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)

Archytas of Tarentum is one of the three most important philosophers in the Pythagorean tradition, a prominent mathematician, who gave the first solution to the famous problem of doubling the cube, an important music theorist, and the leader of a powerful Greek city-state. He is famous for sending a trireme to rescue Plato from the clutches of the tyrant of Syracuse, Dionysius II, in 361 BC. This 2005 study was the first extensive enquiry into Archytas' work in any language. It (...) contains original texts, English translations and a commentary for all the fragments of his writings and for all testimonia concerning his life and work. In addition there are introductory essays on Archytas' life and writings, his philosophy, and the question of authenticity. Carl A. Huffman presents an interpretation of Archytas' significance both for the Pythagorean tradition and also for fourth-century Greek thought, including the philosophies of Plato and Aristotle. (shrink)

This is the first comprehensive study for nearly 200 years of what remains of the writings of the Presocratic philosopher Philolaus of Croton. These fragments are crucial to our understanding of one of the most influential schools of ancient philosophy, the Pythagoreans; they also show close ties with the main lines of development of Presocratic thought, and represent a significant response to thinkers such as Parmenides and Anaxagoras. Professor Huffman presents the fragments and testimonia with accompanying translations and introductory (...) chapters and interpretive commentary. He not only produces further argument for the authenticity of much that used to be neglected, but also undertakes a critique of Aristotle's testimony, opening the way for a quite new reading of fifth-century Pythagoreanism in general and of Philolaus in particular. Philolaus is revealed as a serious natural philosopher. (shrink)

The Pythagorean Precepts by Aristotle's pupil, Aristoxenus of Tarentum, present the principles of the Pythagorean way of life that Plato praised in the Republic. They are our best guide to what it meant to be a Pythagorean in the time of Plato and Aristotle. The Precepts have been neglected in modern scholarship and this is the first full edition and translation of and commentary on all the surviving fragments. The introduction provides an accessible overview of the ethical system of the (...) Precepts and their place not only in the Pythagorean tradition but also in the history of Greek ethics as a whole. The Pythagoreans thought that human beings were by nature insolent and excessive and that they could only be saved from themselves if they followed a strictly structured way of life. The Precepts govern every aspect of life: e.g. procreation, abortion, child rearing, friendship, religion, desire and even diet. (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 long note in his epoch-making book on ancient Pythagoreanism Walter Burkert raised some grave doubts about the authenticity of Archytas Fr. 1 which have recently been challenged in an article by A. C. Bowen. In this paper I have two goals. First, I will evaluate Burkert's doubts and the success of some of Bowen's arguments against them. Second, I will present a further consideration that both clarifies the text of the fragment and also removes the most serious problem (...) raised by Burkert. The upshot of both these points is to increase the likelihood that the fragment is authentic. I reproduce the text of just the first part of the fragment as given in DK followed by the text as it appears in the two primary sources, Nicomachus and Porphyry. (shrink)

In this article I want to clarify the text of one of the short maxims assigned to Pythagoras in the ancient tradition, which are known as symbola or acusmata. Before I turn to the acusma in question, it is important to understand the context in which it appears. It occurs in Chapter 17 of Book 4 of Aelian's Historical Miscellany. Aelian's work was written in the early third century a.d. in Rome, and is a ‘miscellaneous collection of anecdotes and historical (...) material’. It consists of short chapters, usually a page or less long, that are for the most part independent of one another. Chapter 17 of Book 4 is about a page long and is devoted to the sayings and doings of Pythagoras. There is no particular connection between it and the surrounding chapters, and it is clearly meant to stand on its own. The preceding chapter tells us that if we went to Callias for guidance he would turn us into drinkers, … if to Alcibiades, arrogant cheats, if to Demosthenes, orators, … if to Aristides, just men, … if to Socrates, wise men. The following chapter recounts an anecdote about Plato's arrival in Sicily and his reception by the tyrant Dionysius the Younger. The chapter that I am concerned with, Chapter 17, begins by asserting that Pythagoras taught that his ‘lineage was superior to that of ordinary mortals’. This is followed by a list of superhuman acts and traits of Pythagoras, for example his ability to be in Metapontum and Croton at the same time and his golden thigh. The second two-thirds of the chapter are then devoted to the miscellaneous teachings of Pythagoras. Most of these take the form of the brief taboos and maxims known elsewhere as symbola or acusmata, among which is the text on which I want to focus here. (shrink)

