[Titles and Authors are listed at the end of the review.]
“More than is the case for any other era in the history of European philosophy, our information about the Presocratics is subject to interpretation, and to the changing interests of those who have transmitted the texts.” This remark by Georg Wöhrle, which opens the first volume in the series of editions “Traditio Praesocratica” published about ten years ago (first German edition 2009), explains why reception studies have been gaining ground in scholarship on Presocratic philosophy. Fortunately, Pythagoras was one of the very first Presocratic philosophers to have been studied from this perspective. Christoph Riedweg devoted the last part of his classic study Pythagoras (first edition 2002) to the influence that Pythagoras had on various philosophers, scholars, and scientists from Classical Antiquity down to (almost) our time.The companion under review fits within this broader trend in its aim of covering the reception of Pythagoras and Pythagoreanism in the Middle Ages and the Renaissance. (A sibling companion, covering the reception of Pythagoras and Pythagoreanism in the Classical, Hellenistic, and Late Ancient periods is already forthcoming).
The present volume contains a preface by the editors, an introduction written by all three editors illustrating the aim and the scope of the volume and summarizing the main themes of the individual chapters, and four main parts, each dedicated to a different key topic of Pythagorean philosophy. The index of names is adequate and seems reliable. There is no general bibliography at the end, but each chapter concludes with its own list of references to the literature. In what follows, I will briefly discuss the content covered in each of the main parts and then comment on the volume as a whole.
The first part of the volume is dedicated to the reception of Pythagorean number theory and its place in medieval education. As one would expect from this topic, the name Nicomachus of Gerasa (ca. 60–120 CE) appears not infrequently in the contributions in this part of the volume, since it is to this late Platonic philosopher that we ultimately owe a very large part of Pythagoras’ “Nachleben” in the Middle Ages and the Early Modern period. In the first chapter, Cecilia Panti focuses on the long tradition which sees Pythagoras as the “father” of the quadrivium. She shows how this tradition was constructed from Antiquity to the Middle Ages down to the thirteenth century, when the influence of Aristotelianism and Arab philosophy in the Latin West called for a different interpretation of Pythagoras. She explains how important the role of Nicomachus of Gerasa—and subsequently Boethius—was in shaping this tradition. Next, Andrew Hicks takes a closer look at the significance of the figure of Pythagoras for medieval western music theory and harmonics. He examines the origins of this tradition, which he traces not, of course, to the “historical” Pythagoras and the Pythagoreans, but rather to the “mathematical Pythagoreanism” (p. 85) of Nicomachus of Gerasa and the way in which this was received by subsequent Latin authors. In the third chapter, Sonja Brentjes introduces the other major component of the medieval reception of Pythagoras (and of the Presocratics in general) into the discussion, namely the Hebrew and Syro-Arabic traditions. Her contribution offers a very useful overview of the reception of Nicomachean number theory in various Arabic and Persian mathematical texts between the early ninth and fourteenth centuries, including the two known translations of Nicomachus’ Introduction from Syriac and Greek respectively, of which the former is extant only in the Hebrew translation of a commentary-oriented paraphrase of the Arabic text. This Hebrew translation is also the subject of the next chapter by Gad Freudenthal. The translation appears to have been completed in 1317 CE by the Jewish Provençal scholar Qalonymos b. Qalonymos. As Freudenthal demonstrates, however, there are several different layers of text that can be identified between Qalonymos’ text and the Greek text of Nicomachus, a situation which reflects a highly complex but also fascinating reception process spanning different cultures and languages. The first part of the companion concludes with a chapter by Tzvi Langermann, focusing on two further cases of Pythagorean reception in the medieval Hebrew tradition, namely those of Moses Maimonides (d. 1204) and of the Book of Kings authored by Qalonymos b. Qalonymos (1286–after 1328).
