Category Archives: Ancient Philosophy

Hellenistic Italic Philosophers?

For some time now, I’ve been thinking about the place that ancient philosophers from Italy who were not thought to be either Greek or Roman has played in the development of Roman philosophy.  I’m working on a piece for the Oxford Handbook of Roman Philosophy (edited by Will Shearin and Richard Fletcher) on precisely this topic, which is a difficult one for several reasons: first, there exists no well-established scholarly discourse about the topic at present; second, the evidence is often obscure, fragmentary, or (a constant problem nowadays for me) embedded in Hellenistic Platonism-Pythagoreanism; and third, most of the texts have no reliable translations in modern languages.  Before submitting the piece for consideration, I plan to present it as a talk entitled ‘Italic Philosophy’ at the second leg of the Milan-Durham Joint Seminar on Platonism and Hellenistic Philosophy (11-12 December, 2014, at the Dipartmento di Filosofia, Universita degli Studi di Milano).

Tomb Painting from Paestum/Poseidonia, possibly Lucanian (4th Century BCE)

Tomb Painting from Paestum/Poseidonia, possibly Lucanian (4th Century BCE)

By way of preview, here’s a bit I’ve written concerning the Italic people who were thought to have cultivated the most philosophers, the Lucanians.

A number of Lucanian philosophers had been known in antiquity, and some Hellenistic texts purporting to have been written by these figures survive. Their imprint was left on Aristoxenus of Tarentum, who, writing in the late 4th Century BCE, mentions several non-Greek philosophers who hailed from Italy in his list of Pythagorean philosophers. Among the Lucanians, he refers (apud Iambl. VP 267) to two brothers named Occelus and Occilus of Lucania, as well as their sisters Occelo and Eccelo. Texts survive under the name of Occelus and a certain Eccelus, which might have originally been an unnecessary correction of Eccelo, but nothing survives for Occilus or Occelo. Additionally, Aristoxenus refers to two other Lucanian philosophers by name: a Cerambus, otherwise totally unknown, and a certain Aresandrus, whose name might have been corrupted to become ‘Aresas’, a figure who is better known, and for whom a substantial fragment of a work entitled On the Nature of Man survives. The historical Aresas of Lucania was considered the last ‘diadoch’ or leader of the school that traced itself back to Pythagoras, who then imparted his learning to Diodorus of Aspendus, who publicized the Pythagorean acusmata widely in Greece (Iambl. VP 265). Plutarch (de Gen. Socr. 13) believed that Aresas was one of the last Pythagoreans to stay in Magna Graecia, remaining in Sicily after the Cylonian conspiracy tore the Pythagorean communities apart, and visiting with Gorgias of Leontini.  This information would place the historical Aresas in the early part of the second half of the 5th Century BCE, a Pythagorean with connections to sophistry. Such connections between Pythagoreanism after the Cylonian Conspiracy and sophistry are well-attested both in the genuine writings of Archytas of Tarentum and in the Pythagorean Pseudepigrapha associated with Archytas and, as we will see, Aresas of Lucania.  The surviving fragment attributed to Aresas, from a work called On the Nature of Man, features an inquiry into human nature that focuses on human psychology, by reference to law and justice:

The nature of man seems to me to be a standard of law and justice, as well as a standard of the household and the city. For if someone were to pursue its tracks and search for it in himself, he would discover it; after all, law and the justice in him are the order of the soul. For the soul, being triple, gives order in three activities: <mind> produces thought and wisdom, <courage> produces strength and power, and desire produces love and kindness. And all of these things have been ordered with regard to one another in such a way that the most authoritative part leads, the worse part is ruled, and the middle part occupies the middle order, and it rules and is ruled. God contrived these things in the modelling and completion of the human body in such a way that he considered man alone, and none of the other mortal animals, to admit of law and justice.

