The eclectic Pythagoreanism of Alexander Polyhistor

fram M. Gehe Field ed. Avis ho He, Piate and Parka gore an Sin io Fe Fit Cea Fery Be (Cambridge 20155) CHAPTER 7 The eclectic Pythagoreanism of Alexander Polyhistor À. À. Long INTRODUCTION Ask anyone to list some Greek philosophers, and chances are that Pythagoras will be mentioned. His name was, of course, one of the most illustrious throughout the eleven hundred years of Greek philosophy’s creative history, and it became more hallowed the further one gets from the great man’s actual lifetime. The closer we are to that date, however, the less we can say with any security about what Pythagoras thought and taught. Starting in the third century Bc, many works purporting to fill that gap were fabricated. They drew some of their content from material attributed to the late fifth/early fourth-century Pythagoreans Philolaus and Archytas, but most of it from a mishmash of Academic or Peripatetic ideas. This Hellenistic corpus of work on Pythagoras and Pythagoreanism includes one text that is significantly different. I refer to the so-called Pythagorean Commentaries (hypomnemata) recorded by a certain Alexander of Miletus, nicknamed Polyhistor, in the first decades of the first century BC, and thence transmitted by Diogenes Laértius in his Life ofPythagoras (8.25— 33), probably composed around ap 200.” Alexander was one of Diogenes’ lam grateful to Car! Huffman and David Sedley for encouraging me to work on Alexander Polyhistor, and to Phil Horky and Jaap Mansfeld for helpful comments on the draft I delivered to the Cambridge Conference, where I benefited particularly from observations made by the late Anna Ju. I thank Carl Huffman again for further suggestions that have enabled me to improve this final version. By the time this study was alreadyin press I learned that Alexander Polyhistor is the subject ofa chapter that André Laks will contribute to the forthcoming Cambridge University Press volume A History of Pythagoreanism, edited by Carl Huffman. 9 See Thesleff 1965. Commentaries or notes is a better translation of /ypomnemata than Hicks’ ‘memoirs’ (in the Loeb edition of Diogenes Laërtius). According to lamblichus, VP 262, Timaeus of Tauromenium drew on a work entitled People ofCroton’s Hypomnemata for reconstructing his own history of the Pythagoreans, on which see von Fritz 1940: 65~6, and Burkert 1972: 104~5. Hypomuemata is the standard term for Pythagoras’ supposed writings, and is already found in the fabricated Letter of Lysis to Hipparchus (Burkert 1961: 25), where Pythagoras is said to have bequeathed his Aypomnemata to his daughter Damo. For recent discussion of this letter, see Kahn 2001: 74-6, and Riedweg 2005: 120-1.

LONG principal sources for biographical details such as the birthplace of his philosophers, but this passage concerning the Pythagoreans, taken f:l:om Alexander's Successions ofPhilosophers, is the only extended citation of his work that Diogenes has included. We are in no position to determine how much scissors and paste Alexander applied to what he allegedly 'found' (D.L. 8.24) in this Pythagorean manual, or the extent of Diogenes' editing of what he in turn found in Alexander's material. Unlike the typical pseudo­ Pythagorean works, which were composed in a form of Doric, the text Diogenes excerpted is written in regular Attic dialect. In other ways, too, it is unrepresentative of those other works, because of the sheer number of doctrines it records and the variety of philosophical and medical theories it represents, with sources that seemingly range from as early as the fifth century up to and including the late second or early first century BC. For all these reasons Alexander's text (as I shall call Diogenes' excerpt) is of exceptional interest. During the first half of the twentieth century Alexander's text attracted a fair measure of scholarly work (as this study will subsequently note), but some sixty years ago that activity waned. It is time to take a fresh look at this intriguing material, which is mentioned in the most recent studies of Pythagoreanism but only cursorily.3 Most of Diogenes' Life of Pythagoras is a typical compilation of bio­ graphical details, anecdotes and summaries of doctrine. Early on Diogenes (8.6) ridicules reports that Pythagoras left no writings, and gives the titles of several works attributed to him. The content of these works, accord­ ing to Diogenes, was entirely ethical and prescriptive with the exception of metempsychosis, a teaching that he says Pythagoras originated (8.14). Diogenes then asserts that no Pythagorean doctrines were accessible before the time of Philolaus. After recording a long list of so-called Pythagorean precepts (symbola) such as 'Don't stir the fire with a knife' or 'Don't sit down on your bushel', and a further list of prescriptions and exemplary actions, Diogenes gives his report from Alexander's Successions concerning the Pythagorean Commentaries. Pythagorean Commentaries, and what comes after them is stated by Aris­ totle' (8.36). Diogenes' Life of Pythagoras continues for a further fifteen sections of largely anecdotal material. Its doctrinal core is the excerpt from Alexander. This man was the author of an astonishing number and range of works, most of them on places and peoples: hence his nickname Polyhistor. 4 Cited especially by the grammarian Stephanus of Byzantium, Clement of Alexandria and anonymous scholia, Alexander was in essence an antiquar­ ian compiler, whose works consisted largely of excerpts from his volumi­ nous reading. Apart from his Successions of Philosophers, he also wrote a work On Pythagorean Precepts (Clem. Alex. Strom. 1.358). It is a fair guess that Diogenes Laertius garnered his list of symbola from this work. There is nothing else to suggest that Alexander had any special interest in the ideas of philosophers as distinct from details about their lives. He was a Greek by birth, but spent his mature years (c. 8o-6o BC) in Rome, where the mythographer Hyginus was one of his students. Alexander's lifetime gives us a terminus ante quem for the date of the Pythagorean Commentaries, but suggestions about when this work was com­ posed before then have ranged from the late second/early first century Be (Zeller 1903: 108) to as early as the first half of the fourth century (Wellmann 1919, Delatte 1922, and W iersma 1942). Since the publication of Burkert's Weisheit und Wissenschaft in 1962, the favoured date for the work has been the end of the third century.5 Controversy over the compositional date of the Pythagorean Commentaries is inextricably implicated in questions concerning the work's sources and originating doctrines. Zeller found in it strong traces of Stoicism, but most later scholars, with the exception of Mansfeld, have not followed his lead. 6 Wellmann, Delatte and W iersma opted for an early date because they found numerous connections with Pre­ socratic thinkers, especially Heraclitus, Empedocles, Alcmaeon and Dio­ genes of Apollonia, and also with Hippocratic texts. Wellmann (1919: 226) actually proposed that the text, apart from a few Stoic accretions, derives from the circle of such Pythagoreans as Philolaus and Eurytus. His study Diogenes (8.25-33) purports to cite several pages of Alexander's 'find­ ings' from this work, and appends to them a further set of precepts and some doctrinal statements (8.34-5) taken (so he says) from Aristotle's work On the Pythagoreans (fr. 195 Rose). He then rounds off this sequence of excerpts with the words: 'This is what Alexander says he found in the J Sec Burkert 1972: 53; Dillon 1977: 342-4; HufFman 1993: 218-19; Kahn 2001: 79-83 (the fullest discussion, which I discuss at the end of this paper); and Riedweg 2005: 23. 4 I rake this and the following information from the very informative article of Schwanz 1894. 5 A larer dare for Alexander's source rexr is supported by parallels between Aetius +5 (Diels 1879: 391) and D.L. 8.30, where the context of both passages is rhc location of rhe soul's cognitive faculty. Aetius refers to 'certain of rhe more recent thinkers', a formula he uses at 2.29.4 (Diels 1879: 360) to signify Pythagoreans subsequent to 'the research of Aristotle and the assertion of Philip of Opus'. I owe this point to Jaap Mansfeld. 6 See Wiersma 1942: 97, !l2, and Festugiere 1945: r. In my opinion, rhey do not undermine the cumulative effect of the Stoic parallels that Zeller 1903: 103-5, adduced. Zeller's findings have been confirmed and supplemented by Mansfeld 1971: 98-102; see below.