This celebratory Festschrift dedicated to Charles Kahn comprises some 23 articles by friends, former students and colleagues, many of whom first presented their papers at the international "Presocratics and Plato" Symposium in his honor. The conference was organized and sponsored by the HYELE Institute for Comparative Studies, Parmenides Publishing, and Starcom AG, with endorsements from the International Plato Society, and the Dean of the School of Arts and Sciences, University of Pennsylvania. While Kahn's work reaches far beyond the Presocratics and (...) Plato, it is in these subject areas that the distinction of his scholarship has come to be regarded as virtually unrivaled. The articles contributed to this volume are by some of the most renowned scholars working on these topics today, their breadth and depth bearing witness to his profound impact and influence on the discipline of Ancient Greek Philosophy._ Charles Kahn taught Classics and Philosophy at Columbia University from 1957 to 1965, and has since been teaching in the Philosophy Department of the University of Pennsylvania. He spent a year as Visiting Professor at the American School of Classical Studies in Athens, and had additional Visiting Fellowships at Balliol College, Oxford and Clare Hall, Cambridge, and a term as Visiting Professor at Harvard. He is the recipient of several prestigious research grants, from the American Council of Learned Societies, the National Endowment for the Humanities, and the Guggenheim Foundation. In 2000 he was elected Fellow of the National Academy of Arts and Sciences. He is the author of _Anaximander and the Origins of Greek Cosmology, The Verb “Be” in Ancient Greek, The Art and Thought of Heraclitus, Plato and the Socratic Dialogue, Pythagoras and the Pythagoreans, and Essays on Being_. His latest book,_Plato and the Post-Socratic Dialogue_, is forthcoming from Cambridge University Press. _ Contributors: Julia Annas Sarah Broadie Lesley Brown Tomás Calvo-Martínez Diskin Clay John M. Dillon Dorothea Frede Arnold Hermann Carl A. Huffman Enrique Hülsz Piccone D. M. Hutchinson Paul Kalligas Vassilis Karasmanis Aryeh Kosman Anthony A. Long Richard McKirahan Susan Sauvé Meyer Alexander P.D.Mourelatos Satoshi Ogihara Richard Patterson Christopher J. Rowe David Sedley Richard Sorabji. (shrink)

29 o JOURNAL OF THE HISTORY OF PHILOSOPHY 34:2 APRIL t996 J. Burnet, Oxford, 19oz ) is excluded, as are influential works in foreign languages. Popper's The Open Society and Its Enemies, vol. I is included 077); it was later translated into German . The converse does not hold: P. Friedl~inder's Platon 049-43) is included, but its English translation is not. F. Solmsen's Plato's Theology is not included, nor is his "Plato and the Unity of Science,"s although it was reprinted (...) in Solmsen's Kleine Schriften4 and Soimen's German articles reprinted there are included. As the international Plato Forschungsberichte of Ritter5 demonstrate even for the Germany of the early decades of this century, the world of scholarship knows no national bound- aries. The present attempt to impose them on Platonic studies results in a highly artificial work of bibliography. 6 RICHARD McKIRAHAN Pomona College Carl A. Huffman. Philolaus of Croton, Pythagorean and Presocratic: A Commentary on the Fragments and Testimonia with Interpretive Essays. New York: Cambridge University Press, 1993. Pp. xix + 444- Cloth, $1oo.oo. Pythagoreanism used to play a major role in accounts of Presocratic philosophy. Follow- ing the testimony of ancient Platonists, the Pythagoreans were seen as Plato's precur- sors in cosmology, on the soul, and on Ideas and numbers; and attempts were made to reconstruct the systematic philosophy of the Pythagoreans, or even of Pythagoras himself. Now, however,.. (shrink)

