Monday, March 27, 2017


Carl A. Huffman (ed.), A History of Pythagoreanism. Cambridge: Cambridge University Press, 2014. Pp. 530. ISBN 9781107014398. $118.00.

Reviewed by Justin M. Rogers, Freed-Hardeman University (

Version at BMCR home site

[Authors and titles are listed at the end of the review.]

Few figures in the history of philosophy have enjoyed the acclaim of a Pythagoras. The name is synonymous with innovations in mathematics and music, and even with the invention of "philosophy" among the Greeks. But virtually every claim made about Pythagoras and the Pythagoreans in pre-Modern philosophy is historically dubious. Portraits, therefore, are almost as diverse as the scholars who have painted them.

The present volume does not intend to clear away the diversity, but rather to document it. Carl Huffman, the editor of this collection of essays, assembles an international team of scholars from some twelve countries who take various approaches to the source material. Some are minimalists (e.g. Lloyd), and others are more optimistic, at least in certain areas (e.g. Zhmud). The result is an engaging collection that offers not only valuable discussions of relevant source material, but also illustrates crucial methodological differences among modern scholars themselves.

Recent decades have witnessed a renewed interest in early Pythagoreanism, a trend reflected in the volume under review. Nine of the chapters critically examine information relating to Pythagoras and the early Pythagoreans. Especially welcome are separate chapters on Philolaus and Archytas, who have emerged in recent decades as important figures in the history of philosophy. Seven additional chapters treat the evidence from Plato through the early Roman era, including that vibrant age during which a number of Pythagorean forgeries appear. Three chapters then discuss the summary presentations of Pythagoreanism in Late Antique authors, and two final chapters document Medieval and early Renaissance receptions, respectively.

The general editor of the volume is responsible for an introduction, which summarizes each essay and highlights current trends in the study of Pythagoreanism. Huffman notes the methodological diversity, and helpfully compares and contrasts the various approaches taken to common source material.

Chapter One treats the figure of Pythagoras himself. Geoffrey Lloyd contrasts the influential presentations of Guthrie (in his History of Philosophy) and Burkert (in his Lore and Science in Ancient Pythagoreanism), and is skeptical about whether anything of substance can be known of the historical Pythagoras.

Chapter Two discusses Philolaus, the earliest Pythagorean to whom we can confidently ascribe genuine fragments. Daniel Graham asserts that Philolaus should be viewed more as an "inventor" of Pythagoreanism than a "transmitter" of it (48). In particular, Philolaus introduces the concept of "limiters" (περαίνοντα), and makes "unlimiteds" (ἄπειρα) and "limiters" twin principles in all that exists, with a third, "harmony," binding them together. This system informs astronomy as well, for an unlimited (fire) is limited by its placement at the center of the universe. This Philolaus calls the "hearth" (ἑστία), which the earth orbits once each day. Philolaus also asserts the existence of a counter-earth, although its exact function was unclear already in Antiquity.

Chapter Three is devoted to Archytas. Malcom Schofield regards Archytas, a contemporary of Plato, as the first Pythagorean to innovate in the field of mathematics. This may explain, in part, why more pseudo-Pythagorean works are ascribed to him than to any other early Pythagorean. Although Schofield allows some detectable influence in Plato's Republic and Timaeus, he rejects outright the notion that Timaeus is Archytas. He also dismisses any Archytean influence on Aristotle. In general, Schofield remains skeptical about the authenticity of most of the fragments attributed to Archytas.

Chapter Four is a summary treatment of various minor Pythagorean figures in the sixth to the fourth centuries BCE. Leonid Zhmud begins by addressing the difficulty of classifying early figures as Pythagoreans since there was no school as such and there appear to have been no unifying doctrines or lifestyles. Nevertheless, he labels Alcmaeon and Theodorus as Pythagoreans, and regards them as significant witnesses for early Pythagorean science and mathematics.

Chapter Five discusses Pythagorean involvement in politics and polis religion. Catherine Rowett understands a distinctive way of life to lie beneath a "creeping enthusiasm" for Pythagorean principles (119). Rowett is more positive than others about the reliability of late source material, and principally uses this material to discuss the positions of Pythagoras himself.