The second part of the volume, which deals with the reception of Pythagorean ethics, begins with a chapter by Anna Izdebska, who examines how late antique Greek biographical and gnomological texts passed (sometimes through Syriac intermediates) into the Arabic tradition and from there exercised a surprisingly wide ethical and moral influence. Its reception went beyond the narrow philosophical circles, and resulted in the popularization of the figure of Pythagoras in the Arab world as a monotheistic spiritual and moral teacher, whose wisdom might continue to illuminate those who pay careful attention to his wise maxims, sayings, and anecdotes (available in various medieval Arab sources). In the next chapter, Aurélien Robert shifts the focus back to the Latin West providing a similarly learned overview of the reception of Pythagorean ethics in biographical and gnomological texts written in Latin, mainly from the twelfth to the fifteenth centuries. He also rightly emphasizes (see, e.g., pp. 264–265) the twofold way in which Pythagoras was appropriated within the medieval Christian discourse, namely not merely as a “Christian before Christ,” but sometimes even as a pagan “mirror,” within which Christians might see and reflect on their own weaknesses by comparing them with Pythagoras’s alleged moral strength.
The third part of the volume looks in more detail at the medieval reception of Pythagorean teachings about the soul, metaphysics, and theology. Daniel De Smet focuses on occurrences of Pythagorean theory of numbers in Arabic doxography. He argues that the understanding of this theory—especially the part concerning the relationship between God and the number one—in a monotheistic and creationist way can be traced back to pagan and Christian sources from later Antiquity (p. 287). However, in Arabic doxography, this phenomenon must additionally be seen as reflecting a conscious effort on the part of Arab scholars to “Islamize” Pythagoras by putting his so-called “philosophy of unity” at the service of Islamic theology. In the next chapter, Carmela Baffioni discusses a similar case, namely the occurrences of elements of the Pythagorean tradition in the encyclopedia of the “Brethren of Purity.” She is also interested in the reception of Pythagorean number theory, since the Brethren also make use of the concept of the number one, which they then relate to God, as the root of numbers. As she rightly concludes, however, it is not very easy to distinguish here what is genuinely Pythagorean from what might have been taken from other later Islamic onto-cosmologies. At the same time, one is entitled to seek a Pythagorean influence in the several quotations from Nicomachus of Gerasa. In the next contribution, Irene Caiazzo brings the focus back to the Latin Middle Ages, examining how Pythagorean and Aristotelian teachings, especially following the “rediscovery” of Aristotle at the beginning of the Late Middle Ages, were used in the course of the philosophical debate on the transmigration of souls from the eleventh to the thirteenth centuries in the West. The presence of Pythagoras and other Pythagoreans in the Aristotelian commentaries of Thomas Aquinas is the subject of the next chapter by Marta Borgo and Iacopo Costa, who stress that this group of early Greek thinkers—although seen by Thomas primarily through the lens of Aristotle, as is generally the case with the pre-Aristotelian thinkers—seems nonetheless to have exercised a modest, but perhaps not wholly insignificant influence on his philosophical thought. This part concludes with a well-written chapter by David Albertson, who puts together the scattered pieces of the reception of the “mathematical” Pythagoreanism of Nicomachus, as transmitted by Boethius and other medieval commentators in the West, in the works of various scholastic authors and early humanists.
The fourth and final part of the volume is devoted to further developments in the reception of Pythagoras and Pythagoreanism during the Renaissance and the Early Modern era. In the first chapter of this part, Denis J.-J. Robichaud identifies three main currents within the reception of Pythagoreanism during this period: first, the approach adopted by those who attempted to reconcile Pythagorean philosophy with Kabbalah (Pico, Reuchlin, etc.); second, the beginnings of a stronger academic interest in the practical application of Pythagorean mathematics (Lefèvre, Ramus, etc.); and third, the historical-critical stance as already expressed in the works of the early editors of the ancient textual sources about Pythagoras (Scaliger, Bentley, etc.) and contemporary historiography (Brucker). Jean-Pierre Brach then adds more detail to this picture by examining the presence of Pythagoreanism in various forms in this period from the narrower viewpoint of number mysticism, thus tying the whole volume together thematically in a ring composition, since it began with a part dedicated to Pythagorean number theory.
