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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Been checked out lately, but…

Posting has been difficult lately – apologies!  It’s been a torrent of work at the beginning of the academic year in Durham, including talks in Milan (on Pseudo-Archytas’ On Wisdom) and Venice (more on Aristotle on Philolaus), plus another half-talk in Durham at the Ancient Republics Workshop (Part 1) this week, and another talk in Milan in mid-December at the second part of the Durham-Milan workshop on Platonism and Hellenistic Philosophy (on ancient ‘Italian’ philosophy).  Jeez, I just can’t keep still.

Not quite *that* busy, though...Tintoretto, c. 1550 (Gallerie dell'Accademia, Venice)

Not quite *that* busy, though…Tintoretto, c. 1550 (Gallerie dell’Accademia, Venice)

Since the last post, several reviews of Plato and Pythagoreanism have surfaced (one by Federicco Petrucci (Wurzburg) in the Journal of the History of Philosophy, another by Joseph Miller (Illinois Institute of Technology) in Hopos: the Journal of the International Society for the History of Philosophy and Science, another by Michael Weinman (Bard College Berlin) in Archai: Revista de Estudos sobre as Origens do Pensamento Ocidental, and some reactions by Carl Huffman (Depauw) in his ‘Pythagoreanism’ entry on the Stanford Encyclopedia of Philosophy).  Happy to see that the work is generating debate, and also happy to announce that the book will be coming out in paperback next year – Oxford’s even allowing me to make some minor corrections!

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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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Nussbaum Conference 2014 – St Mary’s College, Durham (23-24 May 2014)

Overcoming Intolerance: Nussbaum and Her Critics conference

Martha Nussbaum, by John Springs

Martha Nussbaum, by John Springs

23-24 May 2014
St Mary’s College, Durham University

Conference speakers include: Thom Brooks (Durham), Clare Chambers (Cambridge), Maria Dimova-Cookson (Durham), Phillip Horky (Durham), Peter Jones (Newcastle), Maleiha Malik (KCL), Mozaffar Qizilbash (York), Martha Nussbaum (Chicago), Sara Protasi (Yale)

Overcoming Intolerance: Nussbaum and Her Critics is a two-day event that brings Professor Martha C. Nussbaum to Durham University. Professor Nussbaum is the Ernst Freund Distinguished Service Professor of Law and Ethics at the University of Chicago and one of the leading political and legal philosophers today. She is the author of nearly 20 monographs, including The Fragility of Goodness (1986), Sex and Social Justice (1999), Women and Human Development (2000), Hiding from Humanity (2004), Frontiers of Justice (2006) and Creating Capabilities (2011) among many others.

This event examines these topics under the umbrella of ‘Overcoming Intolerance’ with a first day interrogating her recent The New Religious Intolerance: Overcoming the Politics of Fear in an Anxious Age (Harvard University Press, 2012). Nussbaum argues that we can rise about the politics of fear and toward a more open and inclusive future by expanding our capacity for empathetic imagination and establishing a consistent ethic of decency and civility building off of her past work. Conference speakers include Thom Brooks (Law, Durham), Clare Chambers (Philosophy, Cambridge), Peter Jones (Politics, Newcastle) and Maleiha Malik (Law, KCL). Martha Nussbaum will reply to each paper before the floor is opened for questions.

The second day is organized into two panels. The first focusses on the topic of ‘Capabilities and Political Liberalism’ which will be led by Mozaffar Qizilbash (PPE, York) and include Maria Dimova-Cookson (Government, Durham) with Martha Nussbaum. The second on ‘Civic Emotions and Combatting Intolerance’ which will be led by Sara Protasi (Philosophy, Yale) and include Phillip Horky (Classics, Durham) with Martha Nussbaum. Each roundtable discussions aimed at linking key themes in Nussbaum’s work to these broader issues and their wider implications.

Together, this two-day event brings together leading academics from across a diverse range of academic subjects to engage one of the most significant public intellectuals working today.

Conference registration includes lunch and teas/coffees for both days. (Delegates must make their own accommodation and dinner arrangements.)