In Chapter Six, M. Laura Gemelli Marciano exalts the religious dimension of Pythagoreanism. The strict ethics and oral maxims of the master are not superstitious drivel, but are principles for life in service to the divine. She thus takes the oral traditions of the master (the acusmata) seriously, and regards them as positive evidence for ancient Pythagorean faith and practice.

Chapter Seven treats the relationship between Pythagoreanism and Orphism. Gábor Betegh suggests that the impossibility of clearly defining Pythagoreanism and Orphism in the early centuries prevents us from sketching a precise relationship between them. Doctrines that clearly linked the two in late antique authors, such as vegetarianism and metempsychosis, are inconsistently attested for both branches of thought in early sources. In fact, even the historicity of Orpheus is in doubt among the earliest witnesses.

Chapter Eight deals with mathematics, the area most associated with Pythagoreans in later philosophy. Reviel Netz hypothesizes two "networks" in the history of Greek mathematics, one associated with Archytas, and the other with Archimedes. It is largely due to the reputation of the former that Pythagoreanism became associated with mathematics in general, and the 'Pythagorean theorem' in particular. The older model of Archytas is ultimately superseded by the Archimedean model, except with the Platonists of late antiquity.

Chapter Nine treats Pythagorean harmonics. Andrew Barker carefully separates later developments (post-Plato) from the early Pythagoreans. He asserts that Pythagoras himself contributed nothing, and that recognition of the ratios of the concords predates any Pythagorean. Hippasus, one of the earliest, is probably the first to subject musical ratios to analysis, and Philolaus the first to apply these insights to metaphysics.

In Chapter Ten, John Palmer asserts Pythagorean influence on Plato was substantial, thus confirming, mutatis mutandis, a view traditional since Antiquity. The Gorgias reflects Pythagorean teaching on the good, and the Phaedo a Platonic development of the Pythagorean doctrine of psychic immortality. The Republic includes a polemic against Pythagorean number theory; the Philebus utilizes Philolaus' "limiters and unlimiteds;" and the Timaeus borrows the linkage between order and harmony as the sources of beauty and the good.

In Chapter Eleven, Oliver Primavesi discusses Aristotle's comments on the "so-called Pythagoreans." He extends the discussion, however, to include the late antique Metaphysics commentary of Alexander of Aphrodisias, which, he asserts includes fragments from Aristotle's lost monograph on the Pythagoreans. On the basis of this evidence, Primavesi concludes that Aristotle produces his own synthetic reconstruction of Pythagoreanism rather than a historical report.

Chapter Twelve discusses the Academic adoption of Pythagoreanism. John Dillon assigns to Speusippus and Xenocrates the desire to stress Pythagorean influence on Plato, especially with the doctrine of the One and Indefinite Dyad. A resurgence of this trend occurred in the first century BCE with Eudorus of Alexandria, a development most clearly observed in Philo of Alexandria.

Chapter Thirteen treats Pythagoreanism in the Peripatetic tradition. Carl Huffman concludes that, although there is abundant evidence for Pythagorean activity in the field of mathematics, none of these Pythagoreans appear to be decisive figures. Concerning the Pythagorean way of life, the Peripatetic sources are divided between praise and criticism.

In Chapter Fourteen, Stefan Schorn surveys the historiographic presentation of Pythagoras from Herodotus to Diodorus Siculus. Herodotus asserts a strong Egyptian influence. Timaeus of Tauromenium, like Aristotle, attests that the Pythagoreans were divided into two groups, and maintained strict secrecy. Neanthes of Cyzicus associates Pythagoras with Syria, which perhaps underlies the tradition that Pythagoras borrowed from the Jews. Diodorus praises the Pythagoreans, especially their ethical rigor.

Chapter Fifteen is a survey of the pseudo-Pythagorean corpus. Although Bruno Centrone acknowledges some of these texts were in circulation in the third century BCE, most belong to first-century BCE Alexandria, most notably ps.-Timaeus, ps.-Ocellus, and ps.-Archytas, which seem to assume a common system of thought in the areas of first principles, logic, theology, cosmology, ethics, and politics.

