the previous condition. One option would be to assume, as Van Raalte does (ibid. 353), that something like ‘all things’ (ἄπαντα), in synecdoche for ‘the Universe’, is intended (cf. a similar description at 11b9: πάντ' εἰς τὸ ἄριστον ἄγειν). This interpretation, also advocated by Ross and Fobes (n. 64), 21 (‘reducing the universe’) is in contrast to the interpretations of Laks and Most (n. 1), 12 (‘l'on rapportait [l'argument] à ce qui est dépourvu de parties’), Gutas (n. 1), 135 (‘one should not conceive [of these things] in the same way as if he were reducing to something without parts’) and Henrich (n. 64), 59 (‘daß man vielleicht nicht [alles] auf diese Weise aufzufassen hat, als ob man sie auf etwas Ungeteiltes hinführt’). Another intratextual point of comparison would be the description of Plato's reduction to first principles (ἀνάγειν εἰς τὰς ἀρχάς) earlier at 6b11–15, where Theophrastus described Plato as reducing the things ‘other than’ (τῶν ἄλλων) the first principles. The general sense is rather clear, I think: Theophrastus is referring to all things that are other than ‘the partless’.

⁶⁸ Gutas (n. 1), 342.

⁶⁹ Van Raalte (n. 3), 351–3 adduces two pieces of evidence that, she thinks, demonstrate for Aristotle a relationship of ‘imitation’ between the ‘objects that desire’ and the ‘first principles’ here: Metaph. 9.8, 1050b28 (‘Imperishables also are resembled by things undergoing change, such as earth and fire; for the latter are always active, since they are independent and have motion in themselves’) and Mete. 1.9, 346b35–347a8 (‘This cycle of changes imitates the cycle of the sun: for the moisture rises and falls as the sun moves in the ecliptic’). The latter evidence simply does not refer to first principles at all and can be dismissed. The former is more interesting, however, and warrants further investigation. It is true that Aristotle ascribes to a theory of ‘imitation’, especially, from simple bodies to the ‘cause’ (cf. Gen. corr. 2.10, 337a1–17), but in all passages cited we should note that he never describes these relationships as desiderative. That is, elements such as ‘fire’ and ‘earth’ are not spoken of in these passages as ‘desiring’ to adopt the particular attributes of the prime mover. Moreover, in the description of how the simple bodies reduce to the prime mover in On Generation and Corruption, there is no attempt to describe them as imitating the ‘partlessness’ of the cause. My hunch is that these passages of Aristotle exhibit the affection he sometimes shows for Platonic theories of reduction (esp. those related to the Timaeus), which he aims to modify in part by emphasizing the distinction between potentiality and actualization, but that Aristotle does not throw out the baby with the bathwater.

⁷⁰ Esp. Theophr. Metaph. 11a27–b12.

⁷¹ For comparison, see Dillon's discussion of Theophrastus' critique of the unmoved mover in Aporiae 6–12 (Theophr. Metaph. 5a14–6a14) as a refutation chiefly of Platonist positions.

⁷² It should be noted that it is possible that Speusippus is intended here. If the fragment quoted by Ps.-Iamblichus in the Theologoumena Arithmeticae (pp. 82.10–85.23 = F 28 Tarán) is indeed verbatim, Speusippus believed that magnitudes assimilated themselves (l. 55 ἐοικέναι; l. 58 ὁμοιοῖτο) to numbers. But Damascius (De principiis 1.2.25–3.2 = F 49a Tarán), in attempting to argue that the first One is absolutely ἀμερές, contrasts his own position with that of Speusippus, who (Damascius suggests) conceived of the One as ἐλάχιστον.

⁷³ Cardini, M. Timpanaro, Pseudo-Aristotele: De lineis insecabilibus (Milan, 1970), 38Google Scholar with n. 53.

⁷⁴ Alex. Aphr. In Arist. De princ. doctr. pp. 281–2 Badawi = F 121 IP. This fragment is quoted verbatim by Alexander of Aphrodisias and survives in a translation into Arabic by Al-Dimashqī in the tenth century c.e.

⁷⁵ Cf. [Arist.] Lin. Ins. 968a10–14. In this sense, Xenocrates follows Plato in the Timaeus (53c4ff.) in positing rectilinear planes as the mathematical objects to which fire and other elemental bodies can be reduced. That these arguments are chiefly ‘logico-dialectical’ and relate especially to ontological stratification has been argued by L. Gemelli Marciano, Democrito e l’Accademia (Berlin, 2007), 191–3.