(From  ‘Aresas’ F 1 =Stob. 1.49.27 p. 355 Wachsmuth = pp. 48.20-50.23 Thesleff)

‘Aresas’ expands upon the Platonic theory of the tripartition of the soul, using the same terms Plato employed in the Republic, but adding in concepts and vocabulary from the Peripatetic tradition – adapting ideas that are found equally in Aristotle’s Politics and, perhaps closer to this text, the On Law and Justice attributed to the Pythagorean Archytas of Tarentum, which may be one of the earliest of the Pythagorean Pseudepigrapha (possibly composed in the late 4th Century BCE, as argued publicly by myself and Monte Ransome Johnson in a recent presentation in Durham).  The ghost of Aristoxenus, who wrote a life of Archytas that may have been the ultimate source for the On Law and Justice, is in the background here too, as ‘Aresas’’ Pythagoreanism is presented in terms that resonate with Aristoxenus’ own descriptions of Pythagorean ethics. Moreover, there is a Sophistic tendency here to associate the gift of law and justice to humans by God with ‘Aresas’, echoing similar ideas in the so-called ‘Great Speech’ of Protagoras, and the defense of law and justice in the work known as Anonymus Iamblichi, often thought to be a student of Protagoras. In this way, ‘Aresas’ appears to combine doctrines about the importance of law and justice, familiar from the Sophistic tradition, with a joint Platonic-Pythagorean presentation of the soul.  But things get more interesting philosophically a bit further down in the fragment, after ‘Aresas’ has described how the various parts of the soul must relate to one another when the disposition of the soul is properly harmonized:

Moreover, a certain concord and unity of mind accompanies this sort of disposition. And this sort of disposition would justly be called the ‘good order’ (eunomia) of the soul, the very thing which confers strength of virtue from the fact that the better rules, and the worse is ruled. Friendship, love, and kindness, since they are of the same stock and kind, sprouted from these parts. For mind, when it inspects closely, wins through persuasion, whereas desire loves for its own sake, and courage, filled with might and boiling with enmity, becomes beloved to desire. For mind, since it mixes pleasure with pain, adjusts the high-pitched and excessive part to the light and soluble part of the soul; each part, then, has differentiated a forethought of each thing according to whether it is of the same stock and kind – mind inspecting closely and tracking things, and courage adding impetus and force to the inspections; but desire, being of the same type as affection, refers a property to mind by acquiring pleasure and giving up what is contemplated to the contemplative part of the soul. By virtue of these very things, life for humans seems to me to be best, whenever pleasure is combined with seriousness, and enjoyment with virtue.

(From ‘Aresas’ F 1 =Stob. 1.49.27 p. 355 Wachsmuth = pp. 48.20-50.23 Thesleff)

‘Aresas’ continues the political themes here, referring to the disposition of the harmony of the parts of the soul as its eunomia, a word whose value to philosophical traditions seems to stream out of Sparta all the way back in the 8th Century BCE, obtain confirmation as early as Solon, and flourish among the Socratics, especially Xenophon and Plato, and some Sophists, such as Anonymus Iamblichi. Here, however, something relatively unique is advanced: the state of the soul being properly harmonized is called ‘well-lawed’, which is explained as the disposition in which the better element rules, and the worse is ruled. Some version of this thought is found in Plato’s Republic (462e), where Socrates and Glaucon conclude that a city-state which is well-lawed (eunomos) will, like the soul of an individual person, share in its affections. Similarly, the virtue of temperance, which is applied across the entire city-state of Kallipolis and throughout the entire individual soul, is understood to be “a concord between naturally worse and naturally better as to which of them should rule” (R. 432b).  There is a catch, however, as Socrates later (R. 605b-c) clarifies: in a well-lawed city, those poets who might stimulate and arouse the worse part of the city-state to attack its ‘rational’ part should not be allowed to remain, for the reason that the rational part of the city-state, as well as the rational part of the soul, would be under threat.

Thus ‘Aresas’, the Lucanian ‘Pythagorean’, espouses a tripartite structure of the soul, without any reference to bipartition that would come to be the ‘truer’ version of the Platonic soul, according to Plutarch (de Virt. Mor. 3.441d-442a) in the late 1st Century CE, and that can be found in various parts of the corpus of Pythagorean Pseudepigrapha. The notion that Pythagoras initiated the claim that the soul is tripartite is advanced by Poseidonius, writing sometime around 100 BCE, citing some writings of Pythagoras’ pupils that cannot be identified with confidence (Poseidonius T 151 Kidd). Tripartition is also attested in a similar format by one of the best sources for Hellenistic Pythagoreanism, Alexander Polyhistor, in his Successions of the Philosophers, where he claims to have obtained the information from a work known as the Pythagorean Notebooks (Pythagorika Hypomnêmata), which also seem to date from the late 2nd-mid-1st Century BCE (D.L. 8.25, 8.30). The fragment of ‘Aresas’ represents what is perhaps the best surviving evidence for the psychological theory of the Hellenistic Pythagoreans, since it does not mention the more familiar bipartition found in the other Pythagorean Pseudepigrapha and in the writings of the middle Platonists. Indeed, ‘Aresas’ shows us a very original psychological theory, for he claims that three goods, friendship, love, and kindness, sprout from all three parts of the soul. How does this happen?

