Pythagoras and the Early Pythagoreans – ZHMUD (RA)

ZHMUD, L. Pythagoras and the Early Pythagoreans. Oxford: Oxford University Press, 2012. Resenha de: MCKIRAHAN, Richard. Revista Archai, Brasília, n.13, p. 161-164, jul., 2014.

With an unsurpassed command of primary materials and meticulous scholarship Professor Zhmud gives us a thorough treatment of Pythagoreanism through the fifth century, occasionally ranging into the Pythagoreans of the fourth century as well. He presents a careful treatment of the source material on Pythagoras’ life and activities, and takes up  the rarely discussed problem of who are to count as Pythagoreans. He proceeds to discuss all things (allegedly) Pythagorean, including  metempsychosis  and vegetarianism, politics and the nature of  Pythagorean ‘societies’,  mathematici  and  acusmatici, number theory and numerology, geometry and harmonics, cosmology and astronomy, (surprisingly) medicine and the life sciences, and he concludes by examining Pythagorean views on the soul and the doctrine that all is number.

I have the honor to say a few things about Professor Zhmud’s recent book Pythagoras and the Early Pythagoreans. This is a major revision and  expansion of his 1997 book Wissenschaft, Philosophie und Religion im frühen Pythagoreismus, a book described by one reviewer as the most important  contribution to Pythagorean studies in the previous thirty years. The magnitude of that assessment can be recognized when we bear in mind that that thirty-year period saw the publication of Burkert’s Lore and Science in Ancient Pythagoreanism, which is widely considered the foundation of modern Pythagorean studies. My assessment of Pythagoras and the Early Pythagoreans is that it is even better than Professor Zhmud’s previous book.

There is wide agreement that later (that is, Neopythagorean and Neoplatonic) sources contain far more information than the early sources from the 6th-5th century BCE and that much of this later information is fabricated. Recent treatments of Pythagoreanism present early material, admit that it is too scanty to yield a full picture of Pythagoras and his followers, and then proceed to supplement it by selective use of the later material. Professor Zhmud perforce follows this method, but modifies it in two important ways. First, he is more consistent in rejecting later information that does not have a pedigree going back to the fourth century. This methodological approach considerably reduces what can be safely asserted about Pythagoras and the  early Pythagoreans. Second, he infers the interests and activities of Pythagoras from those reliably attributed to his followers, a move that expands what can be assigned to their leader. These twin procedures lead to some surprising conclusions that challenge widely held beliefs. Consider the following examples.

  • Pythagoras was not a shaman or a wonder-worker.
  • Stories of his travels to Egypt and other lands are probably spurious.
  • His success in Croton was probably not instantaneous but attained gradually, over a period of many years.
  • No single trait marks all known early Pythagoreans (except that they presumably belonged to Pythagorean societies): some pursued mathematics, others natural philosophy, others medicine, and still others athletics.
  • Pythagorean societies were not religious groups or cults.
  • The Pythagorean way of life did not include observing a strict code of conduct that regulated every aspect of their life.
  • The Pythagoreans were not a secret society; their views were known to outsiders.
  • The early Pythagoreans did not attribute their own discoveries to Pythagoras.
  • The distinction between mathematikoi and akousmatikoi was a much later fabrication.
  • It is likely that Pythagoras discovered the Pythagorean theorem, the theory of even and odd numbers and the arithmetic, geometric and harmonic means.
  • Pythagoras was first to use deductive proofs in number theory.
  • Early Pythagoreans and possibly Pythagoras himself made use of experiments to verify their physical theories. • The tetraktys  and the ideas associated with it were unknown to early Pythagoreans.
  • *Very little is known of Pythagorean contibutions to astronomy prior to Philolaus.
  • Pythagoras invented the quadrivium.
  • Alcmaeon was a Pythagorean.
  • Alcmaeon alone taught that the soul is immortal, a theory that has no connection with metempsychosis. It is doubtful that any Pythagoreans believed soul to be a  harmonia.

These conclusions radically undermine traditional interpretations of early Pythagoreanism. They are founded on close readings of the relevant textual evidence and cannot be overlooked.

The remainder of this review will focus on  the Familienähnlichkeit that Professor Zhmud finds among the early Pythagoreans, and his conclusions about Pythagoras’ mathematical activity, but first a brief remark on Professor Zhmud’s view that for Pythagoras metempsychosis was a religious doctrine (e.g., p.20). I question the appropriateness of the word “religious”to describe  metempsychosis. Orphism, from which Pythagoras borrowed the  doctrine, was a religion of sorts, but metempsychosis  does not by itself need to have any religious  implications. Professor Zhmud is right to insist  that Pythagorean communities were not religious θιασοί (144) and that there is no evidence of any special cults or distinctive private worship among the Pythagoreans (144). And for one who believes in metempsychosis the idea that a pure life is the ticket to a better next reincarnation may be no different in kind than the idea that a good diet is the ticket to better health in this life.