⁷⁶ A fuller account would have to answer (a) what sorts of things are partless (across the realms of being), (b) why they are partless and (c) what sorts of objects are clearly ‘intermediary’ in this schema, a project that might want to take into account the testimonies especially of Alexander of Aphrodisias (apud Simpl. in Phys. p. 138.10ff. Diels = F 138 IP), Porphyry (ap. Simpl. in Phys. p. 140.6ff. Diels = F 139 IP) and Themistius (Paraphr. in Arist. De an. p. 11.19ff. Heinze = F 260 IP). For one courageous attempt to make sense of this, see Zeller (n. 57), 587–8 with n. 22.

⁷⁷ Also see Themistius' description of Xenocrates' ontology (Paraphr. in Arist. De an. p. 11.19ff. Heinze = F 260 IP), in which he quotes Xenocrates directly from a work entitled On Nature as saying ‘all things resemble Number’ (ἀριθμῷ δὲ πάντ' ἐπέοικε) in the context of providing a derivational account of Xenocrates' metaphysics.

⁷⁸ For a useful description of the music theory behind the Demiurge's design, see A. Barker, The Science of Harmonics in Classical Greece (Cambridge, 2007), 318–23.

⁷⁹ Cf. Pl. Ti. 92c7–9: μέγιστος καὶ ἄριστος κάλλιστός τε καὶ τελεώτατος γέγονεν εἷς οὐρανὸς ὅδε μονογενῆς ὤν.

⁸⁰ I will quote the fragment in toto in order to allow the reader to understand the larger context (tr. after Dillon): ‘Speusippus’ view was that, since there are things which are sensible and others which are intelligible, of those that are intelligible the criterion is cognitive reason, while of the sensible things it is cognitive sense-perception. And cognitive sense-perception he conceived to be that which participates in the truth which accords with reason (ἡ μεταλαμβάνουσα τῆς κατὰ τὸν λόγον ἀληθείας). To take an example: the fingers of a flute-player or harper possess an artistic activity (τεχνικὴ ἐνέργεια) which is, however, not brought to fruition primarily (προηγουμένως τελειουμένη) through the fingers themselves, but is fully developed (ἀπαρτιζομένη) as a result of training under the co-operative guidance of reasoning; and the sense-perception of the musician, while it possesses an activity capable of grasping the harmonious and the non-harmonious, nevertheless is not self-produced but is acquired by reason. Even so, cognitive sense-perception naturally derives from reason the cognitive experience which it shares, and which leads to unerring discrimination of its proper objects.'

⁸¹ Van Raalte (n. 3), 354 adduces the Pseudo-Aristotelian On the Cosmos (396b7–11) as evidence for cosmic ‘concordance’ in Aristotelian writing, but does not explicitly argue that the claim under investigation (2) thereby refers to Aristotle's ideas. Mariska Leunissen reminds me that Aristotle does indeed analogize the universe to an army or a household (Metaph. 12.10, 1075a11–25). But there Aristotle emphasizes the ‘order’ (τάξις) of these groupings and does not explicitly broach the subject of the ‘fitting together’ of parts or ascribe this to any theory of musical harmonization. On these types of analogies in Aristotle's writing, see Van Raalte (n. 3), 354–6.

⁸² Archytas F 1 Huffman (Porph. in Harm. 1.3). On the topic of Plato's criticism of Archytas in this passage, see especially Huffman, C.A., Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King (Cambridge, 2005), 63–5CrossRefGoogle Scholar.

⁸³ Cf. Barker (n. 78), 316 with n. 14.

⁸⁴ Cf. Alexander of Aphrodisias' report, likely culled from Aristotle's works on the Pythagoreans (F 203 Rose = in Metaph. 38.20), which discusses how the motions of the bodies lead the Pythagoreans to assume that ten is the ‘perfect number’ (τέλειος ἀριθμός).

⁸⁵ Huffman (n. 9), 240–61 and 279–83.

⁸⁶ Cf. the texts entitled On Kingship attributed by Stobaeus to Diotogenes and Ecphantus (ed. Thesleff p. 72.15–23 and pp. 81.21–82.6). Explicit descriptions of analogy according to ‘imitation’ or ‘likeness’ are ubiquitous, and it is especially interesting to see ‘Diotogenes’ echo Theophrastus in claiming δεῖ … τὸ ἄριστον ὑπὸ τῶ ἀρίστω τιμᾶσθαι καὶ τὸ ἁγεμονοῦν ὑπὸ τῶ ἁγεμονέοντος.

⁸⁷ Cf. Huffman (n. 9), 54–77 and, more recently, ‘Philolaus and the central fire’, in Stern-Gillet, S. and Corrigan, K. (edd.), Reading Ancient Texts, Volume I: Presocratics and Plato, Essays in Honour of Denis O'Brien (Leiden, 2007), 57–94Google Scholar, at 86–9.

⁸⁸ The only fragment that remains of Philolaus that pays any heed to political organization does so in the form of an analogy between mathematics and colonial rule (T A7a = Plut. Quaest. conv. 718e): ‘Geometry [is] the origin and mother-city of the other sciences’ (γεωμετρία … ἀρχὴ καὶ μητρόπολις οὖσα τῶν ἄλλων [μαθημάτων]).