According to ‘Aresas’, the parts of the soul, when they have been harmonized into eunomia, work quite effectively together. Each performs its own duties, preserving the  ‘justice’ so defined as ‘minding one’s own business’ in Plato’s Republic (433b-d).  But ‘Aresas’ departs quite significantly from Plato, and from other writers of the Pythagorean Pseudepigrapha,  in developing a unique psychological theory. For ‘mind’ performs preliminary inspections, and manages to persuade the other parts of the soul to act on its preliminary inspections; ‘desire’, persuaded to act, seeks to protect its own interests by pursuing ‘courage’, which, properly persuaded by mind, acts to defend the whole, and to attack the (external) enemy. How does ‘mind’ accomplish this? Interestingly, ‘Aresas’ claims that it mixes together pleasure and pain and, by doing so, effects the adjustment of the courageous part of the soul (called ‘high-pitched and excessive’), where pain belongs, to the desirous part (called ‘light and soluble’), where pleasure is located. The consequence of this adjustment, which finally leads to total psychic harmonization, is that the courageous and desirous parts of the soul obtain their own peculiar types of reason, exemplified by their capacities for diverse types of ‘forethought’. Mind inspects and tracks objects it pursues; courage impels the soul towards things being further inspected and endure what is to come; and desire discovers its own important role in this process, which is to acquire pleasure and refer intellectual pleasures, which belong not to itself, upwards to mind. ‘Aresas’ claims that humans are at their best when they combine the objects of contemplation and enjoyment together in this psychic system. This is no mention of mind enslaving or controlling the lower parts of the soul – mind’s primary role in ‘ruling’ the lower parts, indeed, is to get the ball rolling in the process of inquiry, rather than to supervise at all times each part of the soul’s activity, or to chastise the other parts of the soul for being disobedient. There is no familiar moderation of emotions, nor less their extirpation, as one would find in Hellenistic Philosophy and the other Pythagorean Pseudepigrapha.

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Flatulence on the Rise: Aristophanes’ Clouds

I’ve just finished a draft of a short popular article for Omnibus, a journal for sixth-formers (ages 16-19) in the UK who are interested in Classics.  The piece, which will be out in January 2015, is on how Aristophanes thematizes ‘up’ and ‘down’ in his representation of Socrates’ Thinkery in the Clouds.

Just who is more cuddly?

This isn’t the first time I’ve treated the character of Socrates in the popular imagination.  In this circumstance, however, I am reminded of Heraclitus’ saying, that ‘the road up and down is one and the same’ (DK22B60), which hints at the point of the article.  Here is a preview, and the entire article is available on my academia.edu web page:

In the history of philosophy, fewer first appearances are more memorable than the fantastic introduction of Socrates in Aristophanes’ Clouds, first performed in Athens in 423 BCE.  Gliding aloft in a basket, propped up by a crane, Socrates asks the simple buffoon Strepsiades, who has come to learn the philosophic arts, ‘why do you call on me, mere creature of a day?’ (Clouds 223).  At once, the audience knows that this strange man isn’t fit for terrestrial pursuits; he ‘walks on air, and studies the sun from above’, so as to mingle his peculiar cleverness with the ether (Clouds 225).  He’s trying to figure out what goes up, and what’s going down, which he wouldn’t be able to do from the ground.  Socrates’ special location, high up in his heroic chariot, also grants him conversational intercourse with the divinities – those lovely ladies known as the Clouds – which lights Strepsiades’ fire, his jealousy brewing.  For the comic action of the play to start, Socrates must descend to Strepsiades’ level and cool the old stallion off; once Socrates orders Strepsiades to ‘sit down on the holy bed’ in order to be initiated into his school of philosophy, the Thinkery, his arrival on earth is complete (Clouds 253).  The audience is now ready to see this ‘wise guy’ (sophos) in action…

