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