Was Plato a Pythagorean? Plato's students and earliest critics thought so, but scholars since the nineteenth century have been more skeptical. With this probing study, Phillip Sidney Horky argues that a specific type of Pythagorean philosophy, called "mathematical" Pythagoreanism, exercised a decisive influence on fundamental aspects of Plato's philosophy. The progenitor of mathematical Pythagoreanism was the infamous Pythagorean heretic and political revolutionary Hippasus of Metapontum, a student of Pythagoras who is credited with experiments in harmonics that led to (...) innovations in mathematics. The innovations of Hippasus and other mathematical Pythagoreans, including Empedocles of Agrigentum, Epicharmus of Syracuse, Philolaus of Croton, and Archytas of Tarentum, presented philosophers like Plato with novel ways to reconcile empirical knowledge with abstract mathematical theories. Plato and Pythagoreanism demonstrates how mathematical Pythagoreanism established many of the fundamental philosophical questions Plato dealt with in his central dialogues, including Cratylus, Phaedo, Republic, Timaeus, and Philebus. In the process, it also illuminates the historical significance of the mathematical Pythagoreans, a group whose influence on the development of philosophical and scientific methods has been obscured since late antiquity. The picture that results is one in which Plato inherits mathematical Pythagorean method only to transform it into a powerful philosophical argument about the essential relationships between the cosmos and the human being. (shrink)

This chapter pursues an understanding of what Cicero thought 'Italic' philosophy to be, and proceeds to develop a broader account of how Cicero's version compares with the surviving textual evidence and testimonia from the Hellenistic period of the philosophy of the 'Italic' philosophers, including the Lucanians 'Ocellus', 'Eccelus', and 'Aresas/Aesara', and the Rudian Ennius. Special focus is placed on their theories of cosmology, psychology, and law. Collocation of 'Italic' with 'Pythagorean' philosophy of this era aids in building a more comprehensive (...) view of what Hellenistic Pythagoreanism may have looked like. Uploaded here is the pre-publication version; please email me for the printed version. (shrink)

The purpose of the conference "On Pythagoreanism", held in Brasilia in 2011, was to bring together leading scholars from all over the world to define the status quaestionis for the ever-increasing interest and research on Pythagoreanism in the 21st century. The papers included in this volume exemplify the variety of topics and approaches now being used to understand the polyhedral image of one of the most fascinating and long-lasting intellectual phenomena in Western history. Cornelli's paper opens the volume (...) by charting the course of Pythagorean studies over the past two centuries. The remaining contributions range chronologically from Pythagoras and the early Pythagoreans of the archaic period (6th-5th centuries BCE) through the classical, hellenistic and late antique periods, to the eighteenth century. Thematically they treat the connections of Pythagoreanism with Orphism and religion, with mathematics, metaphysics and epistemology and with politics and the Pythagorean way of life. (shrink)

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. (shrink)

The history of Pythagoreanism is littered with different and incompatible interpretations. This observation directs this book towards a fundamentally historiographical rather than philological approach, setting out to reconstruct the way in which the tradition established Pythagoreanism s image.".

Pythagoreanism, the claim that ‘all is number’, is rarely taken seriously these days as a candidate for the sober metaphysical truth. This is a mistake. I distinguish various versions of Pythagoreanism. Some such versions are unmotivated, some are subject to serious objections, and some are both. But, I argue, there is a robust version of Pythagoreanism—according to which there is a true theory whose ontology and ideology are wholly mathematical from which every truth follows—that is both well-motivated (...) and not subject to any serious objection. Given that fact, Pythagoreanism ought to be a serious metaphysical contender. (shrink)

Three key elements of Aristotle’s theory of demonstration have Pythagorean antecedents. Demonstration is a revelatory discourse that is 1) inferential, 2) explicitly based on premises that are not themselves demonstrated on the basis of more basic premises, and 3) explanatory, insofar as the premises express those basic facts that are explanatory of the conclusion. The Pythagorean Table of Opposites constitutes a kind of protologic making possible a kind of deduction, which Aristotle would have regarded as a “demonstration,” that reveals the (...) reasons behind Pythagorean commands and prohibitions. Philolaus recognizes ultimate explanatory principles. Both he and Archytas recognize the asymmetry of principles and what is explained on their basis. (shrink)

CORNELLI, G. (2013). In Search of Pythagoreanism. Pythagoreanism as an Historiographical Category, “Studia Praesocratica” 4, de Gruyter, Berlin.

HORKY, P. S. (2013). Plato and Pythagoreanism. Oxford University Press.