 

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Laughter by Mary Beard

Mary Beard has written up a very stimulating and clear discussion of theories of laughter, which I encourage all readers to have a look at.  It does a nice job summarizing some of the main lines of thought on a tremendously difficult subject – one that, in my opinion, philosophers neglect all too often, especially given its historical significance as being considered an essential activity that differentiates humans from other animals.  I suspect that this is a case, however, in which Occam’s Razor doesn’t easily apply – attempts to reduce to a single overarching law of laughter are insufficient, but perhaps this is in part because the term ‘laughter’ lies somewhere between the general and the specific.  Would ‘humour’ work better, I wonder?

Click on this picture to follow the link to Mary Beard’s ‘What’s So Funny?’

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Northern Association for Ancient Philosophy 2014 – University of Leeds

The Northern Association for Ancient Philosophy Annual Meeting 2014

Department of Classics, University of Leeds

Monday April 7th – Tuesday April 8th 2014

books-in-the-brotherton-room-540x2161
 
Venue: The Brotherton Room, Special Collections, Brotherton Library
Monday April 7th
1.00pm-2.00pm
Registration
Parkinson Court, Parkinson Building, University of Leeds
2.00pm-3.15pm
Dr Brian D. Prince (Faculty of Philosophy, Oxford)
“The Forms as Powers in Plato’s Phaedo.”
 
3.15pm-4.30pm
Professor Mario-Jorge de Carvalho (Department of Philosophy, New University of Lisbon)
“A ‘Radiological’ Approach to Pausanias’ Speech (Plato’s Symposium).”
 
4.30pm-4.50pm: tea
 
4.50pm-5.50pm
Mr Nicolo Benzi (PhD candidate, Department of Classics and Ancient History, Durham)
“The semantics of noos, noein and their derivatives in the poetry of Xenophanes and Parmenides.”
5.50pm-6.20pm  Business meeting
Evening: Conference Dinner — University House, University of Leeds
 
Tuesday April 8th
The Justice, Ethics and Conventions of War in Ancient Thought
with the centenary conference: ‘Classics and Classicists in WWI’, April 8th-10th 2014
 
10.00am-11.15am
Professor Neville Morley (Department of Classics and Ancient History, Bristol)
“Might and Right: Thucydides on the ethics of deterrence and pre-emption.”
 
11.15am-11.45am coffee
 
11.45am-1.00pm
Professor Malcolm Schofield (Faculty of Classics, Cambridge)
“Deciding ethically: Cicero on war and tyrannicide (and other problems).”
 
Lunch 
The ‘Classics and Classicists in World War I’ Centenary Exhibition opens Monday April 7th 1.00pm at Special Collections, The Brotherton Library, Parkinson Building.
 
For information on NAAP 2014 and Classics and Classicists in WWI:http://www.leeds.ac.uk/arts/info/20047/classics/2197/legacies_of_war/2
 

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The Market Value of Socrates’ Pimping

Yes, you never thought the terms ‘market value’, ‘Socrates’, and ‘pimping’ might be brought in relation to one another; but then you won’t have read the dynamic work of James Collins (University of Southern California), on Socrates’ pimping – and its important place in the transformation of value…

Socrates pimp

Click here to go to James Collins’ post at the Center for Hellenic Studies Research Bulletin on Socrates’ Brokerage

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And introducing…

You know how in the titles of films, right near the end of the list of actors who will take major roles in the movie, they have the ‘and introducing’ screenshot?  It often refers to a new actor or actress who is getting his/her debut in the film world.  He or she is often portrayed as youthful and wide-eyed, surprised to see that the camera is there, as if to say, ‘well hello, I hadn’t noticed that you’d noticed.’  What has always struck me is how that ‘and introducing’ screenshot could go either way: you might have a total nobody who will remain a total nobody, but it is also possible that you’ll have a Jack Nicholson, or a Jamie Lee Curtis, or even Kevin ‘Thank you Sir, May I have Another’ Bacon.