was sufficiently influential for Kranz to include the entire Alexander pas­ sage in subsequent editions of DKJ But in an extended study from 1945, Festugiere sought to prove that the main body of the text, together with its anatomical observations (D.L. 8.30-1), cannot precede the late fourth/early third century, and that such Stoic words and formulations as it does con­ tain are due to a still later compiler. Subsequently, with the exception of a short article by Boyance (1967), proposing an earlier date for part of Alexander's original text, the findings of Fesrugiere have been seemingly accepted without any question. In view of this complex history of interpretation we had better make no presuppositions concerning the compositional date of the Pythagorean Commentaries, as supposedly quoted by Alexander, and whether a single author was primarily or wholly responsible for the work's composition. For all we know, Diogenes has modified Alexander's text, and Alexan­ der has done the same to the version of the work that he claims to have transmitted. It is virtually certain that Alexander worked from material that already contained the different chronological and doctrinal strata that we find in Diogenes. In the latter's excerpt Alexander's text opens with statements about principles and mathematics that unquestionably reflect the systematic Platonism propagated by Speusippus and Xenocrates. Yet, much of what follows this beginning has no obvious Academic back­ ground and could be inspired by pre-Platonic or post-Platonic ideas, or by both. In which case, the truth about the work's composition as a whole would be partly but only partly grasped by any one of the scholars I have cited. These uncertainties raise many questions about how we should situate this text in the history of Pythagoreanism. Should we think of it as an early instance of the Neo-Pythagoreanism later associated with such names as Moderatus, Numenius, and Nicomachus, or as largely a product of early Academic Platonism, projected onto the name of Pythagoras, or as a text that contains traces of an early and authentic Pyrhagoreanism, or, finally, as a text that has been strongly marked by Stoicism? I will argue that all four of these interpretative options are in order, making Alexander's text too heterogeneous to be associated with a single philosophical movement. That heterogeneity, of course, may still allow the text to be the work of a single historian or doxographer, as I will actually propose in the conclusion of this study. TEXT AND CONTEXT 7 It is presented in OK vol. 1 58 'Pythagorean School' as Bra under the heading of 'Anonymous Pythagorcans' alongside texts of Aristotle. 143 Before taking up these issues, I will comment briefly on the relevance (or irrelevance) of Alexander's text to philosophy in the first century BC, which is this volume's general theme. The passage in Diogenes Laertius takes the form of a doxography, organised topically as follows: I Principles (Monad and Indefinite Dyad), numbers, four elements, uni­ verse (8.25) 2 The Earth: including equality of the opposites up down, light dark, hot cold, dry moist; terrestrial and celestial air (8.26) 3 Heat as the source of divinity, heavenly bodies, human beings and all other living things (8.27) 4 Immortality of soul in general, embryology and sensory functions (8.28-9) 5 Tripartition of human soul in particular and its relation to the body (8.}0) 6 Eschatology: destiny of pure and impure souls and demonology (8.31-2) 7 Ethical principles and rituals (8.33) Festugiere (1945: 5-8) maintained that this order of topics 'must' depend on Theophrastus' doxographical categories, as found in Aetius (in the order principles, universe, earth, soul and seed), but that its primary source is the Timaeus.8 Alexander's topics do correspond to a large extent with Aetius' headings, but the proposed connection with the Timaeus, though some­ times close, is not as consistently obvious as Festugiere maintained. Here, as elsewhere in his important study, Festugiere was overeager to establish a post-Platonic date for all the material in the Alexander doxography. Was this text available to Roman authors of the first century Be? If so, little possible trace of it is evident in Cicero. He drops the name of Pythagoras in no fewer than seven of his philosophical works, but discur­ sively for the most part, and at greatest length in the preface to Tusculans 4, where he endorses the tradition that Pythagoreans had a great influ­ ence on the early culture of Italy but coyly declines to expatiate on its numerous traces (vestigia) . Cicero's Pythagoras is primarily the exalted founder of an esoteric fellowship, renowned for piety, defence of divina­ tion, and an 'absurd' ban on eating beans.9 As far as doctrines are con­ cerned, Cicero cites the soul's immortality, its consisting of number, and 8 For Aetius, see Diels 1879: 181-4; Mansfeld and Runia 2009. For the Timaeus see 27d-3rb, 48a-52d and 53c-57c. 9 ND 1.74: Laws 2.26; Di11. 1.5, 2.119. Cicero firmly rejects the legend that Kino "' Numa was a follower of Pythagoras, Rep. 2.28.