Unable to find any single common characteristic that applies to all known ancient Pythagoreans from the end of the sixth century to the middle of the fourth, Professor Zhmud applies Wittgenstein’s conception of family resemblance as a solution to the problem of Pythagorean identity (111). For  Wittgenstein, the the way in which family members resemble each other is not through one specific trait but depends on a variety of traits. The members of a family do not all possess any single trait, but they all resemble each other in that each of them possesses at least one of the traits and each trait shows up in more than one member of the family. Thus, we have some Pythagoreans (Hippasus, Theodorus,  Philolaus and Archytas) who pursued mathematics, others (Hippasus, Alcmaeon, Philolaus, Menestor  and Hippon) who pursued natural philosophy, others (Democedes, Alcmaeon and Iccus) who worked in medicine, and still others (Milo, Astylus and Iccus) who engaged in athletics (111).Crucially, some  Pythagoreans engaged in more than one of these pursuits: Hippasus and Philolaus in mathematics and natural philosophy, Alcmaeon and Hippon in natural philosophy and medicine, and Iccus in medicine and athletics. Hence the family resemblance.

But some of this is pretty thin. Was Hippon a Pythagorean? We have only Iamblichus’ word for it. Likewise for Iccus, Asylus, Theodorus and Menestor. And Iamblichus is a suspect source. (Even accepting Professor Zhmud’s view that Iamblichus’ catalogue  goes back to Aristoxenus (111ff.) the early Pythagoreans under discussion lived long before Aristoxenus, plenty long enough for the catalogue to have grown to include notable South Italian figures from earlier times who were not Pythagoreans. If these men are excluded then we have a much smaller list: only Hippasus, Philolaus and Archytas for mathematics, of whom only Hippasus was early; only Hippasus, Philolaus and Alcmaeon for natural philosophy; only Democedes and Alcmaeon for medicine; only Milon for athletics (which removes the pursuit of athletics from the list of family traits ascribable to early Pythagoreanism  on the basis of the activities ascribed to known early Pythagoreans). But even of these, Democedes’ identity as a Pythagorean may not be assured simply because he had Milon as a father in law, and Alcmaeon’s  claim to be a Pythagorean is disputed. In fact an  important passage in Aristotle seems to tell against it (Metaph 986b1). If we reject these men too, then there are no early Pythagoreans left who pursued  medicine, leaving only mathematics and natural  philosophy (each represented solely by Hippasus).

Milon presents a different problem as well.  Granted that that great athlete was a Pythagorean, we may ask whether his athletic prowess had anything to do with his Pythagoreanism. Perhaps he was just an athlete who was also a Pythagorean. A possible point of comparison is the Belleville Church Golf League in rural Illinois, consisting of teams from seven local churches (with names like Pres 1 and Pres 2, representing the local Presbyterian church). Do the golfers see participating in this athletic activity as part of their Christianity? Can we detect a family resemblance between golfers and Christians? This question may sound trivial and even frivolous, but it invites a more serious question: is it possible  that the mathematical, scientific, and (for the sake of argument) medical activities characteristic of  some known early Pythagoreans were not part of  their Pythagoreanism? How can we possibly know?

Here is an opposite-minded alternative view. As long as the Pythagorean societies existed membership was the determining feature (146ff.) During that period various kinds of activities (athletics,  mathematics, etc.) were pursued by various Pythagoreans, but not as a requirement of membership. (And we must keep in mind that during the period in question these activities were pursued in the  Greek world by men who were not Pythagoreans.) After the upheavals in the mid-fifth century and the subsequent scattering of the survivors, some  continued to call themselves Pythagoreans and  continued to pursue the same activities as before; if they had followers who did the same, they could be called Pythagoreans too, but their Pythagoreanism could not have been the same as the pre-diaspora Pythagoreanism.

If neither of these approaches can be accepted without methodological reservations, the best hope for unity might seem to rest in the figure of Pythagoras himself. If he introduced the famous  Pythagorean way of life, if he founded the first Pythagorean ἑταιρία, if he also pursued mathematical and scientific activities (for which there is no early evidence), perhaps these are the keys to who is a Pythagorean. But how about medicine and athletics, Professor Zhmud’s other two pillars of Pythagorean identity? Did Pythagoras engage in these activities as well? Are we comfortable with the idea that since Milon was an athlete, Pythagoras was too? Further since so little is reliably attested to Pythagoras, if we define his activities taking his followers’ pursuits as guides to Pythagoras’s own and then say that engaging in those activities makes one a Pythagorean, we have an intolerable circularity.

Finally, regarding Pythagoras’ contributions to mathematics: as Professor Zhmud says (256), in the century and a half passed between Thales (the founder of Greek geometry) and Hippocrates (the author of the first Elements of geometry) a lot of progress was made in mathematics. Professor Zhmud gives evidence that the association of Pythagoras with the famous theorem is attested as far back as the late fourth century (257), although elsewhere he is less than certain that this is the theorem to which source is referring (267). We need to bear in mind that even this date is a century and a half after Pythagoras’s death. Again, it is a better pedigree than Iamblichus, but in my mind it still leaves a good deal of uncertainty.