With that in mind… (drum roll, please)…And Introducing

Book Cover

Plato and Pythagoreanism, by Phillip Sidney Horky (Oxford University Press, 2013).

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Conference Announcement: Philosophos Bios (9-11 May 2013)

Philosophos bios: Philosophical Uses of Biography in the Hellenistic Age and Late Antiquity 

Palazzo Feltrinelli, Gargnano (Lago di Garda)

 9-11 May 2013

Palazzo Feltrinelli, Gargnano, Italy

Organized by T. Bénatouïl (Université de Nancy), M. Bonazzi (Università degli Studi di Milano), Carlos Lévy (Université de Paris IV – Sorbonne), Stefan Schorn (Leuven Catholic University) and Gerd van Riel (Leuven Catholic University)

Thursday 9 May

h. 16.00

1) Dino de Sanctis (Pisa): La biografia nel Kepos: il profilo esemplare del saggio epicureo tra propaganda e didagmata per la felicità.

h. 17.30

2) Phillip Horky (Durham): Authority and First Words: Diogenes Laertius on Heraclitus on Pythagoras

Friday 10 May

h. 9.30

3) Jan Opsomer (KU Leuven): Philosophers in Plutarch’s Vitae parallelae

h. 11.15

4) Karin Schlapbach (Ottawa): The spectacle of a life. Biography as philosophy in Lucian

Afternoon

h. 14.30

5) Stefan Schorn (KU Leuven) : Biographie und Fürstenspiegel. Politische Paränese in Philostrats Vita Apollonii

16.30

6) Philippe Hoffmann (EPHE): Sur les biographies de philosophes dans le néoplatonisme

Saturday 11 May

h. 9.00

7) Irmgard Männlein-Robert (Tübingen): Polemik in der Vita Pythagorica Iamblichs

h. 11.00

8) Franco Trabattoni (Milano): Il filosofo platonico secondo Damascio

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Workshop at Durham University on Ancient Historiography, Science, and Theology

 Paradigm and Method in Ancient Historiography, Science, and Theology

 A CAMNE Workshop at Durham University

 3–4 May 2013

theophrastus

Theophrastus

Polybius

Polybius

Under the auspices of the Centre   for the Study of the Ancient Mediterranean and Near East (CAMNE), the Department of Classics and Ancient History at Durham University is pleased to host an interdisciplinary workshop entitled ‘Paradigm and Method in Ancient Historiography, Science, and Theology’, 3–4 May 2013.  This workshop seeks to develop a scholarly dialogue concerning the epistemological assumptions, writing strategies, and methodological applications employed by ancient authors of historical writings, scientific and technical compositions, and theological works.  Papers will be delivered by a group of scholars whose academic interests pursue the interrelationships between various disciplines of knowledge in ancient cultures.

All events will take place at the Department of Classics and Ancient History, Durham University, 38 North Bailey, Durham, DH1 3EU. This workshop is open to the public, and there is no cost to participate.  Any enquiries can be directed to the organizer, Phillip Horky (Phillip.Horky@Durham.ac.uk).  Postdoctoral students are particularly encouraged to attend the workshop.

Programme

FRIDAY, 3 MAY

(Ritson Room/CL007, Dept. of Classics and Ancient History)

4:00pm–4:15pm: Introductory Remarks by Phillip Horky (Durham University)

Afternoon/Evening Session: Chaired by Luca Castagnoli (Durham University)

4:15pm–5:15pm: Chris Pelling (Christ Church, Oxford University)

‘Herodotus and the Hippocratics’

5:15pm–6:15pm: Phillip Horky (Durham University)

‘The First Words of Pythagoras’ Physics? Diogenes Laertius on Heraclitus on Pythagoras’

6:15pm–6:45pm: Coffee & Tea Break (Seminar Room/CL108)

6:45pm–7:45pm: Stefan Schorn (KU Leuven)

‘Theophrastus on Jewish Sacrifice’

8:00pm: Dinner for speakers

SATURDAY, 4 MAY

(Ritson Room/CL007, Dept. of Classics and Ancient History)

8:30am–9:00am: Coffee & Snacks (Seminar Room/CL108)

 Morning Session: Chaired by John Moles (Newcastle University)

9:00am–10:00am: Nicolas Wiater (University of St. Andrews)