The Conference Programme and Registration information can be found here: https://www.dur.ac.uk/law/events/lawevents/?eventno=20058&aggregated=1

The conference is generously funded by Durham Law School and several of its research groups (including the Criminal Law and Criminal Justice Centre; the Islam, Law and Modernity Group and the Law and Global Justice Group), the Institute of Advanced Studies, the Department of Philosophy and the School of Government and International Affairs all based at Durham University as well as Harvard University Press.

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Plutarch’s Son Autobulus and Pythagorean Geometry

I’m drowning in marking right now, but I thought I’d update with some recent work I’ve been doing on Aristotle and Plutarch on the geometry of the Pythagorean Philolaus of Croton.  This working paper (comments welcome) is for a volume edited by Arnaud Macé on Physis/Historia Peri Physeôs, and derived from a series he has been co-organizing with Luc Brisson and Olivier Renault on ‘Plato and his Predecessors’.  As often happens, however, one cannot really discuss ‘Plato and his Predecessors’ without treating Plato’s successors too.   Case in point is Plutarch’s Table-Talk, where the only surviving reference to Philolaus’ conceptualization of geometry is preserved:

‘Geometry being, according to Philolaus, the origin and mother-city of the rest (?)…’

γεωμετρία κατὰ τὸν Φιλόλαον ἀρχὴ καὶ μητρόπολις οὖσα τῶν ἄλλων…

 (T A7a Huffman = Plutarch, Table-Talk 8.2, 718e; translated after Huffman)

The original context for testimonium A7a is remarkable: it is a staged debate in Plutarch’s Table Talk that takes place between Plutarch and several speakers (Diogenianus, Tyndares, Florus, and Plutarch’s son Autobulus) on Plato’s birthday.[1]  Apropos of the day, the topic set for the symposium is to discover what Plato meant when he allegedly claimed that ‘god is always doing geometry’ (ἀεὶ γεωμετρεῖν τὸν θεόν).[2]  The first speaker, the youthful Tyndares of Sparta, develops a mystical response rooted in his unique interpretation of Plato’s Republic and Phaedo, and in the midst of this he elaborates on the relationship between γεωμετρία and other scientific studies.[3]  Notably, Tyndares believes that geometry – not arithmetic, as one would see in Plato’s Republic and other Platonist traditions that descend from it – is first in pride of place among the mathematical sciences.

Plutarchus Geometricus

Plutarchus Geometricus

Philolaus’ reference to γεωμετρία as the ‘origin’ and ‘mother-city’ implies some sort of generative capacity, as Aristotle in F 203 thought of the Pythagoreans’ ‘unit’ (διὰ τοῦ γεννητικὴν αὐτήν), which generates odd numbers when added to even and even numbers when added to odd.[4]  Aristotle’s assumption seems to be that a unit, when applied to (προστιθεμένη) an odd or even number, produces differentiation between those types of number.

But how could the objects of geometry, e.g. shapes such as triangles and squares, conceivably produce numerical kinds, such as ‘odd’ and ‘even’?  Interestingly, a few chapters after he has quoted Philolaus’ enigmatic geometry testimonium T A7, Plutarch presents a speech, given by his son Autobulus, which appears to feature adaptations of Philolaic ideas in a Platonist vein, including a discussion of how the limit gives definition to the unlimited.[5]  There, Autobulus refers to the cosmological theory of the ‘men of old’ (οἱ παλαιοί), a rather certain reference to Philolaus even in Plato’s work[6], that involves the generation of numbers through the imposition of the limit on matter, which is unlimited (περατοῦντα τὴν ὕλην ἄπειρον οὖσαν):

Τhe form and shape is a limit of everything that is shaped and arranged (ἡ μορφὴ καὶ τὸ σχῆμα πέρας ἐστὶ μεμορφωμένου καὶ ἐσχηματισμένου παντός), in the absence of which everything is, by itself, shapeless and unarranged.  Once the numbers and ratios have been generated in it (ἀριθμῶν δὲ καὶ λόγων ἐγγενομένων), the matter is shackled, as it were, and encompassed by lines and by the figures which are generated by lines, i.e. the solids…

(Plutarch, Table-Talk 8.3, 719d)