as having two parts, which, in this context, he also attributes to Plato.10 He gives no comprehensive doctrinal summary of Pythagoreanism as in Alexander's report. There is just one passage where Cicero chimes to some extent with Alexander's text. In a doxographical survey of basic principles, probably derived from Antiochus, Cicero reports that 'the Pythagoreans take the universe to originate from numbers and mathematical principles' (Luc. rr8). Strikingly, however, Cicero does not follow Alexander and the later Pythagorean tradition in positing the Monad and Indefinite Dyad as the foundation of the system. In the introduction to his translation of the Timaeus, Cicero gives Nigidius Figulus the credit for reviving the long dormant philosophy of Pythagoras.![ Figulus was celebrated for his learning, but there is no scrap of evidence concerning anything he wrote about Pythagorean doctrines. The closest Latin text I have found that has any clear connection with the Alexander material is Varro (Ling. Lat. pr), who says that, according to Pythagoras, 'all the principles of things are binary, such as limited and unlimited, good and bad, life and death' (omnia rerum initia bina esse, ut finitum et infinitum, bonum et malum, vitam et mortem).12 Pythagorean doxography vacillates between monism and dualism. In its oldest form, as attested by Aristotle (Metaph. I, 987a13), the Pythagoreans posit two archai, the limited and the unlimited, a doctrine which in essence goes right back to Philolaus (DK 44 Br). Varro evidently had access to a text that set out a Pythagorean table of opposites, starting with limit and unlimited. Those terms, however, are completely absent from Alexander's doxography, while in Varro's statement there is no mention of numbers. I infer that Varro had access to a text, perhaps a summary of Aristotle's Metaphysics, which gave a quite different account of Pythagorean principles from the one we find in Alexander Polyhistor. Before returning to that document, it is worth noting that Posidonius, according to his own words, as reported by Galen (T91 Edelstein/Kidd), said that no writing by Pythagoras has been preserved 'to us'. Posidonius, however, 'from what some of Pythagoras' pupils have written' infers that Pythagoras agreed with Plato and Hippocrates in assigning a composite nature to the soul.13 Did Posidonius study the work of such pupils? Many scholars have supposed that the Pythagorean doxography reported by Sex­ tus at M 7· 94f£ reached him via Posidonius because the context includes Sextus' allusion to Posidonius' supposed commentary on the Timaeus. r4 But I. G. Kidd (in his commentary on Posidonius) has convincingly shown that there is no reason to extend Posidonius' presence in Sextus' text beyond that single statement. If that is so, we have no secure evidence that Posi­ donius made any reference to the mathematical cosmology credited to Pythagoreanism in the Academy and Lyceum, and reported in Alexander's text.15 In light of these points about Cicero, Varro and Posidonius, it seems quite doubtful whether Alexander's text made any significant impact in Rome during the first century BC. Dillon (1977: 117) suggests that Figulus 'may have learned his Pythagoreanism from' Alexander, who, he says, 'taught in Rome in the 70s' BC. Maybe so, but did Alexander actually do any teaching? Even if we suppose that he did, it is likely to have involved grammar and antiquarianism rather than any formal instruction in philosophy. As to Cicero, Dillon speculates that, though he never mentions A!exander, 'he should have known of him', and 'may not have got on with h1m and perhaps ignored him for that reason'. This amusing comment begs all kinds of questions. At this point, we should leave speculation aside, and take a close look at what Alexander tells us about his findings in the Pythagorean Commentaries. 144 10 ll 12 Tusc. r.ro, 39; 4-1 0. See Dillon 1977: 1!7. See Mansfeld 1990: 182. 'J Cicero, Tusc. 4-IO, credits Pythagoras with anticipating 'Plato's bipartite' distinction between ratio­ nal and non-rational parts of the soul. Plutarch more cautiously ( Virt. mor. 441A) suggests that Pythagoras was probably aware of this distinction. 145 PHILOSOPHICAL CONTENT AND CHARACTER The first section (D.L. 8.25) merits particularly close attention. Principles The starring point [arche] of everything is the Monad. From the Monad rhe Indefinite Dyad subsists [hypostenai] as matter for the Monad, which is cause. If anything is certain about Alexander's material, it is the Academic origin of these allegedly Pythagorean principles and elements. The concepts of Monad (or One) and Dyad originated in the early Academy. They were '4 Sec Burkett 1972: 54-6 . '5 If, however, Posidonius took the Timaeus to be a broadly Pythagorean work, as he may well have done, he could have helped to propagate Roman interest in the specifically Pythagorean tradition. There are a number of intriguing corresponde nces between Diogenes Laerrius' report of Alexander and well-attested Posidonian material. Thus Posidonius wrote a book entitled On heroes and daemons (fr. 24 EK), beings to whom Alexander's Pythagoreans arrribute divinatory powers (D.L. 8. 32) . Much ofAlexander's terminology (D.L. 8.25-7) is also found in Posidonius (cf. Posidonius ap. D.L. 7·138-9, 1 42-3) . I am grateful to the late Anna Ju for drawing my attention to these correspondences.

seemingly first stated by Plato himself in his famous Lecture on the Good.16 Under the influence of Speusippus and Xenon·ates, these concepts (in place of Philolaus' limit and unlimited) came to be assigned as principles to Pythagoras and the Pythagoreans as early as Theophrastus, and thereafter they become ubiquitous in Pythagorean doxographies.17 Thus Aetius (1.3, Lemma on Pythagoras' archai (Diels, DG p. 281)) states that the Monad is called 'the active and everlasting [or 'specific'] cause, i.e. nous God', while the Indefinite Dyad is termed 'passive and material, i.e. the visible world'. However, Aetius' implicit contrast between visible and intelligible worlds reflects Neo-Platonic influence, of which there is of course no trace in Alexander's text. Its account of the Pythagorean archai is quite spare, as compared with parallel accounts given by such later figures as Eudorus and Sextus Empiricus (M ro.261-2).18 Eudorus posits a transcendent One, over and above the other two archai (called Monad and Indefinite Dyad), with good and bad things assigned to these latter two principles respectively. In Sextus, the derivation of the Dyad from the Monad is explained in terms of the contrast between self-identity (autotes, the Monad) and otherness (the Dyad). W hatever that distinction means, it purports to provide an explicit account of the relation of the principles to one another. In Alexander, by contrast, all we get is the vague verb 'subsists' (hypostenai) to state how the Dyad stands with respect to the Monad. Neither here nor anywhere else does Alexander's account use the terms 'limit' and 'unlimited' . In contrast with the comparable treatments by later writers he employs no theology or ethics in characterising the principles. As we have seen, Aetius identifies the Monad with divine nous, and in another Aetian lemma (ps.-Galen 35 (DG p. 618)) Pythagoras is said to have made the Monad God and the good, and assigned bad to the Indefinite Dyad alone with its domain extending over the visible world. Cosmic goodness and badness are completely absent from Alexander's account. This material shows that Alexander's source for his opening section pre­ cedes the development ofNeo-Pythagoreanism in the sense of a movement whose first principle is an absolutely transcendent One. This chronology is confirmed, I think, by the staccato way Alexander continues (8.25). From numbers to the formed universe From the Monad and the Indefinite Dyad issue numbers. From numbers, points; from points, lines; from lines, plane figures; from plane figures, solid figures; from solid figures, perceptible bodies whose elements are four: fire, water, earth, and air. These elements interchange and rum about through and through (di' holon), and from them is generated a world that is ensouled, intelligent and spherical, with the earth, which is itself spherical and inhabited all around, at its cemre. There are also antipodes, and our 'down' is their 'up'. The generation of numbers from the Monad and Indefinite Dyad is repeat­ edly ascribed to the Platonists by Aristotle in Metaphysics M (e.g.ro8ra14, ro98b7). Alexander's five- stage mathematical sequence- points, lines, plane figures, solid figures and perceptible bodies - does not seem to be exactly attested in any extant Academic or Peripatetic material, but Aristotle, in his criticism of Platonist number theory, has the triad line, plane and body (Metaph. M ro85a9). In the same context he criticises those who generate magnitudes from the point, probably in reference to Speusip­ pus (ro85a32).19 Theophrastus refers to the derivation of numbers, planes and bodies in a context where he is criticising those who posit the One and the Indefinite Dyad (Metaph. 