Professor Zhmud credits Pythagoras with the following achievements:

  • Proving the Pythagorean theorem, probably by the use of the arithmetical theory of proportions (256, 271)
  • Discoveriing the ratios of the harmonic intervals (258-9)
  • Discovering the arithmetic, geometric and harmonic means (271)
  • Adding arithmetic and harmonics to astronomy and geometry (subjects already pursued in Ionia) to form the quadrivium (271)
  • Inventing number theory including the five basic theorems about even and odd numbers, which he proved on the basis of definitions of unit, number, and even and odd numbers that we find in Aristoxenus and Euclid (272-73)
  • The use of indirect proof (273)

Here Professor Zhmud carries to extremes his practice of ascribing to Pythagoras the pursuits of his followers. Not only is Pythagoras not said by any early source to have engaged in mathematical pursuits, the only early Pythagorean we know of who did so was Hippasus (275). Professor Zhmud says that the Pythagoreans achieved too much in mathematics in the fifth century for Hippasus alone to have done it (275), and he points out that the discoveries he attributes to Pythagoras are not complex and “correspond fully with the stage mathêmata had reached before Hippasus”(268). Still, it seems to me to be optimistic in the extreme to attribute all of them to Pythagoras. It is safer to limit ourselves to the thought that Pythagoras encouraged others to be active in these areas rather than supposing that he engaged in them himself — a line of interpretation floated by Professor Zhmud himself (141).

Here is another story that seems to me equally plausible. Pythagoras discovered the numerical ratios of the concordant musical intervals or alternatively, he saw the potential of a discovery was made by  someone else (I think of Lasus of Hermione as a  possibility); there is no good evidence that the discovery was due to Pythagoras. He was struck by the thought that numbers could account for something apparently as different from numbers as music, and in a breathtaking generalization paralleled only by other Presocratic thinkers, declared (without more evidence) that number was fundamental to reality. Some of his followers (Hippasus among them)  took up the project of exploring numbers. Among  other things they identified and defined species of numbers (including even and odd) and discovered  (and proved, more likely by pebble diagrams than  by indirect proofs based on definitions) elementary results such as that the sum of two odd numbers is an even number. They also identified properties of ratios of numbers such as those concerned with the three means mentioned above. In this way we have an account of the origin of the Pythagorean tradition of mathematics — and one that accounts for the silence of our sources on Pythagoras’s contribution to it.

These brief discussions of Pythagorean identity and Pythagorean mathematics are not intended to disprove Professor Zhmud’s carefully worked out conclusions, but rather to illustrate the kind of  work that needs to be done in order to to maintain contrary views. I want to conclude by saying that my already considerable admiration for Professor Zhmud has been raised to new heights. I regard his book as a landmark whose arguments and theses cannot be disregarded by anyone who wants to form an  accurate picture of Pythagoras and the Pythagorean tradition. I say with confidence that it will remain a standard reference for the foreseeable future.

Richard McKirahan – Pomona College, Los Angeles.

Acessar publicação original

 

In Search of Pythagoreanism. Pythagoreanism as an Historiographical Category – CORNELLI (RA)

CORNELLI, G. In Search of Pythagoreanism. Pythagoreanism as an Historiographical  Category. Berlin: “Studia Praesocratica”4, De Gruyter, 2013. Resenha de: STAVRU, Alessandro. Revista Archai, Brasília, n.13, p. 171-173, jul., 2014.

This book is the English version of a work  which appeared two years ago in Portuguese.1 Its structure and general aim are clearly outlined 2. I will give a brief sketch of them before moving to more general issues. The volume consists of four chapters. The first two have a methodological character, and deal with the history of modern scholarship on  Pythagoreanism and Pythagoreanism as an historiographical category respectively. Chapters three and four have a more specific character, being focused on two fundamental doctrines of Pythagoreanism such as metempsychosis and arithmology. The interplay between these different aspects, that is on the one hand methodology, on the other the discussion  of sources, is a main feature of the book. Equally noteworthy are the range of ancient and modern materials examined, the variety of scholarly approaches surveyed, and the original insights provided on  different topics.

The author’s main claim is that Pythagoreanism cannot be understood by the conventional  means of scientific investigation. Pythagoreanism is a phenomenon sui generis; it requires therefore a methodology which must also be sui generis. First of all, it is a phenomenon which is not limited in time, as Pythagorean tradition never died3 Secondly, it is a multi-faceted phenomenon which cannot be studied without taking into account its complexity and its contradictions. Last but not least, even the definition of “Pythagoreanism”is a problem: every scholar has more or less his own view of what is “Pythagorean”and what is not, of what belongs  to the tradition going back to Pythagoras and his immediate followers and what has been added to it later.