‘History with(out) Gods: A Fresh Look at Polybius and Theology’

10:00am–11:00am: Thorsten Foegen (Durham University)

‘Memory, Methodology, and Morality: Links between Ancient Technical Writing and Historiography’

11:00am–11:30am: Coffee & Snacks (Seminar Room/CL108)

Morning/Afternoon Session: Chaired by Amy Russell (Durham) 

11:30am–12:30pm: Lucas Herchenroeder (Durham University)

‘Polybius and Political Causality: the Case of the Hannibalic War’

12:30pm–1:30pm: Luke Pitcher (Somerville College, Oxford University)

‘The Doctor’s Dilemma: Polybius, Science, and Philosophy’

1:30pm–1:45pm: Closing Remarks by Lucas Herchenroeder (Durham University)

This workshop is generously supported by the Department of Classics and Ancient History and the Faculty of Arts and Humanities at Durham University.

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Conference Announcement: Dialectic and Aristotle’s Logic

Below is a call for papers received from Matt Duncombe (Groningen); please do consider applying if you are working on Aristotelian logic!

Dialectic and Aristotle’s Logic

September 2-4 2013
Faculty of Philosophy, University of Groningen (Netherlands)

https://sites.google.com/site/therootsofdeduction/conference-dialectic-in-aristotle-s-logic

Aristotle’s logic is often treated as though it falls into two quite distinct parts: the deductive syllogistic system, discussed in the Prior and Posterior Analytics and the dialectical system, discussed in the Topics and Sophistical Refutations. Each of these parts has received sustained, independent attention: logicians have done much to articulate the structure of Aristotle’s syllogistic, while commentators have seen Aristotle’s dialectic as key to his whole philosophical enterprise.

This conference aims to examine the (putative) dialectical grounding for Aristotle’s logical theories in general (in particular, but not exclusively, syllogistic), and thus to emphasize the coherence and continuity of his logical writings by taking multi-agent dialogical interactions such as dialectic as the founding concept.

Confirmed speakers

Luca Castagnoli (Durham)
Marko Malink (Chicago)
Mathieu Marion (UQAM, Montreal)
Ana Maria Mora (Copenhagen)
Carrie Swanson (Bloomington)
Paul Thom (Sydney)
Matthew Duncombe (Groningen)
Catarina Dutilh Novaes (Groningen)

Call for Papers

There will be a number of slots for contributed papers. Contributions may address the following themes, among others:

The pragmatic context of Aristotle’s syllogistic
Game-theoretic construals of Aristotle’s logic
Aristotle’s account of fallacies
Dialectic in the Organon (including the Categories and On Interpretation)
Dialogical readings of Aristotle’s logic by ancient and (Latin and Arabic) medieval commentators

The organizers invite submissions from scholars at all levels (graduate students, junior and senior researchers). Please submit abstracts of up to 1000 words (in PDF format) by March 15th 2013 to rootsofdeduction ‘at’ gmail.com.

Abstracts should be prepared for blind review. Notification of acceptance will be sent by April 15th.

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A Game of Source Criticism

I’ve got a game for you to play, but you’ll have to bear with me until the end.  I’ll be presenting a paper at the Institute of Classical Studies in London in the Ancient Philosophy Seminar next week on 28 January (Room 243 at the Senate House, Malet Street, London, WC1E 7HU), and I’m feverishly trying to wade through the mushy snow to get to the office and write this one up!  Who wants to help?

The talk, entitled ‘Aristotle on Pythagorean Number-Substance’, represents a sustained defense of Fragment 6 of the Pythagorean Philolaus of Croton, whose authenticity Luc Brisson recently challenged at a talk I gave in Paris.  It occurred to me that I haven’t really seen anyone do a comprehensive analysis of Aristotle’s Fragment 203 Rose, which – or so I will argue – preserves several references to Philolaus’ work.  Alexander of Aphrodisias seems to get this precious information from a lost work of Aristotle’s called On the Opinions of the Pythagoreans, probably a treatise not totally unlike Theophrastus’ doxographical On the Opinions of the Natural Scientists (if that is what it was called).  For fun (not so much), and by way of preview, I’ll give my translation and the Greek text of Alexander which will be the focus of this presentation (in Metaph. p. 40.7-24 Hayduck):

The bodies that move the greatest distance to move [the Pythagoreans thought to be] the fastest, those that move the least distance to be slowest, and the intermediate bodies to move in proportion to the size of their orbit.  Indeed, on the basis of these likenesses in beings with regard to numbers and things, they supposed that beings are both composed out of numbers and are particular numbers.