6a25f). Alexander's full sequence recurs with much more detail in Sextus (M 10.276-83), which reads like a greatly expanded version of this section of Alexander's text, and is attributed to Plato himself by Plutarch (Quaest. Plat. roo2a).20 We can conclude that Alexander's text depends on Academic doctrine, the rationale of which was to fill out the traditional Pythagorean theory that number is the world's metaphysical and epistemological foundation. I turn now to the last two items in rhe mathematical sequence - solid figures and perceptible bodies. In the parallel passage in Sextus (M 10.283) the perceptible bodies are identified in the first instance with earth, water, air, and fire, which in turn are taken to be derived from 'solids' (sterea schemata). We are presumably to understand solids in mathematical terms, such as the cube, pyramid, dodecahedron and icosahedron of Plato's Timaeus. Alexander's text is similar, but confusingly expressed. Instead of saying 'perceptible bodies whose elements are four', it would have been better to write: 'the perceptible bodies, earth, air, fire and water, which are the elements of the world' . However, the general point is clear enough. '6 Sec Burkert 1972: 17-22, and Dillon 2003: 17-21. Thphr., lvfetaph. IIa27-b7; see Burkert 1972: 58-9. For Speusippus and Xenocrates, in detail, see Dillon 2003: 40-63 and 98-nt. ' 8 On Eudorus, cited by Simplicius, in Phys. 181, wff. Diels, sec Dillon 1977' 126ff. and Bonazzi 2007b. '7 147 19 Sec Annas 1976: 185. Cf. Burkert 1972: 247, Cherniss 1976: 49, and rhe references cited by Fesrugiere 1945: 13.

Ir seems certain, as Festugiere has fully argued, that this portion of the cosmology has been ultimately inspired by the Timaeus.21 It shares with that account the world's sphericity and intelligent soul. Plato also envisions constant inter-transformations between three of the elements, though he exempts earth from that process ( Tim. 55d-58c). Early Pythagoreanism, by contrast, adopted neither the four-element theory nor the notion of a world soul. Its distinctive cosmological notions such as the central fire, the earth's revolutions around that fire and the counter earth are strikingly absent from Alexander's Pythagorean Commentaries. 22 I have not found any exact parallel for Alexander's statement that the earth is 'inhabited all around' , which he implies to be a consequence of its spherical shape. Festugiere (1948: 2of.) appropriately refers to Phaedo 109a9-b4, where Plato writes about people living in many hollows of the spherical earth. Reminiscence of Plato is probably confirmed by Alexander's ensuing reference to 'antipodes, where our "down" is their "up'", an idea that recalls Timaeus 63a. However, the geography of Alexander's text may also reflect authentically old Pythagorean doctrine, because Aristotle alludes to Pythagoreans in connection with his own account of right and left, and of up and down. 23 There, in a discussion of the stars' risings and settings, Aristotle contests the view of the Pythagoreans, who 'situate us above [in the upper hemisphere] and to the right, and situate those [who live in the opposite region] below and to the left'.24 Is Academic doctrine sufficient to account for the rest of this first sec­ tion of Alexander's text? Not quite. The statement concerning the four elements' 'through and through inter-transformations' specifically recalls the early Stoic doctrine of the elements' origination from one another in cosmogony, and the phraseology (metaballein kai trepesthai di' holon) , call­ ing attention to the elements' mutual co-extension, is distinctively Stoic25 Zeno was sufficiently interested in Pythagoreanism to write a work so entitled (D.L. 7.4). Nothing is known about its contents, but, with the exception of its explicit mathematics, Alexander's account of principles and cosmology is quite consistent with Stoicism. As in his 'Pythagoreanism', so too in early Stoicism we have: a pair of anrithetical and coordinate principles, one active the other passive, with the passive principle stand­ ing to the active one in a relation of matter to form; four interchanging elements, earth, air, fire, water; and an intelligent and ensouled spherical universe. 26 These Stoic affinities do not cast doubt on the primarily Academic and Peripatetic provenance of Alexander's Pythagorean principles and cos­ mology. Plato's Timaeus both directly and through its Academic and Peri­ patetic interpreters exercised a major influence on the development of Stoic physics.27 According to Theophrastus, Plato could even be credited with two principles, god (or the good) and matter, which strikingly anticipate and correspond to Stoic doctrine.28 Alexander's text, however, seems to signifY an author who wanted to mark doctrinal convergences between so-called Pythagoreanism and Stoicism, probably because the latter was the dominant philosophy at the time of composing this account. Stoic influence on Alexander's original will emerge still more clearly when we turn to the dominant role his text assigns to heat. Alexander's opening section moves clearly and coherently from the two basic principles to the formed universe with the earth at its centre. The next two sections (8.26-7) treat features of the universe and the earth, but without comparable coherence. There are three dominant notions: first, equality of opposite powers; second, a theory about air and aether, and third, the role of heat as the essence of divinity and the cause of life. I will take these notions in order. 21 Fcsrugiere 1945: 17-18 with references; cf. Zeller 1903: 104 n. 2. 22 The attempt by Wellmann 1919 to assign Alexander's evidence to a Pythagorean contemporary of Plato, drawing on fifth-century Pythagoreanism, is trenchantly refuted by Festugiere 1945· Delatte ( 1922: 198-201) provides numerous Pythagorean texts to illuminate Alexander's material, but they are largely drawn from Nco-Pythagorean sources. Wiersma (1942: 98-9) recognises that Alexander's first section is Academic in origin bur defends Wellmann's general thesis concerning the early date of the main bodv of the text. 23 De Crzelo 2. 2. 285b22, cited by Delatte 1922: 205. 24 Cf. Cicero, Rep. 6.21 in Scipio's discourse on two opposite habitable zones, which Cicero may intend to sound Pythagorean. 25 See SVF 1.!02 and 2.413. The Stoic affinity is noted by Zeller 1903= 104 n. 2, Fcstugiere 1945: q, and Mansfeld 1971: 99· I49 Equality ofopposite powers: light dark, hot cold, dry moist (D.L. 8.26) Light and dark have equal shares in the universe, and so too, hot and cold, and dry and moist. In the case of the larrer, when hot predominates, summer comes; when cold, winter; when dry, spring; and when moist, autumn. If they are all of equal strength, the year is at its finest; it is healthy during the freshness of spring, but unhealthy in the decay of autumn. During the day too the morning is fresh but the evening is in decay, and therefore more unhealthy. 26 The sphericity of the universe attested by Philolaus B7 is the only early Pythagorean doctrine here; see also Burkert 1972: 303-5. 27 See Reydams-Schils 1999. 28 Theophrastus Fr. 230 in Fortenbaugh eta/. 1992. At D.L. 3.69 Plato's principles are god and matter. See Sharples 1995: 69, and Sedley 1998b: 349-50.