As the author puts it, the uniqueness of  Pythagoreanism depends on the fact that this phenomenon is both diachronic and synchronic. It is diachronic because it can be understood only if one deals with the different strata of its tradition. Every stage of Pythagoreanism is a construction (or even a re-construction) whose reliability depends both on the trustfulness of the elements which constitute it and the soundness of the methodological criteria applied. Since the times of August Boeckh, 4 scholars have been analyzing these elements trying to sort out doxographical trees of succession which would enable to grasp fragments of lost texts of Pythagoreanism. This task has been accomplished by studying late authors such as Porphyry and Iamblichus, whose accounts turned out to rely on earlier texts such as those of Aristotle and his followers. But  however successful (or unsuccessful) these studies have been, 5 other problems arose from them. The data made available by Quellenforschung showed that Pythagoreanism had always been a multifaceted as well as an extremely controversial movement, and that reconstructing its tradition from Neoplatonism up Aristotle and Plato could not help in explaining its inconsistencies. On the contrary, the more “original”testimonies emerged from Hellenistic and Roman literature the more it became evident that Pythagoreanism was characterized by two apparently incompatible strands of knowledge, i.e. the “mystical”one of acousmata and metempsychosis and  the “scientific”one of cosmology and mathematics.

Cornelli gives full account of the interpretations which led to this impasse. His scrutiny of  Pythagorean scholarship is both exhaustive and  stimulating. The different hermeneutic approaches to Pythagorean literature make clear that a purely diachronic approach to the historical development of tradition is not sufficient to grasp its uniqueness. Cornelli suggests therefore to combine this approach with another one, which he calls «synchronic ». As he puts it, «to synchronically understand Pythagoreanism is to recognize its place within the categories ordinarily used to describe ancient philosophy»,  namely: «“pre-Socratic”, “school”, “science”, “religion”, “politics”, or even “philosophy”» (54). But as none of these standard categories is multifaceted enough to apply to Pythagoreanism, an adjustment in methodology becomes necessary. A truly  synchronic understanding of Pythagoreanism must be multidisciplinary, in order to overcome «the  dichotomies between science and magic, writing  and orality, Ionians and Italics, to which historiography usually appeals”(55). Such an approach had already been attempted by Walter Burkert, who in his seminal book of 1972 pointed out the necessity to have a treatment of Pythagoreanism as «many- sided as possible».6 Cornelli follows this path, but goes further. He claims that if Pythagorean wisdom is polymathy, as Heracleitus puts it (fr. 22 B 40 and 129 DK), the study of it must suit its nature, and thus turn into a « methodological polymathy » (54). This leads Cornelli to claim that  Pythagoreanism itself must be considerated as an historiographical category. It does not fall under the “conventional”categories of Presocratic philosophy such as religion, politics and science, but encompasses them all.

Cornelli’s aim is ambitious: he maintains that one has to understand Pythagoreanism not through already existing categories, but as a category on its own. This « will permit Pythagoreanism to emerge from the mists of its complex history » (54), and in turn enable to get a better understanding of other categories of ancient philosophy. Such a methodology may even be of great impact outside the field of Pythagoreanism, as it will likely have consequences also for the study of the pre-Socratics in general.7

One may wonder whether such an holistic approach, which aims at eliminating barriers between disciplines, is altogether possible, given the ultra- specialized character of contemporary scholarship. Another problem concerns the subjects of research which characterize Pythagoreanism. These appear to be fundamentally heterogeneous: on the one  hand science, on the other religion: can we cope with such diverse topics using one single approach? Cornelli’s book leaves many questions open: only  time will tell if its ideas will be able to convert into reality. One thing is certain: a holistic approach to Pythagoreanism may be difficult if not altogether impossible to attain. But even more so, there is no doubt that such an approach represents a highly  wished desideratum in scholarship, where compartmentalization of the different facets of Pythagorean knowledge has become more and more increasing, thus making it difficult to study the context of their origins, development, and interdependency.

But  Pythagoreanism is not only an historiographical category. Cornelli goes further this categorization, and tackles key-issues linked to it, namely the definition of Pythagoreanism and the criterion for being Pythagorean.8 To answer these questions, he focuses on three distinct strands of Pythagorean tradition,  namely: way of life as attested in the akousmata and symbola, immortality and transmigration of the soul, and numerology. Cornelli’s idea is that all of these  forms of knowledge, though different, go back to  “Proto-pythagoreanism”, 9 that is to the most ancient stage of this philosophical movement, and that they remained a distinct feature of Pythagoreanism also in later ages. In two distinct chapters he deals in detail with these topics (chapter 3, on metempsychosis;  chapter 4, on numbers), which showcase how varied and multifaceted Pythagoreanism is. Here we learn, among other things, that Pythagoreanism appears to be « both mystical and scientific, because on the one hand, the theory of metempsych ō sis does not respond only to a soteriological mystique, but also becomes an explanatory element of a reality that is irreducibly interconnected, as well as being the foundation of  epistemology in the practice of anám n ē s is» (192).