In conclusion, this is a very erudite, coherent, and carefully edited volume. I noticed no typographical mistakes. Moreover, what I found particularly successful was the organization of the content in thematic divisions corresponding to the focal aspects of Pythagorean philosophy. These divisions enabled the contributions focusing on different traditions (Christian Latin, Hebrew, and Arabic) to supplement each other, and thus to demonstrate as fully as possible the historical and philosophical interactions between East and West, which were also vital for the reception of Pythagoras and Pythagoreanism during the Middle Ages. It is only unfortunate that, given the volume’s title, the Byzantine component has been left out (a decision the editors explain in the introduction, p. 3). That said, the companion under review, with its broad scope and wealth of detail, definitely constitutes a welcome contribution to the field and an indispensable reference source for all students of the transmission of ancient Pythagoreanism (and to some extent also of Platonism), as well as of Presocratic philosophy.
Titles and Authors
Introduction: Pythagoras, from Late Antiquity to Early Modernity. A Multicultural Approach (Irene Caiazzo, Constantinos Macris, and Aurélien Robert)
Part 1: Pythagorean Number Theory and the Quadrivium
1. Pythagoras and the Quadrivium from Late Antiquity to the Middle Ages (Cecilia Panti)
2. Music and the Pythagorean Tradition from Late Antiquity to the Early Middle Ages (Andrew Hicks)
3. Nicomachean Number Theory in Arabic and Persian Scholarly Literature (Sonja Brentjes)
4. The Tribulations of the Introduction to Arithmetic from Greek to Hebrew via Syriac and Arabic. Nicomachus of Gerasa, Ḥabib Ibn Bahrīz, al-Kindī, and Qalonymos ben Qalonymos (Gad Freudenthal)
5. Medieval Jewish Pythagoreanism. Remarks on Maimonides and on Sefer Melakhim (Tzvi Langermann)
Part 2: Pythagorean Way(s) of Life, East and West
6. Popular Pythagoreanism in the Arabic Tradition. Between Biography and Gnomology (Anna Izdebska)
7. Pythagoras’ Ethics and the Pythagorean Way of Life in the Middle Ages (Aurélien Robert)
Part 3: Theology, Metaphysics and the Soul
8. Pythagoras’ Philosophy of Unity as a Precursor of Islamic Monotheism. Pseudo-Ammonius and Related Sources (Daniel De Smet)
9. The “Brethren of Purity” and the Pythagorean Tradition (Carmela Baffioni)
10. “Pythagoras’ Mistake”: The Transmigration of Souls in the Latin Middle Ages and Beyond (Irene Caiazzo)
11. Pythagoras Latinus. Aquinas’ Interpretation of Pythagoreanism in His Aristotelian Commentaries (Marta Borgo and Iacopo Costa)
12. Latin Christian Neopythagorean Theology. A Speculative Summa (David Albertson)
Part 4: New Trends in Early Modern Pythagoreanism
13. Pythagoras and Pythagoreanism in the Renaissance. Philosophical and Religious Itineraries from Pico to Brucker (Denis J.-J. Robichaud)
14. Pythagorean Number Mysticism in the Renaissance. An Overview (Jean-Pierre Brach)
 G. Wöhrle (ed.), The Milesians: Thales, transl. and suppl. with additional material by R. McKirahan (Traditio Praesocratica 1), Berlin/Boston 2014, p. 1
 C. Riedweg, Pythagoras. Leben – Lehre – Nachwirkung, Munich 20072, pp. 150–174.
 C. Macris, C. Riedweg and I.-F. Viltanioti (ed.), Brill’s Companion to the Reception of Pythagoras and Pythagoreanism: From the Classical Period to Late Antiquity, Leiden/Boston (forthcoming).