The development of a compositional model shows the incoherence of such notions as levels of being and both bottom-up and top-down causality. The mathematization of nature through the partial considerations of physics qua quantities is seen to lead to Pythagoreanism, if what is not included in the partial consideration is denied. An ontology of only probabilities, if not Pythagoreanism, is equivalent to a world of primitive dispositionalities. Problems are found with each. There is a need for properties as (...) well as quantities and these properties must be qualitative as well as dispositional. So there is a need for physical qualia (qualities) for the depiction of the intrinsic character of the finest interstices of nature. (shrink)

This book presents an up-to-date overview of the main new directions taken by ancient philosophy in the first century BC, a period in which the dominance exercised in the Hellenistic age by Stoicism, Epicureanism and Academic Scepticism gave way to a more diverse and experimental philosophical scene. Its development has been much less well understood, but here a strong international team of leading scholars of the subject reconstruct key features of the changed environment. They examine afresh the evidence for some (...) of the central Greek thinkers of the period, as well as illuminating Cicero's engagement with Plato both as translator and in his own philosophising. The intensity of renewed study of Aristotle's Categories and Plato's Timaeus is an especially striking outcome of their discussions. The volume will be indispensable for scholars and students interested in the history of Platonism and Aristotelianism. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Plato and Pythagoreanism by Phillip Sidney HorkyGabriele CornelliPhillip Sidney Horky. Plato and Pythagoreanism. Oxford University Press, 2013. xxi + 305 pp. Cloth, $74.Ceci n’est pas un livre sur Pythagore. With these clever and rather playful words, Horky’s book starts its literary journey through a wide range of Pythagorean sources, including Epicharmus, Empedocles, Philolaus, Eurytus and Arquitas, and Pythagorean themes, like numbers, immortality of the soul, limitness/unlimitness, (...) among others.From this explosive incipit, one would think that Horky agrees with Kahn’s almost forty-year-old observation about the fact that new theories of Pythagoreanism are not necessary in our present day and age (1974, 163, n. 6):It’s hard enough to satisfy minimal standards of historical rigor in discussing the Pythagoreans, without introducing arbitrary guesswork of this sort where no two students can come to the same conclusion on the basis of the same evidence. In fact, the direct testimony for Pythagorean doctrines is all too abundant. The task for a serious scholarship is not to enrich these data by inventing new theories or unattested stages of development but to sift the evidence so as to determine which items are most worthy (or least unworthy) of belief.On the contrary, however, Horky’s approach seems surprisingly to direct the reader towards a fundamentally historiographical rather than philological brand of work, that is, one devoted neither exclusively to the exegesis of Pythagorean sources nor even to the theoretical approach of one of the themes that received specific contributions from Pythagoreanism, such as mathematics, cosmology, politics, or the theory of the immortal soul. This is mainly true when one recognizes, from the title on, that the main goal of the book is to try to determine, once and for all, what is the extent of Pythagorean influence on Plato’s thought. Rather an historiographical problem, I would say. And a good one.In order to do so, Horky needs to trace down a sort of history of mathematical Pythagoreanism from a huge variety of informed ancient sources and perspectives. Horky’s approach to the sources is well-grounded, not only in Burkert’s fundamental works, but also in the recent revival in Pythagorean studies which took over ancient philosophy scholarship in the last two decades: Huffmann’s works on Philolaus (1993) and Arquitas (2005); Zhmud (1997) and Kahn (2001) on early Pythagoreans; Riedweg on Pythagoras (2002), among many others. After the publishing of Horky’s book, two sorts of Companions to Pythagoreanism confirm the trend of the revival: Cornelli, McKirahan, and Macris (2013), acts of the On Pythagoreanism seminar held in Brasilia by Archai [End Page 353] UNESCO Chair, and Huffman (2014). Luckily, Pythagorean scholarship has now gotten rid of that old-fashioned scepticism, starting from Zeller’s famous statement that the relevant sources are a “mixture of fables and poetry.” As Horky’s book seems to suggest, the job can be done. And he has definitely proved to be able to force his way through, with both clear philological arguments and refined historiographical hypotheses.Not surprisingly, a work on Plato and Pythagoreanism starts with a chapter on Aristotle: “Aristotle on Mathematical Pythagoreanism in the Fourth Century BCE” (chap. 1). The idea of the chapter is to rely on Aristotle’s distinction between the mathematical and acousmatic branches of Pythagoreanism. While acousmatic Pythagoreans supposedly did not engage in demonstration, the so-called mathematical Pythagoreans engaged in investigations based on mathemata in order to give an account (the reason why of the world they perceived). Horky seems to drive Aristotle’s account to a specific goal: mathematical Pythagoreans would have established some kind of correspondence between numbers and sensibles, and their ontology would have a direct relation to social and political organization.Chapter 2, “Hippasus of Metapontum and Mathematical Pythagoreanism,” is entirely dedicated to the account of the later doxographical tradition on Hippasus, the alleged progenitor of mathematical Pythagoreanism. Avoiding the risk of falling into the “bottomless pit” of research on the Pythagoreans—in Guthrie’s famous words (1962, 146, n. 1)—Horky manages his inquiry boldly and in a quite elegant way. Between the peripatetic systematization and the platonic derivation of Hippasus’ philosophy, Hippasus... (shrink)