The equality of opposites has an archaic ring.29 It recurs in different guises in Parmenides, Empedocles and, most relevantly perhaps, in Alcmaeon, who (OK 24 B4) explained health in terms of the isonomia of such opposites as moist dry, cold hot and sweet bitter, as does Plato in the physiology of Timaeus 82a.3° Comparable passages occur in the early Hippocratic corpus, where, as in Alexander, seasonal changes are explained by the temporary dominance of one such opposite over another.3' Aristotle and the Stoics seem to have viewed the terrestrial elements as equal in as much as they are incessantly subject to interchange, as with Alexander's Pythagoreans, but his application of opposites to explain the seasons, and the healthiest and most noxious times, could well go back to late fifth-century sources. The next section is highly compressed and poorly organised, but it does have a primary controlling idea, the vital power of heat. Air and aether, heat, divinity and the source oflifo (D.L. 8.26-8) The air around the earth is stagnant and noxious and everything within it is mortal; but the uppermost air is in perpetual motion, pure and healthy, and everything therein is immortal and therefore divine. Sun, moon and the other stars are gods; for in them heat predominates, and heat is the cause of life. {The moon gets its light from the sun.} Gods and human beings are akin, because the human being shares in heat. Therefore God cares for us. {Fate is the cause of the world order both in general and in particular.} The sun's ray penetrates the aether, both that which is cold and that which is dense- they call [here Alexander switches to direct speech] the [terrestrial) air cold aether, but sea and moisture they call dense aether - and this ray sinks into the depths and therefore bestows life on everything. Setting aside the intrusive references to the moon's light and to fate, I paraphrase as follows: the universe is divided into a terrestrial region, the living contents of which are impure and mortal, and a celestial domain, which contains immortal gods, including the heavenly bodies. This con­ ception of the universe is marked by differences between the quality of the air within its upper and lower divisions. Heat (whose source is the sun) is 29 See Kahn 2 001: 81. Fesrugiere (1945 : 32-9) surveys this material in great detail. Rather than allowing it to be direcrly influenced by fifth-century ideas, he proposes that Alexander's 'Pythagorean' has derived it from Plato. 31 See Hippocrates Nat. 4 and Airs ro-II, with commentary by Delane 1922: 2 05-7 , and Longrigg 1993 : 91-2 . Stoics explain the seasons by variations in the sun's temperature, owing to its distance from the earth, with spring due to eukrasia of the air; cf. D.L. 7-151-2. If Philo of Alexandria ( SVF 2.6 16) reflects the Stoics, we can attribute to them isonomia of the four elements and their reciprocity to one another. 3° responsible for all life, both the celestial life of the immortal gods and our human selves, and, at the lowest extreme, the life of plants. Differences of air are in fact differences of a single substance aether, such that fire is hot aether, air cold aether, and water dense aether. The passage raises numerous questions. Here, I shall pursue just three: the division of the universe into lower and higher; the notion of vital heat; and the aether terminology. In a late doxography (Aetius, Plac. 2, Diels, DG 336 (= OK 44Ar6)) Philolaus is reputed to have made a tripartite division of the world into a top region containing purity of elements, a middle domain, where the planets, sun and moon are located; and a sublunar region of biological changeY Diels took this passage to be probably derived from Theophrastus, but Burkert rightly found traces of the Timaeus in it.33 In Philolaus, on the other hand, the primary and most honourable part of the world is the central fire.34 By deifying the upper region of the universe Alexander's Pythagoreans are in line with Plato, Aristotle and Stoicism. The emphasis his text lays on vital heat is striking, together with the analysis of three of the traditional four elements as species of air, here redescribed as types of aether.35 Festugiere rightly notes that Plato in the Timaeus distinguishes three different types of air (58d), but unlike our text, Plato confines the word aether to the brightest kind of air. There is no suggestion in Alexander's text that the hot aether has anything more than a name in common with Aristotle's fifth element.36 In Presocratic contexts aether is typically distinguished from air, so Alexander's 'Pythagorean' use of the term for all species of air appears anomalous. With its emphasis on heat and sunlight as the cause of life, we may be warranted in finding a monistic tendency in this part of the text, as in Anaximenes, Diogenes of Apollonia and a time-honoured inter­ pretation of Heraclitus' dominant element fire.37 There are further hints that Alexander's text has incorporated pre-Platonic material. According to D.L. 9.22 Parmenides invoked the sun to explain the origin of human beings, while the sea, as the location for the origins of life in general, harks back to several early Greek thinkers.38 As to specific reminiscences of old Pythagorean doctrine, the most promising text to adduce is probably For the doxogtaphical context, see Mansfeld and Runia 2009: 3 94-408. JJ Burkert 1972: 244-5 , followed by Huffman 1993 : 3 98. 34 See Huffman 1993 : 242- 6 . 35 See Solmsen 19 7 and Mansfeld 1971: 83 -103. 5 36 See Boyance 196 7, who convincingly contests the proposal of Festugicre 19 4 : 23-6 that Alexander's 5 Aristotle. and Plato of ence u infl the shows her et a 37 As suggested by Wellmann 1919' 228-3 1, and \'V'iersma 1942: ror-6 . J8 See Delatte 1922: 2 1o-rr.