⁸⁹ e.g. Aët. Plac. 1.7.30 = F 213 IP; 4.5 = F 205 IP.

⁹⁰ Aristotle's criticism of the Platonic Forms in On Ideas challenges arguments put forward by Xenocrates in particular. See e.g. Arist. De ideis 22.16ff. Harlfinger (Alex. Aphr. In Arist. Metaph. 79.15ff. Hayduck) = F 92 IP, with comments by Isnardi Parente (n. 52), 321–5.

⁹¹ See especially Dillon (n. 35), 99–107.

⁹² On the emphasis on ‘inequality’ in the metaphysics of Plato, Speusippus and Xenocrates, see the useful summary of positions by Isnardi Parente (n. 52), 330–3. What is notable about the idea that the Indefinite Dyad could play so important a role in the generation of other entities in Aporia 24 of Theophrastus is the relationship between this statement and a fragment attributed to Speusippus by Proclus (in William of Moerbeke's translation of that text into Latin) which claims that, for Speusippus, ‘the Indefinite Dyad is the principle of entities’ (interminabilem dualitatem entium principium induxerunt). For Burkert (n. 3), 63, and others who follow him, this is evidence for the correlative ideas that (a) Speusippus posited the ‘Indefinite Dyad’ as the material principle and (b) that it is the principle of entities, a phrase, I might add, reiterated in Aporia 24 (οὐχ οἷον τε ἄνευ ταῦτης τὴν τοῦ ὅλου φύσιν). But Tarán's objection (n. 51), 350–6 with 224–6, that the text itself might be tainted especially with the Neopythagoreanism of Nicomachus, has not been sufficiently addressed. Also see Zhmud, L., Pythagoras and the Early Pythagoreans, tr. Windle, K. and Ireland, R. (Oxford, 2012), 424–5CrossRefGoogle Scholar.

⁹³ Cf. Tarán (n. 51), 224–6, following Cherniss (n. 10), 87–8. The association of the term ‘Indefinite Dyad’ specifically with Xenocrates occurs in the important description of his metaphysics in Plutarch's On the Generation of the Soul in Plato's Timaeus (1012d ff. = F 199 IP), which I will provide in toto because of its value for our study (tr. after Cherniss): ‘The former [i.e. the followers of Xenocrates] believe that nothing but the generation of number is signified by the mixture of the indivisible and the divisible being (τῇ μίξει τὴς ἀμερίστου καὶ μεριστῆς οὐσίας), the One being divisible and Multiplicity divisible and number being the product of these when the One bounds Multiplicity and imposes a limit on infinity (τοῦ ἑνὸς ὁρίζοντος τὸ πλῆθος καὶ τῇ ἀπειρίᾳ πέρας ἐντιθέντος), which they call Indefinite Dyad too … but they believe that number is not yet soul, for it lacks motivity and mobility, but that after the commingling of sameness and difference, the latter of which is the principle of motion and change while the former is that of rest, then the product is soul, soul being a faculty of bringing to a stop and being at rest no less than of being in motion and setting in motion.’ Note that, for Plutarch, the standard Platonist term is ‘multiplicity’ and it is Xenocrates who is credited with calling it the ‘Indefinite Dyad’.

⁹⁴ See also Henrich (n. 64), 325–6 who in analysing the passage suggests that what Theophrastus is implicitly contrasting here is the Speusippan idea that the material principle is ‘evil’ and the Platonic and ‘Pythagorean’ idea that it is simply ‘shapeless’.

⁹⁵ Cf. Laks and Most (n. 1), 86. One objection that could be raised here would be to say that Aporia 24 does not follow on the passage at Aporia 23 (11a18–26) and was simply inserted there by some later editor. But one would then need to account for Theophrastus' claim that ‘reality, then, is just as good as it happens to be’ (τὰ μὲν οὖν ὄντα καλῶς ἔτυχεν ὄντα), which ties the preceding criticism of Speusippus and the subsequent criticism of Plato and the ‘Pythagoreans’ together argumentatively.

⁹⁶ For two recent general treatments of Hermodorus, see Horky, P.S., ‘Persian cosmos and Greek philosophy: Plato's associates and the Zoroastrian magoi’, OSAPh 37 (Winter 2009), 47–103Google Scholar, at 84–91 and Dillon (n. 35), 198–204.

⁹⁷ Among attested titles are (Diog. Laert. 4.6–15 = F 2 IP) On Being, On Ideas, On the Good, On Philosophy, On Wisdom, and we might also consider a text (not mentioned by Diogenes Laertius, but from which Simplicius apparently quoted) called On the Life of Plato. See Dillon (n. 35), 96–7 with n. 27.