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  3. A History of Pythagoreanism
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2014
      April 2014
      ISBN:
      9781139028172
      9781107014398
      9781316648476
      DOI:
      https://doi.org/10.1017/CBO9781139028172
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.88kg, 530 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.76kg, 532 Pages
      • Subjects:
      History of Science and Technology, Classical Philosophy, History, Philosophy
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    Subjects:
    History of Science and Technology, Classical Philosophy, History, Philosophy
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    Book description

    This is a comprehensive, authoritative and innovative account of Pythagoras and Pythagoreanism, one of the most enigmatic and influential philosophies in the West. In twenty-one chapters covering a timespan from the sixth century BC to the seventeenth century AD, leading scholars construct a number of different images of Pythagoras and his community, assessing current scholarship and offering new answers to central problems. Chapters are devoted to the early Pythagoreans, and the full breadth of Pythagorean thought is explored including politics, religion, music theory, science, mathematics and magic. Separate chapters consider Pythagoreanism in Plato, Aristotle, the Peripatetics and the later Academic tradition, while others describe Pythagoreanism in the historical tradition, in Rome and in the pseudo-Pythagorean writings. The three great lives of Pythagoras by Diogenes Laertius, Porphyry and Iamblichus are also discussed in detail, as is the significance of Pythagoras for the Middle Ages and Renaissance.

    Reviews

    '… The book is remarkably comprehensive in its scope, and each chapter serves as a summary of primary texts and secondary scholarship on each respective subject. As a result, the volume is an excellent resource for specialists and novices alike. Anyone interested in the history of philosophy, of mathematics, of music and harmonics, or of the Pythagorean tradition as a whole should utilize this volume.'

    Justin M. Rogers Source: Bryn Mawr Classical Review

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    Contents

    Contents
    • Chapter 1 - Pythagoras
      pp 24-45
    • View abstract

      Summary

      The evidence for Pythagoras in Aristotle's lost work on the Pythagoreans is problematic, and what he has to say about him in the extant treatises amounts to very little. This chapter discusses the issues by going back some fifty years, to 1962, which happens to be the date of two highly influential books by supremely distinguished scholars. Plato has one important reference to Pythagoras, namely to the point that he taught his followers a way of life which later Pythagoreans continued to pursue. Pythagoras was certainly a historical figure and no mere legend, unlike Orpheus, Musaeus, Abaris and others. Certainly there is some convergence on the point that his teaching on the soul was exceptional, with most of our early sources suggesting that he taught a doctrine of metempsychosis. It is only in the Hellenistic period that Pythagoras' reputation as a mathematician, harmonic theorist and cosmologist takes off.
    • Chapter 2 - Philolaus
      pp 46-68
    • View abstract

      Summary

      This chapter examines Philolaus of Croton the philosopher in an attempt to understand his contributions to fifth-century thought. The phrase "having number" seems to have a set meaning in the Pythagorean tradition. From Anaximander on, philosophy was often understood as the study of nature, and the study of nature began with cosmogony and cosmology. Carl Huffman has done much to rehabilitate Philolaus astronomy as a viable theory in the context of fifth-century knowledge. The chapter attempts to add some support for Huffman's assessment. Philolaus' astronomical scheme is praised on the one hand for anticipating the heliocentric theory, and damned on the other for being based on a priori assumptions. Aristotle describes the development of Greek philosophy in terms of different views about the principles (archai) and causes (aitia) among the early philosophers, and about how many principles and causes there are and of what sort.
    • Chapter 3 - Archytas
      pp 69-87
    • View abstract

      Summary

      Archytas, a citizen of Tarentum on the Adriatic coast of southern Italy, and a contemporary of Plato, is a significant figure in the history of ancient Greek science. Carl Huffman offers a restrained account of Archytas so far as his work on music and in geometry is concerned. Diogenes Laertius includes an account of Archytas in the Pythagorean Book 8 of his Lives. The chapter discusses the main substance of Diogenes' biographical account. In commenting on Aristotle's Categories the sixth-century-AD Neoplatonist Simplicius quotes extensively from earlier authorities, included among them Archytas. The "Archytean writings" sounds like an abbreviated reference to the Extracts; and if that work demonstrated similarities between Plato's dialogue and passages from Archytas, the Timaeus' account of the receptacle and the movements to which it is subject would be a natural candidate for treatment.
    • Chapter 4 - Sixth-, fifth- and fourth-century Pythagoreans
      pp 88-111
    • View abstract