DK 44 A27, where the Anonymus Londiniensis claims that, according to Philolaus, our bodies are constructed out of heat, on the evidence that sperm and the womb are hor.39 In the middle of this section, as we have seen, Alexander's text makes big claims about gods and human beings, but with lightning brevity. What connects the two races is heat, which, in its celestial form as hot aether confers not only life but also immortality. Immortality pertains in the first instance to the gods and heavenly bodies, but by implication, owing to our kinship (syngeneia) with the gods, are we too immortal? Divinity cares for us (pronoeisthai) because in our heat we resemble the divine! And in the next section, our immortality will be made explicit on the grounds that soul as such is immortal. This entire passage closely recalls Alcmaeon, who, according to Aristotle (de An. 1.2-405a29 ( = DK 24 At2)), declared the soul to be immortal because of its resemblance to immortal beings, and by virtue of this property stated that the soul is in everlasting motion, just like the heavenly bodies. Similarly Alexander's text situates the heavenly bodies within ever-moving air or hot aether. Immortality of soul is a thesis that a Pythagorean of any vintage must defend. Strikingly, though, Alexander's Pythagoreans are physicalists, through and through. Our text eschews any hint of incorporeal or transcendent reality, and the psychology, to which we shall come shortly, is represented in entirely physical terms. This section has introduced us to equal elements, seasonal changes, sub-lunar and super-lunar domains, purity and impurity, mortality and immortality, vital heat and sunlight, divinity and types of air or aether. This is a lot to take in. As with the opening section on principles, reso­ nance from the Academy is still strong, but here it is evident in general rather than specific points, many of which are shared by the Stoics. When it comes to the passage's most distinctive details- vital heat, divine prov­ idence's concern for human beings, and strong physicalism - we are very close, exempting immortality, to early Stoicism. The seemingly intrusive statement (between the theology and the doctrine on the sun) concerning fate (heimarmene) is further proof that this passage has passed through the hands of someone whose intellectual background includes Stoicism.4 0 Mathematics and numbers have dropped out completely, and there is noth­ ing that points specifically to Aristotle or Theophrastus. Some theories may have a pre-Platonic lineage, and the air/ aether doctrine appears to be quite unique. From cosmology and theology, Alexander's text now turns to the soul, reproduction and embryology. 39 See Huflinan 1993: 29off. 40 So roo Festugiere 1945: 59· 1 53 Soul, reproduction, embryology (D.L. 8.28-9) Everything that shares in heat is alive- hence plants too are living beings- although not all living beings have soul, which is a detachment (apospasma) of aether, both the hot and the cold, since the soul shares in cold aether. Soul is different from life: it is immortal since that from which it is detached is immortal. Living beings are generated from one another by seeds, and their generation out of earth is impossible. The seed [sc. of animals] is a droplet (stagon) of brain containing hot vapour within itself. When this droplet is applied to the womb, it emits from the brain ichor, moisture and blood. From these [brain fluids] flesh, sinews, bones, hairs and the whole body are formed, while soul and sentience (aisthesis) emerge from the vapour. First congealing in forty days, it [the embryo] acquires form, then according to the ratios (logoi) of harmony in seven or nine or at most ten months the completed foetus is brought forth. Within itself it contains all the ratios of life and, with these ratios systematically strung together, the newborn infant is made coherent with each of its parts accruing at determinate times. By comparison with the stark brevity of the preceding section, this account of biology and embryology is quite full. It also hints for the first time at taking a stand on controversial issues. Plants are zoia, living beings, but, unlike Platonic and Aristotelian plants, they lack soul, or so I interpret the implication of the statement '+'vxi)v iJEVTOl !Ji) EXEIV m:XVTo:, where the negative me instead of ou suggests the statement's concessive depen­ �ence on the assertion that plants are zoia: 'although not all living beings (I.e. plants) have soul'. The obvious source for the denial of soul to plants is Stoicism.41 Resonance of Stoicism continues in Alexander's calling soul 'a detachment of hot and cold aether' (an expression a Stoic could have used in reference to psychic pneuma) and in the emphasis here and in the next section on blood as the soul's nutriment.42 However, Alexander's Pythagore­ ans, as we would expect, posit immortality of soul, which the Stoics do not. The second hint at adopting a controversial position is the insistence that all reproduction requires seeds, with the attendant denial of spontaneous generation from the earth. Stoics probably rejected that popular theory. 41 SVF 2. 708-11, 714. See Long 1996: 237-9. See SVF r.u8, 14 0, 2.633.

As to the bizarre embryology that follows, the three items emitted from the brain under the seed's influence- ichor, water (to hygron), and blood- form a series of fluids that seem to range from the most to the least refined.4 3 These fluids and attendant processes indicate a physiology that is quite distinct from Stoic theory, in which the heart is the primary organ for embryological development. 44 The description of the seed as a drop of brain might go back to Alcmaeon (Aetius. Plac. 5.3-3) or even to Philolaus, though it most probably echoes Plato, Timaeus 73cd on seed, marrow and brain. 45 The most intriguing feature of this section is the repeated mention of the logoi of harmony in the context of the embryo's development.46 Here, we have a notion that looks authentically Pythagorean, connected as it is with precise numbers signifYing months for gestation. In late Pythagorean material, starting with Varro, the number of days for a seven-month or nine­ month pregnancy are computed on the basis of precise multiplications. 47 We can probably infer from this material that Alexander's 'ratios of har­ mony' are intended to invoke numbers pertaining to musical harmonics, as in Hippocratic texts, where numerical ratios are adduced in computing the number of days for different periods of gestation. 48 Unfortunately, the chronology of the relevant Hippocratic works is too uncertain to warrant any inferences from them concerning which way the influence goes, so far as Alexander's text is concerned. The extract continues (8.29) with a few lines concerning sense­ perception in general and vision in particular, with all sensory functions attributed to 'very hot vapour' (atmos). 49 I pass over this passage except for one particularly intriguing point it contains. Alexander reports that Pythagoras called the eyes 'gates of the sun'. That is a Homeric expression, taken from the beginning of Odyssey 24, where Hermes summons the souls of the dead suitors. Lines 9-12 of that book read as follows: Hermes the kindly healer led them down broad paths. They went along past Ocean's streams and the White Rock, and past the gates of the sun and the land of dreams. 154 43 Ichor is sometimes used for a viral fluid distinct from blood (as in Homer), or as the warcry part of blood (e.g. Plato, Tim. 83c, Arisr., PA 651a18) or as a generic term for bodily discharges. 44 See Long 1996: 243-445 There may be a genuine reminiscence of Philolaus B13, which Burkert 1972 and Huffman 1993 take to be authentic (see Huffman 1993: 307-32). This fragment, cited by Nicomachus, purports to give Philolaus' theory of 'the four principles of the rational animal', viz. head for intellect, heart for life and perception, navel for initial growth, and genitals for sowing seed. The brain is said to be the hurnan being's origin. 46 Zeller (1903: 105 n. 6) relates the expression 'all the logoi of life' to the Stoic notion of spermatikoi logoi. 47 See Delatte 1922: 216-19. 45 See Burkert 1972: 262-4. 49 These lines on aisthesis seem our of place. The suitable context for them is the next section on psychology, where aistheseis arc mentioned all over again. 