This description of how the geometric shape, as limit, comes upon the unlimited and generates numbers is surprisingly unusual in antiquity, despite the fact that it forms the basis for some modern interpretations of the relationship in Pythagorean philosophy between limiters and unlimiteds.[7]  The generation of number is initially obscure in Autobulus’ account.  A little later, however, Autobolus returns to the topic and explains with greater precision how he thinks ‘numbers and ratios’ can be generated in matter:

Reason (λόγος)[8] seizes upon [matter], circumscribes it, and marshals it into types and differentiations (τοῦ δὲ λόγου καταλαμβάναντος αὐτὴν καὶ περιγράφοντος καὶ διανέμοντος εἰς ἰδέας καὶ διαφοράς), from which all things that grow possess generation and structure (ἐξ ὧν τὰ φύομενα πάντα τὴν γένεσιν ἔσχεν καὶ σύστασιν).

(Plutarch, Table-Talk 8.3, 719e)

This is a remarkable passage, since it does not, in fact, reflect Plutarch’s own views about the first principles, but nevertheless seems to represent a reputable opinion that comes to contribute to Plutarch’s own formulation.  For Plutarch himself in the speech that follows (Table-Talk 8.2, 720a-c) gently rebukes his son and explains, echoing the Timaeus, that the three first principles are in fact the One/God, Matter/Indefinite Dyad, and the Form, not simply the limit and unlimited.[9]  Although Plutarch does not refer to Philolaus as the authority behind Autobulus’ speech, he appears to be thinking of the Pythagoreans (‘men of old’) – and quite possibly he is deriving this information from Aristotle’s lost works on the Pythagoreans, which understood the first principles as limit and unlimited (πέρας ἄπειρον) and as equivalent to odd and even.[10]

I suggest that Autobulus’ speech can therefore help us to conceive of how Aristotle’s Pythagoreans might have conceived of the ‘unit’ as generating odd and even numbers.[11]  If the ‘unit’ in Aristotle’s language stands in for the ‘limiters’ (περαίνοντα) in Philolaus’ presentation, and ‘reason’ (λόγος) in Autobulus’, then the ‘unit’ would be thought to interact with a limitless continuum in such a way as to produce numerical types (i.e. ‘odd’ and ‘even’), which could thereby be differentiated from one another epistemologically.  In this scenario, Aristotle would be attributing to the Pythagoreans’ ‘unit’ the role of the formal cause, which, in its modality as limiter, would give definition to the unlimited, in its modality as matter.[12]  In fact, Aristotle has more to say about this process elsewhere.   In the context of discussing Philolaus’ student, the mathematical Pythagorean Eurytus of Metapontum, and his theory of defining natural objects through number, Aristotle attacks some anonymous Pythagoreans who (a) equivocated number with harmony and (b) thus absurdly supposed that number could be formal cause[13]:

Nor yet has it been determined in what sense numbers are the causes of substances and of being, whether as boundaries (ὠς ὅροι)[14] (for example, as lines are to magnitudes – in this sense Eurytus assigned which number belongs to which thing, e.g. this number for man, that for horse; just as those who arrange numbers into geometric figures like the triangle and the square, so he [sc. Eurytus] assimilated the shapes of natural objects to pebbles), or because harmony of numbers is a ratio [of numbers] (ἢ ὅτι λόγος ἡ συμφωνία ἀριθμῶν)[15], and likewise so is man and everything else?

How could the attributes white, sweet, and hot, be numbers?  And it is clear that numbers are neither a substance nor formal causes[16], since the ratio is the substance, whereas the number is matter.  For example, the substance of flesh or bone is a number [only] in this sense: it is three parts of fire, and two of earth. Again, number, whichever it is, is always a number of things, either of portions of fire or earth or units, whereas substance is the proportion of one quantity to another in a mixture.  But this no longer remains a number, but a ratio of the mixture of numbers, whether corporeal or otherwise.  So number – whether number in general or number that consists of abstract units – is neither an efficient cause, nor matter [sc. material cause], nor ratio and form, of things [sc. formal cause] (οὔτε…ὕλη οὔτε λόγος καὶ εἶδος τῶν πραγμάτων).  Nor again is it the final cause.