One might think that in Cornelli’s view the definition of Pythagorean identity is a complex one, similar to that of Pythagoreanism as an historiographical category. But this is not the case, as for Cornelli the criterion for being Pythagorean is « membership in a community and a shared bíos consisting primarily in observing Pythagorean  akoúsmata and symbola, rather than the acceptance of certain philosophical and scientific theories » (82). This means that if on one hand there is no contradiction between the acousmatic and the  mathematical Pythagoreanism, on the other there is no doubt that the acousmatic moment is decisive: not science but way of life and belonging to a Pythagorean koinonia 10 is the ultimate criterion for identifying a Pythagorean.11

So we see: the concern of an historiographical Pythagoreanism which encompasses the contrasts and differences of tradition does not impede the  author to provide the distinctive feature of what is specifically Pythagorean and what is not. A major achievement of the book lies in the productivity of this ambivalence: very different figures of tradition like Philolaus and Apollonius turn out to be similar as soon as their adherence to a special lifestyle and a community comes to the fore. We can therefore conclude that Cornelli’s Pythagoreanism is not just a “historiographical category”, as it has to do not with the doctrines, but with the lives of its protagonists. It is a category  in flesh and blood, which cannot  be separated from the charismatic manners and  attitudes of the representatives of Pythagoreanism in its different historical stages.

Notas

  1. G. Cornelli, O pitagorismo como categoria historiográfica, “Classica Digitalia Brasil”, CECH- Universidade de Coimbra/Annablume, Coimbra/São Paulo 2011. In the same year the author organized a conference on Pythagorean tradition in Brasilia, the proceedings of which have appeared recently (On Pythagoreanism, eds. G. Cornelli, C. Macris, R. McKirahan, de Gruyter, Berlin 2013).
  2. See the reviews of the Portuguese version of Cornelli’s book: Francesc Casadesús Bordoy, Archai 7 (2011), 159-162 and Manuela Dal Borgo, Digressus 12 (2012), 64-71.
  3. 53: «Rather, the proposed methodology aims to understand how, through the intertwining of diachronic and synchronic dimensions, the category of “Pythagoreanism”survived the expected dilution of a multifaceted movement, a movement that is not only radically and extensively diverse in its authors and subjects, but that additionally spans over a thousand years of the history of Western thought. In fact, the unique challenge of this project among to the problems associated with the history of pre-Socratic philosophy lies in the fact that Pythagoreanism has properly never died».
  4. A. Boeckh, Philolaos des Pythagoreers Lehren nebst den Bruchstücken seines Werkes, Vossische Buchhandlung, Berlin 1819.
  5. Seminal Quellenforschung in Pythagoreanism has been done since the last decades of 1800. See E. Zeller, E. Rohde, Die Quellen des Iamblichus in seiner Biographie des Pythagoras, Rheinisches Museum für Philologie 26 (1871), 554-576; J. Mewaldt, De Aristoxeni Pythagoricis sententiis et Vita Pythagorica, Dissertation Berlin 1904; W. Bertermann, De Iamblichi vitae Pythagoricae fontibus, Dissertation Königsberg 1913; A. Delatte, Études sur la littérature pythagoricienne, Slatkine & Fils, Paris 1915, Essai sur la politique pythagoricienne, Slatkine & Fils, Paris 1922, La vie de Pythagore de Diogène Laërce, Lamertin, Bruxelles 1922; H. Jäger, Die Quellen des Porphyrios in seiner Pythagoras-Biographie, Dissertation Zürich 1919; I. Lévy, Recherches sur les sources de la legend de Pythagore, Leroux, Paris 1927; A.-J. Festugière, Sur la ‘Vita Pythagorica’ de Jamblique, Revue des études grecques 50 (1937), 470-484; K. von Fritz, Pythagorean Politics in Southern Italy. An Analysis of the Sources, Columbia University Press, New York 1940 and ‘Pythagoras’, RE 47, 1963, 171-203; W. Burkert, Lore and Science in Ancient Pythagoreanism, Cambridge University Press, Cambridge 1972, esp. 53-83 and 97-109. The achievements reached by these scholars have been recently doubted by Leonid Zhmud, who claims that «attempts to reconstruct authentic Pythagorean texts from the fifth and fourth centuries brought to no result», and that «perhaps because of the absence of palpable success in this area of Quellenforschung, in recent decades very few scholars have ventured far into it» (Pythagoras and the Early Pythagoreans, Oxford University Press, Oxford 2012, 9-10). Despite Zhmud’s skepticism, many scholars do nowadays still believe that later authors (such as Iamblichus) use sources going back to texts of the 5th and 4th centuries (such as Aristotle’s works on Pythagoreanism). A recent work going in this direction is P.S. Horky, Plato and Pythagoreanism, Oxford University Press, Oxford 2013, esp. 85-88.
  6. W. Burkert, Lore and Science, 12: «Most studies of Pythagoreanism have dealt with only one restricted aspect; even Zeller confined himself to the development of philosophical concepts, left mathematics aside, and bracketed out religious and ethical questions; and later works have been even more specialized, whether in the philosophical area, in that of mathematical, astronomical, and musical problems, or that of religion». This approach has been severely criticized by Leonid Zhmud, who thinks that Pythagoreanism can be studied only by sorting out single issues «which may prove amenable to solution» (L. Zhmud, Pythagoras, 12; on this issue see also Zhmud’s latest paper On the Fallacy of the Holistic Approach to Pythagoreanism, held in Berlin on October 20, 2013 at the workshop “Pythagorean Harmonics from Philolaus to Leibniz”).
  7. Thanks to its complexity, Cornelli’s Pythagoreanism turns out to be a paradigmatic hermeneutic category which forces to overcome the traditional boundaries that characterize the study of ancient thought and culture: «In the case of Pythagoreanism, it will be necessary to overcome the rigid dichotomies of a historiography too accustomed to distinguish, for example, between sciene and magic, writing and orality, Ionian and Italian. None of these alone seems to capture the complexity of Pythagorean social organization and doctrine» (55).
  8. In Cornelli’s view, the criteria which are commonly used for defining “what is Pythagorean”are not sufficient: «The criteria commonly used to classify someone as a Pythagorean did not seem to stand up to our methodological test: because one cannot think of the Pythagorean school as something doctrinally homogeneous. Further, neither geographical criteria nor doxographical trees of succession serve as adequate ways to define the category» (84).
  9. The term “Proto-Pythagoreanism”is not new in scholarship: see, e.g., G. de Santillana & H. von Dechend, Hamlet’s Mill. An Essay on Myth and the Frame of Time, Gambit, Boston 1969. New is the systematical use of it Cornelli makes in his book (5-6, 42-44, 49, 51, 60-61, 73, 84-85, 87, 91, 94, 97-99, 119, 126, 132, 134, 135, 137, 144, 145, 147, 185, 188, 190, 192, 194).
  10. The issue of Pythagorean koinonia  is debated at pages 67-77 of the  volume. To define the specific character of Pythagorean “clubs”Cornelli opts for the neutral term koinonia, thus rejecting other definitions such as “sect”(Rohde, Burkert, Riedweg) and “church”(Toynbee, Jaeger). On this and related issues see also G. Cornelli, Sulla vita filosofica in comune: koinonía e philía pitagoriche, in: S. Giombini & F. Marcacci (eds.), Il quinto secolo. Studi di filosofia antica in onore di Livio Rossetti, Aguaplano, Perugia 2010, 415-436.
  11. In Cornelli’s view, these two aspects are linked: «However, the possibility of adherence to a particular way of life implies, at least in its inaugural pre-Socratic times, the actual existence of a community that is structured around that same way of life» (59). Bruno Centrone (Review of Zhmud, Wissenschaft, Philosophie und Religion im frühen Pythagoreismus, Elenchos  20 (1999), 441) and Carl Huffman (Two Problems in Pythagoreanism, in P. Curd & D.W. Graham (eds.), The Oxford Handbook to Presocratic Philosophy, Oxford University Press, Oxford 2008, 301) have similar claims, but they do not connect these two aspects.