      Summary

      In the variety of the figures of the sixth-, fifth- and fourth-century Pythagoreans it is possible to perceive partly overlapping categories, but hardly any feature common to all of them. This chapter talks about a "family resemblance". This means that certain Pythagoreans had characteristics in common with some Pythagoreans, but not with others. Thus, Hippasus, Theodorus of Cyrene, Philolaus and Archytas shared an interest in mathematics; Democedes, Alcmaeon and Iccus were engaged in medicine; Alcmaeon, Hippo, Philolaus and Ecphantus wrote on natural philosophy; Milo, Astylus of Croton, Iccus and Dicon of Kaulonia were Olympic victors, whereas Milo, Democedes, Hippasus and Archytas were involved in politics. The Pythagorists of comedy and the real Pythagorizers launched the tradition of the existence (and then the coexistence) within Pythagoreanism of different groups, as a result of which two fictional categories of Pythagoreans appeared, the scientific mathematici and the religious acusmatici.
    • Chapter 5 - The Pythagorean society and politics
      pp 112-130
    • View abstract

      Summary

      This chapter draws on a variety of evidence about the political life of the period, and the Pythagoreans' involvement in it, some from authors concerned with the Pythagorean heritage, and some from historians interested more generally in the cities of southern Italy. For the period before his emigration from Samos, the ancient biographers mention his birth, parentage, upbringing, higher education and research travels. In Dicaearchus' imagination, Pythagoras' influence flowed from a charismatic personality. It has been suggested that age-group assemblies indicate that Croton was a traditional society organized into age-related clubs. In Iamblichus' account, Pythagoras urges women to avoid animal sacrifice, to offer frugal home-baked goods, and to take their offerings to the sanctuary in person. Most scholars think that these writers are confusing the circumstances of several periods of political opposition, which they combine into a single story of the end of Pythagorean control in the region.
    • Chapter 6 - The Pythagorean way of life and Pythagorean ethics
      pp 131-148
    • View abstract

      Summary

      The ethical-religious dimension of ancient Pythagoreanism is complex and has a conservative side linked to tradition, but also a certain "otherness" in comparison to contemporary customs. There is almost universal agreement that the precepts known as acusmata ("things heard"), or symbola ("tokens", "passwords"), short maxims which were handed down orally and put into practice in everyday life, form the original nucleus of the bios pythagorikos. The author dwells in particular on precepts and practices concerning their relationship with the gods, the daimones, the dead, the family, the group and the outside world. The earliest sources consider silence to be the hallmark of the movement. Pythagoreans thought that after gods and daimones one should pay the greatest attention to parents. Friendship (philia) is the cement that holds the group together and is based on "harmonious equality" as defined by the Pythagoreans.
    • Chapter 7 - Pythagoreans, Orphism and Greek religion
      pp 149-166
    • View abstract

      Summary

      Modern assessments of the extent, nature and direction, of the connection between Orphism and Pythagoreanism remain widely divergent. This chapter examines a number of examples and concentrates on individual actors, phenomena, and specific texts. It focuses on those features that are most commonly considered as the principal areas of overlap between Orphism and Pythagoreanism. The chapter suggests that a number of texts coming from Pythagorean and Orphic sources share a general methodology of giving new religious relevance to concepts issuing from and integrated into natural philosophy. Thus, the connection between Orphism and Pythagoreanism might take subtler forms than adherence to metempsychosis and a vegetarian diet. Greek religion is marked by a high degree of variation at the level of local communities and individual conceptions. It turns to the level of literary phenomena, texts written by Pythagoreans and poems attributed to Orpheus, and the more specific doctrinal points expressed in them.
    • Chapter 8 - The problem of Pythagorean mathematics
      pp 167-184
    • View abstract