(Aristotle, Metaphysics 14.5, 1092b8-25)

Aristotle seeks to identify the proper ontological status of numbers by reference to, I suggest, mathematical Pythagoreans in general, and Eurytus and Philolaus in particular.  He associates the definitional activities of Eurytus with the geometry of some anonymous others, whose activity of arranging numbers into geometrical shapes Aristotle sees as anticipating Eurytus’ assimilation of numbers to objects in nature, such as human beings and horses.  If we are in doubt to whom Aristotle is referring, one possible clue comes at the end of the passage, where he notes that it would be absurd to think that number (of any sort) could be the formal cause, i.e. the ‘ratio and form of things’ (λόγος καὶ εἶδος τῶν πραγμάτων), a phrase which recalls Philolaus’ appeal to the ‘being of things’ (ἁ ἐστὼ τῶν πραγμάτων) as an entity prior to limiters and unlimiteds, and which, so I have speculated elsewhere, Philolaus probably identified with harmony (ἁρμονία).[17]  If the ‘things’ to which Philolaus appealed when he referred to ‘limiters’ and ‘unlimiteds’ were to be thought of as numbers, as Aristotle seems to have assumed in his reformulation of Fragment 1 of Philolaus[18], then the ‘limiters’ would likely be odd numbers, and the ‘unlimiteds’ even numbers.  The position Aristotle seems to be attacking, then, is one which conflates a formal cause like ‘ratio’, ‘harmony’, or ‘proportion’, which Aristotle considers a legitimate candidate for such an activity, with ‘number’, which is not a legitimate candidate for formal cause, on the grounds that number is that which is acted upon by the formal cause, which in this case is ‘ratio’ (λόγος); this in turn would function as the limiter that acts upon number, which is here figured (at least provisionally) as matter that is acted upon.

[1] For a biographical discussion of these figures, see Cartledge and Spawforth 2002: 166.

[2] Plut. Quaest. Conv. 8.1, 718c.

[3] Plut. Quaest. Conv. 8.1, 718c-f.

[4] ] Arist. F 203 Rose = Alex. Aphr., in Metaph. p. 40.15–20 Hayduck: ‘…they thought the unit to be the origin of numbers, since it was composed out of the unlimited and the limited; for the unit was simultaneously even-odd, which he [Philolaus?] 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.’

[5] I suspect we are dealing with a Platonized version of an Aristotelian description (probably from the lost works of Aristotle on the Pythagoreans) that predates the 1st Century BCE (since Autobulus does not actually attribute this cosmology to the Pythagoreans, and it does not resonate particularly well with other 1st Century BCE accounts of Pythagorean philosophy, e.g. the account of Alexander Polyhistor).  But it preserves a skeleton of a Philolaic original, which cannot be accounted for by its antecedents in Plato’s works (the discussion of limit and unlimited in Philebus – see the next note – and the cosmogony of mathematical objects and elements in the Timaeus).  Moreover, Autobulus’ account does not bear the marks of an Early Platonist reinterpretation of the Timaeus or with Eudorus of Alexandria’s adaptation of those ideals, since it does not posit the One and the Indefinite Dyad/Multiplicity as first principles.  Finally, it shows no strong correlation with Stoicism whatsoever.

[6] This term is directly borrowed from the Philebus (16c5-d4), where Socrates says that the ‘men of old’ passed down the tradition from Prometheus that holds that ‘the things that are said to be eternal have come from the One and the Many, but they had limit and unlimited innate in themselves.’  For a discussion of how this term is a coded reference to Philolaus, see Horky 2013: 224-227.  Autobulus’ version interestingly removes the reference to the One and the Many.

[7] See, for example, Huffman 1993: 52, who imagines that Philolaus ‘is approaching something akin to a distinction between form and matter’, although Huffman does not believe, as Barnes (1982: 387-389), that limiters are only shapes, and he says nothing about how numbers are generated. Also cf. Huffman (2005: 70), where he strengthens his resolve somewhat by claiming that ‘limiters and unlimiteds are very broad categories, but one of the primary things that Philolaus is referring to is the imposition of shape and structure on indeterminate continua including stuffs.’  Huffman, however, finds it difficult to know where number fits into this formulation (ibid.): ‘However, even in Fragment 1 we were warned that number was coming.  For the limiting shapes and the unlimited stuffs are “fitted-together” by the principle of harmonia, which is numerical for Philolaus.’