Alessandro Stavru – Freie Universität, Berlin.

Acessar publicação original

O pitagorismo como categoria historiográfica – CORNELLI (RA)

CORNELLI, G. O pitagorismo como categoria historiográfica. Tradução de Maria da Graça Gomes de Pina Col. Classica Digitalia Brasil. Coimbra: CECH- Universidade de Coimbra. São Paulo: Annablume, 2011. Resenha de: BORDOY, Francesc Casadesús. Revista Archai, Brasília, n.7, p.159-162, jul., 2011.

Os estudos que se realizaram até aos nossos dias sobre a figura de Pitágoras e sobre o pitagorismo depararam-se com um paradoxo que parece insuperável ou, em todo o caso, se mostra de muito complicada e difícil solução: isto é, a constatação de que a personagem da filosofia pré-socrática de quem possuímos, contrariamente a outras, mais informações apresenta-se-nos sob uma névoa tão espessa que impede que o estudioso extraia conclusões claras. Com efeito, e nisto consiste precisamente o paradoxo, de nenhum outro filósofo da Antiguidade nos chegaram três biografias como as que nos transmitiram Porfírio, Jâmblico e Diógenes Laércio (além de muitos outros testemunhos) e, apesar disso, acerca de nenhuma outra personagem da Antiguidade nos sentimos tão inseguros quando chega o momento de falar dos seus supostos conhecimentos, habilidades e façanhas. Sem dúvida esta frustrante realidade foi determinante no momento de abordar com critérios científicos a figura de Pitágoras e o pitagorismo. Isso porque, desde a Antiguidade, mas muito mais sobretudo a partir das pretensões científicas dos estudiosos e historiadores da filosofia grega no século XIX, a atenção dos investigadores se tem orientado para tentar dirimir a questão da credibilidade que se deve conceder às fontes que de maneira tão generosa nos falam de Pitágoras e dos seus seguidores, os pitagóricos. Por este motivo, qualquer estudo sobre o pitagorismo, após a grande quantidade de livros e artigos publicados, deve tentar esclarecer qual é a sua posição face ao que se começou a chamar de “questão pitagórica”. Dito por outras palavras, um estudo com garantias de rigorosidade científica deve informar qual a sua opinião sobre os testemunhos pitagóricos, para poder fazer um uso consequente deles. Como é bem sabido, os trabalhos que circulam sobre Pitágoras e o pitagorismo movem- se entre os extremos de uma aceitação acrítica das fontes e uma atitude hipercrítica que se nega a aceitar e, por conseguinte, a considerar como válidos a maioria dos testemunhos transmitidos, até ao extremo de pôr em dúvida a relevância do pitagorismo na história da filosofia grega.