      Summary

      This chapter considers the development of Greek mathematical culture as a whole, and turns specifically to Pythagorean mathematics. A significant part of the Greek creative achievement in pure mathematics may be assigned to two such networks: the one found in Proclus' summary of early Greek mathematics, standardly understood to derive from Eudemus' history of geometry, and the one constituted by Archimedes, his correspondents. Proclus list includes three names from the archaic era: Thales, Mamercus and Pythagoras. Archytas was a major mathematician as well as a "Pythagorean". Some people Aristotle identified as "Pythagoreans" engaged in the systematic analogy between mathematical terms (numerical and musical) and other, cultural and physical phenomena. Certain ideas, or even members, are shared between groups and so the history of culture becomes a network of networks. The group of south Italian "Pythagoreans" was interested in pursuing analogies based on mathematical concepts, especially those of music and number.
    • Chapter 9 - Pythagorean harmonics
      pp 185-203
    • View abstract

      Summary

      Ptolemaaїs is the only Greek woman on record as a musical theorist. Most writings in Pythagorean harmonics after the fourth century BC were heavily influenced by Plato's Republic, with its rejection of empirical considerations and its insistence on the authority of reason, and especially by the cosmological and psychological implications of his musical construction of the World-Soul in the Timaeus. One of the Pythagorean approaches that Ptolemaїs describes seems nevertheless to preserve a pre-Platonic character, privileging reason over perception but still focused at least in part on the analysis of audible music; and so too do the Pythagoreans discussed by Ptolemy and Porphyry. The principle that a concord's ratio must be either multiple or epimoric has a significant consequence: the interval of an octave plus a fourth (which sense-perception, according to Aristoxenus, Ptolemy and many others, unquestionably recognizes as a concord) cannot really be concordant.
    • Chapter 10 - The Pythagoreans and Plato
      pp 204-226
    • View abstract

      Summary

      This chapter concentrates on the recognizable uses of Pythagorean material in Plato's own writings. The Socrates of the Gorgias and Republic differs from the Socrates of earlier dialogues in having a definite conception of what is properly beneficial for humans as such and thus of what constitutes human well-being. Earlier in the Gorgias, Callicles had ridiculed Socrates' suggestion that individuals capable of governing their own appetites and pleasures are regarded as superior and worthy of governing others. In the Gorgias Plato had focused on reason's control of the body's irrational desires, while in the Phaedo he emphasizes reason's impulse to fulfill its own proper desire. These two views coalesce in the Republic. The vision of the beautiful order of the cosmos itself as based upon mathematical principles deeply attracted Plato. Although there are intimations of such view in the Republic, it finds its fullest expression in the Philebus and Timaeus.
    • Chapter 11 - Aristotle on the “so-called Pythagoreans”: from lore to principles
      pp 227-249
    • View abstract

      Summary

      This chapter analyzes the most comprehensive account of the Pythagorean theory of principles in Aristotle's extant work: the first part of Metaphysics A5. It looks at the passage where Aristotle indicates what he considers to have been the intermediate steps, the additional premises, as it were, between the initial act of taking up the mathēmata and the fully fledged Pythagorean theory according to which the principles of the mathēmata are the principles of all things. The chapter deals with a piece of historiographical reasoning, which claims that some of the opinions attributable to the so-called Pythagoreans actually caused the coming-to-be of other opinions equally well attributable to them. The testimony provided by Alexander of Aphrodisias enables one to assess the function of the resemblances in Aristotle's historiographical reconstruction as outlined in Metaph. A5.
    • Chapter 12 - Pythagoreanism in the Academic tradition: the Early Academy to Numenius
      pp 250-273
    • View abstract

      Summary

      The influence of Pythagoreanism of one form or another on Platonists from Speusippus in the Old Academy to Numenius of Apamea in the later second century AD can be seen to be pervasive, though never forming more than one element in the mix, along with Aristotelianism and Stoicism. If Speusippus and Xenocrates of Chalcedon established the doctrinal parameters of later Pythagoreanism, it is to another, rather idiosyncratic, member of the Old Academy that must go the honor of contributing significantly to the later life-myth of Pythagoras, namely Heraclides of Pontus. Philo of Alexandria shows in every aspect of philosophy how pervasive Pythagorean influence had become in the emerging amalgam that is Middle Platonism. To see how this influence develops further, one may turn to the major figure in the Platonist tradition from the later part of the first century AD, Plutarch of Chaeronea.
    • Chapter 13 - The Peripatetics on the Pythagoreans
      pp 274-295
    • View abstract