This chapter traces Plato's philosophical responses to the puzzle of Epicharmus' “Growing Argument” in the earlier and middle dialogues of Plato, especially Euthyphro and Cratylus. Plato's approach to this problem is rooted in his metaphysical propositions, including the correlative assumptions of participation of sensibles in Forms and imitation as a vehicle for names to obtain the properties of their governing Forms. By attacking a Sophistical version of the “Growing Argument” given by Cratylus, Plato simultaneously appropriates certain principles of ontological predication (...) given by Philolaus of Croton, thus pitting, in effect, the ideas of one mathematical Pythagorean against those of another. (shrink)

Recently, the Pythagoreans have received rather more attention, both in their own right and as part of the developing picture of Presocratic thought, than they received for much of the twentieth century. Thanks to these studies, a new and more complicated picture is emerging. This article refines this picture critically examining Aristotle's claims about Pythagorean influence on Plato, along with the related question of who among early Greek thinkers actually counts as a Pythagorean. It provides a reminder that Aristotle's account (...) of the history of earlier thought is always a history of just a part of the philosophy of his predecessors, and makes clear that the eagerness with which some present-day scholars find Pythagorean influence on later thought may be misplaced. (shrink)

In the spiritual and philosophical proposals by the ancient Greco-Romans for taking care of oneself (epiméleia heautoû), the listening-related ones stand out. Listening has been characterized by exercises, such as reading, writing, memorizing, and meditating, the first and most crucial ways of owning the truth about the subject. Based on analyses carried out by Michel Foucault regarding taking care of oneself in Hermeneutics of the Subject and going through fundamental commentators of Pythagorean thought, this research has the purpose of approaching (...) listening, possibly in its old orientations such as the process of self-control and ascetic practice. Facing the demands of listening and silence as a required exercise of introduction and permanence at school, the Pythagorean disciple was asked to change in the constant search for knowledge as their master did. (shrink)

In a well-known quotation from Speusippus in the Theologumena Arithmeticae , said to have been derived from Pythagorean sources, especially Philolaus, occur the following sentences: And again a little later: Similarly Sextus Empiricus , drawing evidently on a relatively early Pythagorean source, writes as follows: And Aristotle himself writes of the Pythagoreans : There were, in fact, certain Pythagoreans who equated the number 2 with the line because they regarded the line as ‘length without breadth extended between two points’; and (...) likewise the number 3 was equated with the plane and 4 with the solid. (shrink)

For the first time, the reader can have a synoptic view of the reception of Pythagoras and Pythagoreanism in the Middle Ages and the Renaissance, East and West, in a multicultural perspective. All the major themes of Pythagoreanism are addressed, from mathematics, number philosophy and metaphysics to ethics and religious thought.

This chapter describes the kinds of Pythagoreans who may have existed from the sixth through fourth centuries bce and their philosophical activities based on the evidence preserved by Aristotle. It identifies the characteristics that distinguished the mathematical Pythagorean pragmateia from the pragmateia of the rival acousmatic Pythagorean brotherhood in Magna Graecia. It argues that Aristotle establishes this distinction by appeal to the divergent philosophical methodologies of each group. The mathematical Pythagoreans, who are the same as the “so-called Pythagoreans” in Metaphysics (...) A, employ superordinate mathematical sciences in establishing something that approximates demonstrations that explain the “reason why” they hold their philosophical positions, whereas the acousmatic Pythagoreans, who are distinguished from the “so-called” Pythagoreans in Metaphysics A, appeal to basic, empirically derived “fact” in defense of their doctrines. (shrink)