155 A page or so later Alexander's text (D.L. 8.31) refers to Hermes and his escorting of souls. Pythagoreans, even Pythagoras himself, may have called the eyes 'gates of the sun' without any interest in the original eschatological context of this striking phrase.so In Alexander, however, the contextual coincidence, if that is what we have here, clamours to be noticed. The human soul (D.L. 8.29) The human soul is divided three ways into nous, phrenes and thumos. Nous and thumos are also present in the other animals, but phrenes are only present in the human being. The soul's domain (arche) extends from the heart up to the brain. The part that is in the heart is thumos, while the parts in rhe brain are phrenes and nous. Sensations (aistheseis) are secretions (stagones) from these [latter] . The rational part (to phronimon) is immortal, but the rest is mortal. The soul gets its nourishment from the blood, but the soul's logoi are winds. The soul itself and the logoi are invisible, because the aether is invisible. The veins, arteries and sinews (neura) are the soul's linkages (desma). When it is strong and has become self-contained and at rest, logoi and actions become its linkages. This passage, remarkable for its obscurity, terminology and eclecticism, merits a whole paper to itsel£51 The tripartition of the soul sounds Platonic, and features of the text, including the anatomy and the immortality of the rational part, call the Timaeus specifically to mind.52 But Alexander's text maintains the physicalism I have emphasised before, and there are too many other differences of detail to posit Plato as more than one likely influence. Immediate questions that the passage raises are the use of the old Homeric word phrenes to refer to the soul's rational part and the consequential down­ grading of nous; the interpretation of stagones in reference to aistheseis; the statement that the soul's logoi are winds; and, lastly, the repeated application of desma, which I translate 'links', to the soul. 50 Pythagoreans liked to align mythological expressions with empirical phenomena: 'sun like' and 'fiery' are words they are said to have applied to the eyes. See Delatte 1922: 221. 5' Fesrugiere (1945: 43fi) discusses the passage at great length, mainly by citing medical texts, especially ones deriving from Diodes of Carystus. I find the passages he cites more tangential than genuinely illuminating. His neglect of Stoic pneuma is a major shortcoming, and also his lack of comment on the curiously literary terminology. 52 The doxographical tradition often assigns Platonic ttipartition to Pythagoras and Pythagoreans; see Burkert 1972: 74·

As regards Alexander's use of phrenes, I first quote Kahn (2oor: 82) : 'This archaic use of phrenes seems . . . to have been preserved in medical usage, as the term phreneitis for brain-fever shows.' 53 That is true enough, but medical usage does not explain why an account of supposedly Pythagorean material should have used this largely anachronistic term. In the doxographical tradition, the Pythagoreans are credited with the doctrine that the heart is the seat of the vital principle (zotikon), and the head that of the rational (logikon) and intelligent principle (noeron) . 54 These three terms call for no comment, but no one, to the best of my knowledge, has come up with a convincingly philosophical or medical parallel for Alexander's use of phrenes. I tentatively suggest that it may be explained as a result of the Pythagorean extension of rational capacity (logikon) to all animals. 55 That notion, probably a consequence of metempsychosis, leaves Alexander's Pythagoreans needing a different word for specifically human rationality. Whatever the merits of this suggestion may be, we should note that the combination of cardiovascular and brain-centred theories for the soul's bodily vehicles is typical of this text's eclecticism and syncretism. My next question is what to make of the claim that aistheseis are stagones from 'these' , where 'these' refers to the cerebral phrenes and nous. Stagon is literally a drop of liquid. I had initially found such a reference quite out of place in this account, both because Alexander has previously told us that aesthesis in general and vision in particular are 'exceedingly hot vapour' (8.29), and also because of his account's overall affinity with Stoic pneuma, which he seems to underline with his reference to the soul's logoi (rational principles?) being 'winds'. 56 On further consideration, I am inclined to think that the liquidity he alludes to with the word stagones is blood (to which stagon commonly alludes) and that aistheseis here are particular sensations, not the sense faculties. 57 Blood, as Alexander immediately observes, is what nourishes the soul, and he has already indicated that the soul's activity involves transmission from the heart to the brain. Sup­ port for the notion that stagones are secretions of blood may be drawn from Alexander's next observation concerning the soul's 'linkages' (desma) . Desma is not a word one expects to find in a doxographical text on psychology and anatomy, especially with this largely archaic plural instead of the more familiar form desmoi. 58 The triad of desma - 'veins, arteries, and neura' - may suggest that Alexander's original source has hedged its bets between cardiovascular and neurophysiological theories of the soul's channels of communication in the body, but the imprecision of the entire passage favours the translation 'sinews' for neura rather than nerves.59 Alexander's point is, presumably, that the blood vessels and the sinews are the linkages by means of which the soul communicates with the rest of the body in executing its basic nutritive and sensory functions. I have wondered whether the use of desma could be due to a Pythagorean thought to the effect that the veins and so forth keep the soul chained to the body.60 Against this, however, is the fact that Alexander describes a strong and self­ contained (mature?) soul as having logoi (thoughts or reasons) and actions (erga) as its 'linkages' . The language is bafflingly obscure. The best I can suggest is that the soul is here being characterised in what we moderns would call its function as mind or centre of consciousness. If that is right, we can understand why the mature soul's relevant links to the whole person are expressed in mental rather than anatomical terms. 53 Fesrugiere (1945: 44f.) refers ro Anon. Lond. 1V.14-I7• where phrenes actually alludes ro the brain. However, the Hippocratic author of On the sacred disease, 2 0, rakes phrenes to signify diaphragm, and dismisses irs having any connection with intelligence. 54 Aerius 4-5-10 (Diels 1879: 391-2). 5 5 See Aetius 5.20-4 (Diels 1879: 432), who says: 'Pythagoras a n d Plato say that even the souls o f so­ called non-rational animals are rational, but they do not act rationally because of their bodies' poor composition, and their nor having the capacity to speak, as in the case of apes and dogs; for they are intelligent (noousi) bur do not speak' (phrazousi) . Burkert (197 2 : 75) says that this last sentence explains the distinction between nous and phrenes in Alexander's text. How so? Burkert seems to be aligning phrenes with phrazousi, bur he gives no support for this linkage. 56 Alexander's earlier mention of logoi, in the context of embryology, had seemingly mathematical connotations, bur they are our of place here. If anemoi is a literary equivalent to pnewnata, as seems likely, I propose Stoicism again as the ancestor of Alexander's eccentric terminology. Cf. Cleanthes (SVF 1.467), who, with allusion to Heraclitus, compares the unification and separation of cosmological constituents to the way 'certain rational principles (!ogoz) pertaining to parts unite and combine in the seed, and then separate our, as the parts develop'. I 57 Eschatology and rituals Alexander's text moves on from psychology to eschatology and the soul's postmortem destiny (8.31-2) . The treatment of this latter topic draws on familiar mythology, in specifYing Hermes as the escort of souls and a celestial domain for the pure, but it also incorporates the following peculiar 57 I follow a tentative suggestion from the anonymous referee for Cambridge University Press that Alexander means to say that the senses are drops of blood, since this is what nourishes the soul (D.L.8.30 fin.), in which case it might be implied that there is a difference between aesthesis and aestheseis, such that the latter are the acrualisarions of the former. I also note rhe role that Aristotle attributes to the blood and to blood vessels in transmitting sensory movements: de !nsomniis 2 .461a8ff. 58 Plato, Tim. 73b, calls marrow life's chains (desmoi) . 59 Fesrugiere (1945: 47) insists that neum should be translated 'nerves', but I prefer sinews since I find no other evidence that Alexander's text was inHuencd by the latest Hellenistic medical discoveries. Thus Epictetus (1.9.!1), echoing Plato's Phaedo warns his students against suicide, even though he grants the rectitude of treating their attachment to the body and to possessions as desma.