      Summary

      The Peripatetic view of Pythagoras mirrors the split in the tradition that was present in the earliest sources: Aristoxenus of Tarentum follow Empedocles in being overwhelmingly positive, whereas Dicaearchus and Hieronymus are heirs to Heraclitus' bitter critique. In terms of amount of material, the Peripatetics put greatest emphasis on the way of life of Pythagoras and later Pythagoreans. Theophrastus succeeded Aristotle as head of the Lyceum in 322 and remained until 287. He certainly referred to the Pythagoreans in his contribution to the Peripatetic survey of human knowledge, the Physical Opinions, which systematically collected early Greek views about the natural world. A text about the Pythagoreans in the later tradition can, with more or less plausibility, be traced back to Eudemus. Dicaearchus, writing at the same time as Theophrastus, Eudemus and Meno, focuses not on Pythagorean contributions to the sciences but rather on the life of Pythagoras himself.
    • Chapter 14 - Pythagoras in the historical tradition: from Herodotus to Diodorus Siculus
      pp 296-314
    • View abstract

      Summary

      Taking a look at the preserved works of classical historiography, which for the most part focus on political and military history, one gets the impression that Pythagoras and Pythagoreanism were of rather marginal interest to historians. The earliest historian who mentions Pythagoras is Herodotus, who refers to him and Pythagorean doctrine in two problematic passages. Neanthes of Cyzicus' crucial role as an intermediary can also be seen in the fragments in Diogenes Laertius that relate to the Pythagorean Empedocles. One can able to see that he systematically quoted, corrected and added to the reports of Timaeus of Tauromenium. Book 10 of Diodorus Siculus' Library contains a long section on the life of Pythagoras and the history of Pythagoreanism as a part of the history of the western Greeks. In addition to the fragments of Book 10, Pythagoras is mentioned occasionally in the preserved books of Diodorus.
    • Chapter 15 - The pseudo-Pythagorean writings
      pp 315-340
    • View abstract

      Summary

      The content of the pseudo-Pythagorean writings results from a blending of Platonic and Aristotelian doctrines, which is typical of Platonism, beginning in the first century BC. Platonic doctrines are mediated by the academic tradition, which shapes the basic orientation of the treatises towards systematization and classification. Pythagoreanism became inextricably entwined with Platonism and came to exercise a far wider influence than its actual standing should have permitted. The theory of principles plays a fundamental role in all spheres of knowledge, but its very formulation contains innovative elements, which make the pseudo-Pythagorean system more than simply a repetition of early Academic doctrines. The Aristotelian doctrines are integrated within a Platonizing system: Aristotle's hylomorphism is thus interpreted in the light of the doctrine of Ideas, identified with Aristotelian Forms, and traced back to the two fundamental principles. The same reduction of Aristotelian notions to two principles occurs in cosmology, ethics and politics.
    • Chapter 16 - Pythagoreans in Rome and Asia Minor around the turn of the common era
      pp 341-359
    • View abstract

      Summary

      This chapter focuses on the city of Rome from the Late Republic up to and including the Julio-Claudian period, and on Asia Minor in the first and second centuries AD. It also discusses, in the case of Rome, both people to whom the label Pythagorean was applied and other members of the educated elite with an interest in Pythagoreanism. As for Asia Minor, two men who in the author's evidence are presented as not just following Pythagorean precepts, but as consciously modeling their public image after Pythagoras, are the center of attention: Apollonius of Tyana and Alexander of Abonouteichos. Both received biographical treatment, laudatory in the former case, defamatory in the latter. A treatment of Pythagoreanism at Rome during the Julio-Claudian period would be incomplete without mentioning the ongoing discussion about the subterranean basilica discovered in 1917 near the Porta Maggiore.
    • Chapter 17 - Diogenes Laertius’ Life of Pythagoras
      pp 360-380
      • By André Laks, Universidad Panamericana and Université de Paris-Sorbonne
    • View abstract