[8] I translate ‘reason’ here, so as to establish the difference between logos (singular) and logoi (plural), which occurred earlier on in the passage and clearly means ‘ratios’ there.  But if Autobulus is describing Philolaus’ own cosmogony, he could be referring to ‘ratio’ insofar as ‘harmony’ in Philolaus’ fragments is a type of ratio.

[9] This is by contrast with his position elsewhere that there are two first principles, namely God/the One and the Indefinite Dyad (on which, see Dillon 1977: 199-206).

[10] As they are called at Metaph. 1.5, 986a23 and 1.8, 990a8-9; elsewhere (Metaph. 1.5, 986a18-19), by reference to the properties of their first principles, Aristotle describes the odd as πεπερασμένον and the even as ἄπειρον.

[11] Note that the appeal to ‘types and differentiations’ in matter corresponds with Aristotle’s description of how in the Pythagorean cosmogony, the void, by being breathed in, causes ‘separation and distinction of the series of things’, which Aristotle says is especially applicable to ‘numbers’, on the grounds that ‘their nature was first defined by the void’ (Phys. 4.6, 213b23-29; also see Aristotle F 201 Ross).

[12] For Pythagorean ‘number’ as formal cause, see Zhmud 2013: 334 n. 38.

[13] It is worth bringing to bear another passage, from Pseudo-Alexander of Aphrodisias (in Metaph. p. 512.23-36 Hayduck), which is relevant here: ‘Some people – Aristotle is referring to some Pythagoreans – are confused about the circle and the triangle, as well as the line, since, as they say, one should neither define these things in terms of lines nor say that ‘a circle is a plane figure circumscribed by a single line’, or ‘a triangle is a plane figure circumscribed by three lines’, or again, ‘a line is a continuous length extended in one dimension.’  For a line underlies a circle or triangle as its matter (ἡ γὰρ γραμμὴ τῷ τε κύκλῳ καὶ τριγώνῳ ὠς ὕλη ὑπόκειται), and likewise continuity underlies a line as its matter (ὁμοίως δὲ καὶ τὸ συνεχὲς τῇ γραμμῇ), just as flesh and bone do for a man, and bronze for a statue…For this reason, viz. their saying that the line and the continuous are, as it were, the matter for the triangle, etc., they [sc. the Pythagoreans] reduce all these things to numbers, on the grounds that numbers are neither material, nor have any substratum as a matter, but they are themselves in themselves (αὐτοὺς καθ’ αὑτούς).’  I suspect that Pseudo-Alexander is not referring to Philolaus or Pythagoreans like him, but more likely to Speusippus, perhaps from his lost treatise On Pythagorean Numbers (F 28 Tarán).  For Speusippus’ doctrine that numbers are separately existing individuals, see Tarán 1981: 35-36.

[14] For a discussion of how this might be conceived, see Schofield 2012: 165.

[15] Accepting Bonitz’ excision of the definite article before λόγος.

[16] Literally, ‘causes of the form’, which I take to be periphrasis for the ‘formal causes’, although it is also possible that he means ‘causes of the shape’.

[17] For ‘being of things’ as ‘harmony’, see Horky 2013: 146 with n. 86 (identifying the chiastic presentation in Philolaus’ Fragment 6).  For a discussion of ‘the being of things’ and its relationship to harmony in Plato’s reception of Philolaus, see Horky 2013: 153-158.

[18] One possible counterargument to my analysis would lie in Aristotle’s wavering about whether numbers are material or not.  Aristotle initially seems to accept the proposition that ratio is the formal cause that acts upon the material, i.e. numbers; but he later contradicts himself by adding that number is not matter.  Aristotle seems to waver on the issue of whether numbers can be considered material causes (cf. Primavesi 2012: 260 n. 84).

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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

Venue: The Brotherton Room, Special Collections, Brotherton Library
Monday April 7th
Parkinson Court, Parkinson Building, University of Leeds
Dr Brian D. Prince (Faculty of Philosophy, Oxford)
“The Forms as Powers in Plato’s Phaedo.”
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
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
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
Professor Malcolm Schofield (Faculty of Classics, Cambridge)
“Deciding ethically: Cicero on war and tyrannicide (and other problems).”
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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