ideas- 'unbreakable bonds' (desma again) imposed by the Furies for the fate of the impure, and transmission, by souls 'called daimons and heroes', of dreams and prophetic signs not only to human beings but even to sheep and other grazing animals.61 Could this remarkable interest in supernatural messages to livestock hint at or make up for the most striking omission from Alexander's explicit text Pythagoras' theory of metempsychosis? It is the final section (8.33) that has the most obvious affinity with Pythagoreanism as a cult marked out by specific rituals and prescriptions. Here we are told that virtue, health, all goodness and divinity are harmony. Alexander's text gives instructions on how we should worship gods and heroes. Finally, we are offered rules, many of them culinary, about how to stay pure. First, the eclecticism is so extreme that it is difficult to credit the text to the ultimate authorship of anyone actually calling himself a Pythagorean. Whoever wrote the work in its final form was familiar with much of what became standard Pythagorean (but in origin early Academic) doxography. That is clear from the opening section on Monad and Dyad. Thereafter, apart from some possible echoes of Philolaus and Alcmaeon, the text veers away from anything distinctively Pythagorean before getting to the final material on eschatology and ritual. The central sections principally reflect a physiology that reads chiefly like a mishmash of Stoicism and medical theory, together with some apparent reminiscence of Presocratic ideas. My second reason for preferring Kahn's second option is the literary character of this text. As we have seen, it includes unusual words for a doxography- e.g. ichor, stagon, phrenes, desma- and the style in general seems to me more literary or mannered than one expects to find in this kind of handbook writing. Third and finally, I like Kahn's suggestion of a 'learned Hellenistic scholar' because I doubt whether there already existed a Pythagorean dox­ ography corresponding to all the sections of Alexander's text- basic prin­ ciples, cosmology, psychology and so forth. In that case, what we have here must be counted as a piece of pseudo-Pythagoreanism after all, but a piece that registers an exceptional range of reading, and some authentic information, on the part of its author.62 Who better to be that author than Alexander Polyhistor himself ? 63 Could his reporting what he 'found' (D.L. 8. 24) in the Pythagorean Commentaries be itself an elaborate literary forgery, making his Commentaries into an ancient likeness of a Borges essay, such as only an immensely learned antiquarian could write? CON C L U S IONS To conclude, I start by quoting the following statement by Kahn (2001: 83): This curious text thus claims to reflect a living cult that maintains a number of ritual observances characteristic of the Pythagorean tradition from the earliest times. On the face of it, this text represents the updated doctrines or doxography of a Pythagorean community from the third or second century BC, which has preserved features from both the theoretical tradition of the ma thema tik oi and the ritual tradition of the akousma tikoi, all of this blended in a strange medley of Presocratic, Platonic, and Stoic elements. If this impression is correct, this text is the only unmistakable trace of a Pythagorean (or Neopythagorean) ritual community from the Hellenistic centuries before roo B C . In a footnote to these comments, Kahn suggests, as a much less prob­ able alternative, that Alexander's original text 'might represent a purely literary phenomenon, the creation of a learned Hellenistic scholar who is more interested in older traditions and more successful in avoiding glaring anachronisms than the usual authors of pseudo-Pythagorica'. Kahn's expression 'strange medley' is entirely apt. But, in deciding berween his options- traces of a Pythagorean ritual community from the Hellenistic epoch, or the work of a learned Hellenistic scholar- I incline to the latter for the following reasons, though without giving the author Kahn's compliment of composing an account that has some chronological plausibility. 61 These 'daimons' are presumably deparred souls: sec Schibli 1 99 3 : 147-9, 1 5 4-7 . 6' 159 In its range, Alexander's Pythagorean Commentaries is probably closest to the tracts attributed to the Peripatetically influenced Occelus and also to Timaeus Locrus (see Thesleff 1 96 5) but it differs from these texts i n its radical eclecticism. Much of Occelus is devoted to establishing the eternity of the world, but Alexander's text leaves that question untouched. 6J As originally proposed (though later retracted) by Diels 1 8 90. Burkert 1 96 1, supported by Riedweg 2005: 121 , argues persuasively that the pseudo-Pythagorean Letter of Lysis (see n. 2 above), with its mention of Pythagoras' lrypomnemata, was written in order to authenticate this fabricated work, which, in its turn, must be identical to the Pythagorean Commentaries that Alexander purports to record. Modern suggestions concerning the compositional date of the Lysis Letter (which is rransmitred both by lamblichus and anonymous sources of Greek epistolography) range from about 250 BC (Burkert 1 96 1 : 23-5) to the early Roman Empire (Stiidele 19 8 0). I owe to Carl Huffman rhe intriguing suggestion that if, as I conjecture, Alexander composed the bypomnemata (as distinct from excerpting an independently existing text), he probably wrote the Lysis Letter too.