      Summary

      This chapter reviews the content of Book 8 of Lives and Opinions of Eminent Philosophers and explains its place within Diogenes Laertius' work. It discusses some specific features of Diogenes' picture of Pythagoras. If one wants to detect an overall interest in Diogenes' Life of Pythagoras, they must certainly locate it in the Pythagorean mode of life as reflected in the long lists of religious and ethical precepts. The chapter gives an analysis of the extended report about Diogenes' doctrines which plays a central function in the overall construction of the book. The report excerpted by Alexander Polyhistor and copied by Diogenes is itself a sample of pseudo-Pythagorean literature. The chapter addresses the problem of Diogenes' attitude towards Pythagoras. The Pythagorean Notes would be a testimony of an eclectic Pythagoreanism and also of an eclectic Pythagoreanism.
    • Chapter 18 - Porphyry's Life of Pythagoras
      pp 381-398
    • View abstract

      Summary

      For centuries, Porphyry's Life of Pythagoras (Vita Pythagorae (VP)) and Iamblichus' On the Pythagorean Way of Life have conveyed idealized pictures of Pythagoras that continued to be canonic down to the nineteenth century. Before examining the VP this chapter looks at the History of Philosophy (HP) as a whole in order to find out how Pythagoras' biography fitted into this ambitious work. One of the aspects of the HP that immediately catches the attention is its essentially antiquarian, scholarly, and at the same time compilatory and derivative character. Porphyry probably organized his material in roughly chronological order by individual philosophers, i.e., neither by schools of thought nor by philosophical themes or questions. The chapter concludes that reading Porphyry's VP gives access to the state of Pythagoreanism in the first centuries AD and to its views of Pythagoras and the Pythagorean tradition.
    • Chapter 19 - Iamblichus’ On the Pythagorean Life in context
      pp 399-415
    • View abstract

      Summary

      Iamblichus' work On the Pythagorean Life (Vita Pythagorae (VP)) is the most extensive and richest source of information on Pythagoras and his school to have reached one from antiquity. True Platonism is Pythagoreanism, the true legacy of Plato is Pythagorean. To see this more clearly this chapter looks beyond On Pythagoreanism and considers other parts of Iamblichus' philosophical production. The chapter then comments briefly on each of the parts of On Pythagoreanism. It sketches the way in which Iamblichus constructed his patchwork, and also looks at the patches and at the materials used by Iamblichus in composing the VP. A considerable amount of work has been done in more recent studies on the compositional structure of Iamblichus' VP. The chapter summarizes some results of this research, with a view to dealing with the question as what the purpose might be that is intended by this compositional structure.
    • Chapter 20 - Pythagoras and Pythagoreanism in late antiquity and the Middle Ages
      pp 416-434
    • View abstract

      Summary

      This chapter surveys broad themes in the late ancient and medieval use of Pythagoras and the Pythagoreans beginning with a summary of Pythagoras' quadrivial legacy, followed by a resume of the music-theoretical heritage of Pythagoras musicus, and the natural philosophical heritage of Pythagoras physicus. Boethius begins the Fundamentals of Arithmetic with an account of philosophical knowledge from the standpoint of ontology. Fully in accord with what Proclus explicitly deems a Pythagorean classification of the mathematical sciences, Boethius divides the objects of mathematics into discrete quantity and continuous quantity. Cosmic music concerns the harmonic structures and periods of the celestial bodies, the delicate balance of the four elements, and the cyclical succession of the seasons. Undoubtedly the most important of Boethius "Pythagorean" legacies is his presentation of Pythagorean music theory in the Fundamentals of Music. There are two hints one lexical, the other contextual that Boethius intends sensus as sense perception.
    • Chapter 21 - Pythagoras in the Early Renaissance
      pp 435-453
    • View abstract

      Summary

      The Renaissance story of Pythagoras and Pythagorean wisdom, its religious and its scientific aspects alike, is a complicated one. One of the arresting dimensions of early Renaissance Pythagoreanism is consequent on the rediscovery of certain ancient sources. From Marsilio Ficino's viewpoint, Pythagoras' musical and theological debts were unquestionably to Orpheus. Not only did Ficino confront the twin Pythagorean notions of metensomatosis and metempsychosis, but he was drawn into speculating about the cycle of lives and of deaths, deaths that are inter-lives as lives are inter-deaths. This chapter shows that Ficino specifically identified as Pythagorean in his Platonic Theology 4.1.14-16, one that focuses, on the mystery and the symbolism of 12. It can serve to introduce what the Renaissance saw as Pythagoras'mathematical, though to us it is his arithmological legacy. Iamblichus gives the fullest ancient listing of the Symbola in his Protreptic, but provides long list in On the Pythagorean Life.

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