And thinking that numbers are prior to nature as a whole as well as to beings in nature (for, they thought, it is not possible for any being either to be or to be known at all without number, whereas it is possible for numbers to be known even without other things), they assumed that the elements of numbers and the first principles of all these [sc. numbers] are the first principles of all beings.  These elements were, as has been said [?], even and odd, of which they thought the odd to be limited and the even unlimited; of numbers, they thought the unit to be the first principle, being composed out of the unlimited and the limited; for the unit was at once even-odd, which he [?] demonstrated by way of the unit’s being generative of both the odd and the even number.  For the unit added to an even generates an odd, and the unit added to an odd generates an even.

And assuming as obvious from the first likenesses between numbers and harmonic combinations, on the one hand, and the attributes and parts of heaven, on the other, they demonstrated that the heavens are composed out of and in accordance with harmony.

κινεῖσθαι δὲ τάχιστα μὲν τὰ τό μέγιστον διάστημα κινούμενα, βραδύτατα δὲ τὰ τὸ ἐλάχιστον, τὰ δὲ μεταξὺ κατὰ τὴν ἀναλογίαν τοῦ μεγέθους τῆςπεριφορᾶς. ἐκ δὴ τούτων τῶν ὁμοιοτήτων ἐν τοῖς οὖσι πρὸς τοὺς ἀριθμοὺς τὰ μὲν πράγματα καὶ τὰ ὄντα ἐξ ἀριθμῶν τε συγκεῖσθαι καὶ ἀριθμούς τινας εἶναι ὑπελάμβανον. 

τοὺς δὲ ἀριθμοὺς ἡγούμενοι πάσης τῆς φύσεως καὶ τῶν φύσει ὄντωνπρώτους (μήτε γὰρ δύνασθαί τι τῶν ὄντων χωρὶς ἀριθμοῦ εἶναι μήτεγνωρίζεσθαι ὅλως, τοὺς δὲ ἀριθμοὺς καὶ χωρὶς τῶν ἄλλων γιγνώσεσθαι)τὰ τῶν ἀριθμῶν στοιχεῖα καὶ τὰς ἀρχὰς τούτων πάντων τῶν ὄντωνἀρχὰς ἔθεντο.  ταῦτα δὲ ἦν, ὡς εἴρηται, ἄρτιον καὶ περιττόν, ὧν τὸ μὲν περιττὸν πεπερασμένον τὸ δὲ ἄρτιον ἄπειρον ἡγοῦντο εἶναι˙ τῶν δὲ ἀριθμῶν τὴν μονάδα ἀρχὴν εἶναι, συγκειμένην ἔκ τε τοῦ ἀρτίου καὶ περιττοῦ˙ εἶναι γὰρ τὴν μονάδα ἅμα ἀρτιοπέριττον, ὃ ἐδείκνυε διὰ τοῦ γεννητικὴν αὐτὴν εἶναι καὶ τοῦ περιττοῦ καὶ τοῦ ἀρτίου ἀριθμοῦ˙ ἀρτίῳ μὲν γὰρ προστιθεμένη περιττὸν γεννᾷ, περιττῷ δὲ ἄρτιον.

καὶ ὅσα μὲν εἶχον ὁμολογούμενα ἔν τε τοῖς ἀριθμοῖς καὶ τοῖς κατὰ τὰς ἁρμονίας συνθέσεσι πρὸς τὰ τοῦ οὐρανοῦ πάθη τε καὶ μέρη, ταῦτα μὲν αὐτόθι ὡς φανερὰ λαμβάνοντες ἐδείκνουν τὸν οὐρανὀν ἐξ ἀριθμῶν τε συγκεῖσθαι καὶ καθ’ἁρμονίαν. 

Let’s play a game, then.  Can anyone identify specifically (a) which portions come from Aristotle’s De Caelo and Metaphysics, and (b) which definitely refer to (i.e. summarize) Philolaus’ fragments?  Help me out!

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