Além do mais, a tudo isto é preciso acrescentar que os estudos sobre o pitagorismo, que, como se disse, oscilam entre a hagiografia e o ceticismo mais radical, acabaram por criar um emaranhado de interpretações hermenêuticas que o estudioso deve conhecer muito bem para poder conquistar uma posição ponderada e objetiva. É por isso que, desde já, consideramos acertado que o livro que estamos resenhando trate, como indicado no título, do pitagorismo como uma “categoria historiográfica”. De fato, é muito provável que não haja uma maneira mais lógica e consequente de aproximar-se do seu estudo, dadas as características do que conhecemos na atualidade como “pitagorismo”, e que abarca desde as abundantes fontes primárias e secundárias até as diversas leituras e interpretações que, até aos nossos dias, se têm realizado sobre elas.

Por tudo isto, resulta muito acertada a distribuição do livro em quatro grandes blocos com as divisões e subdivisões correspondentes. Aliás, pode-se afirmar que a estrutura do livro constitui já, em si mesma, toda uma declaração de princípios, pois oferece  grosso modo, uma panorâmica acerca de qual é o método que o autor considera mais idóneo para adentrar-se nos meandros dos estudos sobre o pitagorismo. Assim, no primeiro deles, intitulado “História da Crítica: De Zeller a Kingsley”, oferece-se uma panorâmica ampla e atualizada da opinião dos mais importantes estudiosos do pitagorismo que, a partir do século  XIX, determinaram as principais linhas de investigação. Deste modo, o leitor tem um fácil acesso ao status questionis das principais correntes e linhas de interpretação, de uma perspetiva cronológica e temática, o que faz com que seja especialmente útil para todos os leitores que desejem familiarizar-se, desde o início, com a larga e consolidada história das investigações sobre o pitagorismo. No segundo, intitulado “O pitagorismo como categoria historiográfica”, aborda-se o estudo do pitagorismo conjugando uma focalização sincrónica e diacrónica da qual sobressaem as dificuldades que apresentam as interpretações dos principais estudiosos, condicionadas em grande parte pela problemática suscitada pela transmissão das fontes que, na maioria dos casos e dadas as suas características particulares, condicionam por sua vez as possíveis interpretações do movimento pitagórico. Apoiando-se de modo crítico nessas fontes, o autor oferece uma análise pormenorizada dos traços mais característicos da organização e estrutura da escola pitagóricas. No terceiro, intitulado  “Imortalidade  da  alma  e metempsicose”, trata-se a questão da conceção imortal das almas e as suas transmigrações a partir da análise das fontes mais antigas e relevantes. Nesta questão, central no estudo do pitagorismo, oferece-se uma visão bastante completa da conceção da alma pitagórica, tal como a sua vinculação ao orfismo e a sua receção em Platão. Por último, no quarto capítulo, sob a epígrafe de “Números”, aborda-se a questão da importância do número no seio da filosofia pitagórica, com a intenção de esclarecer qual foi o seu verdadeiro estatuto, entre a numerologia e a matemática, e qual o alcance da sua consideração de princípio identificado com o conjunto das coisas, tal como fora formulado por Aristóteles. Neste último capítulo mostra-se novamente como o autor age com desenvoltura tanto no âmbito das fontes antigas, sobretudo no tratamento de uma figura-chave como Filolau, quanto no manuseio da ampla bibliografia que trata esta questão controversa.

Afirmamos que esta distribuição do livro merece ser considerada uma declaração de princípios por parte do autor, porque pressupõe algo que o torna particularmente valioso: isto é, que – de modo principal e prévio, como se se tratasse de uma lição introdutória e propedêutica, – nele se proporcionam as chaves interpretativas que os interessados pelo pitagorismo devem conhecer para obterem em primeira mão uma informação básica sobre quais foram as principais linhas de investigação, desde Zeller até aos nossos dias. Em relação a este assunto, como faz o autor, a questão capital é discernir qual foi a posição de cada estudioso ante as fontes pitagóricas para comprovar até que ponto esta determinou a orientação das investigações posteriores. Em todo o caso, deste resumo se extrai uma primeira consideração que afeta os estudos modernos sobre o pitagorismo: os comentadores tiveram muita consciência da fiabilidade problemática que as fontes apresentam, o que motivou, desde os inícios modernos dos estudos sobre o pitagorismo, a necessidade de concentrar-se sobre a sua investigação de forma rigorosa. Abriu-se assim o caminho para a  Quellenforschung  das vidas pitagóricas e das que dependem em boa parte das informações transmitidas.