The Athenian sophist Philostratus completed a romanticised biography of Apollonius of Tyana in the second or third decade of the third century A.D. One of the most striking aspects of the presentation of this firstcentury Pythagorean sage and miracleworker in the Vita Apollonii (VA) is his role as 'politically active philosopher'. Not only does the protagonist of the VA regularly intervene in situa-tions of conflict in Greek cities and instruct their citi-zens on how they ought to live together, but he (...) also appears in contact with Parthian and Indian kings and Roman emperors. The present study deals with this promi-nent facet of Philostratus' portrait of the Tyanean sage. There are three main issues. The first is the question of the extent to which the Apollonius tradition provided support for the image of the contacts of the protagonist of the VA with cities and monarchs. The second is consideration of how the author dealt with and elaborated these elements in his source material. The third is the question of to what extent the protagonist of the VA may be regarded as a spokesman for the explicit political views of Philostratus. In other words, the aim is to analyse the image of the protagonist of the VA as a 'politically active philosopher' as the result of the interaction between the traditions associated with a sage and miracleworker who was regarded as a representative of Pythagorean wisdom, on the one hand, and the paideia, cultural baggage and mentality of a sophist, on the other. (shrink)

This paper critically examines the use of the name 'Pseudo-Archytas' to refer to two aspects of the reception of Archytas of Tarentum in antiquity: the 'author-inflection' and the 'authority-inflection'. In order to make progress on our understanding of authority and authorship within the Pythagorean tradition, it attempts to reconstruct Porphyry's views on the importance of Archytas as guarantor of Pythagorean authenticity in the former's lost work On the History of the Philosophers by considering a fragment preserved in Arabic by Ibn (...) Abī Uṣaybi‘a. The article finally argues that a range of problems attend our use of the term 'pseudo-Archytas', which is not fit for purpose when considering the evidence regarding authorship and authority in the Pythagorean tradition. It recommends a more critical approach to the notion of authenticity within the Pythagorean tradition and suggests a new term, 'Archytism', as a more useful point of reference. (shrink)

For the first English edition of his distinguished study, Weisheit und Wissenschaft: Studien zu Pythagoras, Philoloas und Platon, Mr. Burkert has extensively ...

The present work is an excellent translation of Walter Burkert’s Weisheit und Wissenschaft: Studien zu Pythagoras, Philolaus, und Platon, first published in 1962. It is very probably the most illuminating and comprehensive study of Pythagoreanism yet produced by a modern scholar. Obviously Pythagoreanism is a protean historical phenomenon, equally mysterious both in its origin and development, and in all epochs its interpretation has indicated as much about the winds of cultural doctrine as about the nature of Pythagoreanism (...) itself. Burkert’s study is the product of an astonishingly thorough penetration of all the relevant ancient evidence and all the critically significant modern literature, and it evinces the author’s remarkable ability to weave the diverse threads of Pythagoreanism into a comprehensible historical picture. (shrink)

Too often the historians of philosophy tend to relegate a philosopher to a meaningless anonymity by rigidly classifying his thought into one particular category. De Vogel feels that this has been done to Pythagoras and the Pythagorean tradition. He claims that because philosophical scholars have relied chiefly on Platonic and Aristotelian accounts of Pythagoras, two misleading effects have ensued: 1. We have lost sight of the man Pythagoras and his charismatic influence on the people of Croton and Magna Graecia; 2. (...) Pythagoras, cosmic theory of numerical ratios has been emphasized to the neglect of, and in separation from, his political and social teachings. De Vogel hopes to remedy these two impressions by returning to "neglected evidence" and reconstructing the life of Pythagoras. He hopes to remove Pythagoras from that vague classification as one of the οἱ φυσικοί into which Aristotle had placed all the pre-Socratic thinkers. Furthermore, the author wants to show the essential unity of Pythagoras' cosmic, social, and political thinking. The neglected evidence on which De Vogel bases his reconstruction is mainly the testimony of Timaeus, an historian of Southern Italy and Sicily; Aristoxenus, a follower of Pythagoras; and Dicaearchus, a writer of cultural history. In addition to these last mentioned sources, the author cites the testimony of coins and quotes leading archaeologists; he refers to the many historians and biographers of Pythagoras; and especially, he draws from the four speeches of Pythagoras that are recorded by Iamblichus. With these source materials, De Vogel reconstructs a Pythagoras who is a charismatic preacher-moralist; one who gives precepts of life governing justice, friendship, love, health, education, rhetoric, and medicine. What is more, all of these social and political teachings are shown to be integrated with the cosmic theory of numbers which De Vogel removes from the realm of abstract and idle theory. Pythagoras emerges as a leading figure in Croton and throughout Magna Graecia. All in all, this volume is an excellent contribution to Pythagorean scholarship.--J. J. R. (shrink)