Chapter Sixteen discusses Pythagoreans in Rome and Asia Minor in the early Imperial Age. Jaap-Jan Flinterman rejects the use of Nigidius Figulus and the Porta Maggiore basilica as positive evidence that Pythagoreanism was widespread in Rome; however, he does find evidence in Cicero and Ovid that Pythagoreanism may have had some popularity as a native Italian philosophy.

Chapter Seventeen treats the account of Pythagoreanism in Diogenes Laertius. André Laks recognizes the potential source-critical utility of the account (especially for reconstructing Alexander Polyhistor), but also emphasizes the importance of reading Diogenes in his own terms. In fact, his Life of Pythagoras is far more coherent than the material around it, and may reflect a contemporary community, or may indicate the quality of his research or his sources.

In Chapter Eighteen, Constantinos Macris discusses Porphyry's Life of Pythagoras, which he takes to be a chapter of the much larger History of Philosophy. Porphyry regards all of the ps.-Pythagorica known to us as genuine, and thus sees Pythagoras as the ideal ascetic Platonist seeking to release his soul from the body.

Chapter Nineteen treats Iamblichus' On the Pythagorean Life. Dominic O'Meara emphasizes that this work is the first chapter in a monograph on Pythagoreanism in general. The soul of Pythagoras, Iamblichus says, did not merely descend, but was sent to humanity to share divine wisdom with us. Whereas, for Porphyry, Plato developed Pythagoras' teaching, Iamblichus asserts that Platonism is merely reissued Pythagoreanism.

Chapter Twenty handles the reception of Pythagoreanism from late antiquity to the Middle Ages. Andrew Hicks shows that Pythagoras was received as the founder of philosophy, and in the Middle Ages was credited with inventing the quadrivium, forming the basis for music theory, and developing natural philosophy.

In Chapter Twenty-One, Michael Allen discusses Pythagoreanism in the early Renaissance. Pythagoras was not the greatest of philosophers (this honor went to Plato), but he was an essential link in the chain of ancient wisdom stretching from Moses and Zoroaster to Plato. In addition to music theory, the doctrine of reincarnation, arithmology, and various Pythagorean precepts were popular fodder in the early Renaissance.

Each chapter is well-edited, and few typographical errors can be found. There is some variation from one chapter to another over the transliteration of Greek terms, but this probably reflects authorial choice rather than editorial inconsistency.

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.

Table of Contents

Introduction / Carl A. Huffman
1. Pythagoras / Geoffrey Lloyd
2. Philolaus / Daniel W. Graham
3. Archytas / Malcolm Schofield
4. Sixth-, fifth-, and fourth-century Pythagoreans / Leonid Zhmud
5. The Pythagorean Society and Politics / Catherine Rowett
6. The Pythagorean Way of Life and Pythagorean Ethics / M. Laura Gemelli Marcianio
7. Pythagoreans, Orphism, and Greek Religion / Gábor Betegh
8. The Problem of Pythagorean Mathematics / Reviel Netz
9. Pythagorean Harmonics / Andrew Barker
10. The Pythagoreans and Plato / John Palmer
11. Aristotle on the "So-Called Pythagoreans:" From Lore to Principles / Oliver Primavesi
12. Pythagoreanism in the Academic Tradition: The Early Academy to Numenius / John Dillon
13. The Peripatetics on the Pythagoreans / Carl A. Huffman
14. Pythagoras in the Historical Tradition: from Herodotus to Diodorus Siculus / Stefan Schorn
15. The Pseudo-Pythagorean Writings / Bruno Centrone
16. Pythagoreans in Rome and Asia Minor around the turn of the Common Era / Jaap-Jan Flinterman
17. Diogenes Laertius' Life of Pythagoras / André Laks
18. Porphyry's Life of Pythagoras / Constantinos Macris
19. Iamblichus' On the Pythagorean Life in Context / Dominic J. O'Meara
20. Pythagoras and Pythagoreanism in Late Antiquity and the Middle Ages / Andrew Hicks
21. Pythagoras in the Early Renaissance / Michael J. B. Allen

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