Com esta bagagem, identificado o lugar de cada um dos estudiosos no interior da tradição dos estudos pitagóricos, o livro embarca-se na aplicação destes conhecimentos prévios, metodológicos e hermenêuticos em três âmbitos fundamentais, que serão tratados com profusão em cada um dos restantes três capítulos. O primeiro afeta a sua própria essência e identidade histórica, pois tenta elucidar o que se deve entender por pitagorismo, tendo em conta que, na Antiguidade, a existência deste movimento alcançou quase mil anos. Neste ponto o autor deixa claro que em caso algum põe em dúvida a existência do pitagorismo, desde as suas origens protopitagóricas, embora delimite com nitidez os seus contornos. Limites que se distinguem melhor se se deixarem de lado preconceitos anacrónicos e divisões dicotómicas que chegam a anular qualquer possível definição positiva. A conclusão é que, superando o ceticismo iniciado com Zeller, tal como a problemática distinção entre pitagorismo, religião e magia ou a suposta existência de dois grupos no pitagorismo (como seriam os matemáticos e os acusmáticos), este teve na Antiguidade uma continuidade histórica cheia de novas incorporações e matizes, até ao ponto de erigir-se ele mesmo como categoria historiográfica. Deste modo, o autor parece querer chegar a uma posição conciliadora que, consciente das dificuldades que a posição hipercrítica oferece, aceita que o pitagorismo, longe de apresentar uma forma rígida e unitária, é algo muito mais versátil e plural, susceptivel de ser analisado a partir de muitos pontos de vista. Em suma, o que hoje em dia entendemos por “pitagorismo”é apenas a soma dos diversos pitagorismos que, ao longo do processo histórico, se foram sobrepondo até gerar a amálgama que nos transmitiram as fontes tardias. Estratificar o processo, considerar a evolução diacrónica, tendo em conta os dados sincrónicos, é o caminho que o autor oferece para analisar com garantias a realidade histórica do pitagorismo.

Assentes estes pressupostos, e uma vez estabelecida a existência histórica assim como o seu estatuto historiográfico, o livro apresenta os dois capítulos seguintes com a intenção de analisar os dois campos temáticos que a tradição e as fontes antigas mais vincularam com o pitagorismo: a noção de imortalidade da alma e a função atribuída ao número.

No primeiro caso, e após ter examinado as fontes mais antigas, com o apoio da receção da noção de imortalidade da alma nos diálogos de Platão, assim como as suas afinidades com o orfismo, o autor conclui que essa ideia, apesar das reticências manifestadas por alguns estudiosos, formou parte central do pensamento pitagórico desde as suas origens. Ou melhor, o pitagorismo desempenhou um papel fundamental na absorção de elementos procedentes do orfismo que, convenientemente moralizados, foram desenvolvidos por Platão. Esta concepção do pitagorismo como um movimento vivo que foi evoluindo e mudando com o tempo permite compreender  a  passagem  à  noção  de transmigração da alma, própria do primeiro pitagorismo, a sua transformação em conjunto órfico-pitagórico que entende o ciclo da alma imortal como uma sucessão de prémios e castigos para as almas boas e más, respetivamente.

Para finalizar, no último capítulo aborda-se o segundo aspeto tradicionalmente relacionado com o pitagorismo: a função exercida pelo número, sobre a qual tantas discussões irromperam no mundo académico. Neste âmbito, o autor volta a aplicar os mesmos critérios historiográficos já comentados na busca pela solução de síntese. Assim, se é certo que Aristóteles é uma fonte essencial para aceder ao conhecimento do que os “chamados pitagóricos”entenderam por número, não é menos certo que o seu mestre Platão fez uso, transpondo-os, de princípios matemáticos procedentes do pitagorismo (neste contexto mostra-se capital a análise da passagem do Filebo  16  C -23 C). A isto se deve acrescentar que alguns fragmentos de Filolau, que (contra a opinião da corrente mais cética que os considera uma falsificação de inspiração aristotélica) o autor aceita como genuínos e, por conseguinte, analisa com detalhe, oferecem uma informação que deve ser tida em consideração para obter uma apropriada aproximação ao conceito de número no seio do pitagorismo. Deste modo, como acontece no caso da imortalidade da alma, constata-se de novo um processo, após ter combinado o estudo sincrónico com o diacrónico, que demonstra que a concepção do número sofreu uma evolução que o levou de uma visão mística a outra muito mais epistemológica. Apesar dessa evolução, isto não significa que uma conceção se tenha imposto sobre a outra, como prova a tendência das fontes neoplatónicas a regressarem às exposições numerológicas do primeiro pitagorismo mais do que avançarem nas suas extraordinárias possibilidades científicas. Em todo o caso, após ter analisado criticamente as fontes, o autor deixa claro que é a função epistemológica do número que prevaleceu no seio do pitagorismo na época de Filolau: a conceção do número como instrumento para conhecer o mundo mais do que, como pretendia Aristóteles, uma simples identificação física entre número e a realidade das coisas, formulada com o axioma “tudo é número”e que tantas confusões criou na interpretação do seu verdadeiro sentido.

Em conclusão, o livro mostra-se muito aconselhável a quem deseje conhecer quais são as principais questões que rodeiam a investigação sobre o pitagorismo. A sua leitura garante uma rápida familiarização com os grandes temas discutidos durante mais de um século e meio, aproxima-nos de uma interpretação ponderada e crítica das fontes, ao mesmo tempo em que nos oferece uma base sólida sobre a qual procedecer, construindo em nossos dias a ampla e apaixonante história do pitagorismo.

Francesc Casadesús Bordoy – Professor da Universitat de les Illes Balears.

Acessar publicação original