This volume is a Festschrift dedicated to Charles Kahn comprised of more than 20 papers presented at the conference "Presocratics and Plato: Festschrift Symposium in Honor of Charles Kahn", 3-7 June 2009. The conference was held at the European Cultural Center of Delphi, Greece, and was organized and sponsored by the HYELE Institute for Comparative Studies and Parmenides Publishing, with endorsement from the International Plato Society, and the Dean of the School of Arts and Sciences, University of Pennsylvania. Contributors: Julia (...) Annas - University of Arizona; Sarah Broadie - University of St. Andrews; Lesley Brown - University of Oxford; Tomás Calvo-Martínez - Universidad Complutense de Madrid; Diskin Clay - Duke University; John M. Dillon - Trinity College, Dublin; Dorothea Frede - Humbolt University, Berlin; Arnold Hermann - HYELE Institute for Comparative Studies; Carl A. Huffman - DePauw University; Enrique Hülsz Piccone - Universidad Nacional Autonoma de Mexico; D.M. Hutchinson - St. Olaf College; Paul Kalligas - National and Kapodistrian University, Athens; Vassilis Karasmanis - National Technical University, Athens; Aryeh Kosman - Haverford College; Anthony A. Long - University of California, Berkeley; Richard McKirahan - Pomona College; Susan Sauvé Meyer - University of Pennsylvania; Alexander P.D. Mourelatos - University of Texas at Austin; Satoshi Ogihara - Tohoku University, Japan; Richard Patterson - Emory University; Christopher J. Rowe - Durham University; David Sedley - University of Cambridge; Richard Sorabji - University of Oxford. (shrink)

In Archytas of Tarentum, Carl Huffman reconstructs Archytas’ theory of definition by linking definitions to the mathematical study of ratios and proportions. This paper considers whether and how Archytas used definitions and whether he possessed a theory of definition. Our evidence does not support the claim that Archytas has a theory of definition, and his approach to the science of harmonics suggests that he relied on analogies and proportions in the practice of inquiry. We understand sounds and other (...) entities by placing them in a network of relations governed by mathematical proportions. Although he does not seem to have formulated definitions of sound, Archytas pursued inquiry into motion and rest by formulating definitions in such a way that they fit into a larger network of causal explanations. (shrink)

A review of Carl Huffman's new edition of the fragments of Archytas of Tarentum. Praises the extensive commentary on four fragments, but argues that at least two dubious works not included in the edition ("On Law and Justice" and "On Wisdom") deserve further consideration and contain important information for the interpretation of Archytas. Provides a complete translation for the fragments of those works.

To explain the phenomena in the world of our experience, to answer the question “why?” rather than only the question “what?”, is one of the foremost objectives of all rational inquiry; and especially, scientific research in its various branches strives to go beyond a mere description of its subject matter by providing an explanation of the phenomena it investigates. While there is rather general agreement about this chief objective of science, there exists considerable difference of opinion as to the function (...) and the essential characteristics of scientific explanation. In the present essay, an attempt will be made to shed some light on these issues by means of an elementary survey of the basic pattern of scientific explanation and a subsequent more rigorous analysis of the concept of law and of the logical structure of explanatory arguments. (shrink)

The classic logical positivist account of historical explanation, putting forward what is variously called the "regularity interpretation" (#Gardiner, The Nature of Historical Explanation), the "covering law model" (#Dray, Laws and Explanation in History), or the "deductive model" (Michael #Scriven, "Truisms as Grounds for Historical Explanations"). See also #Danto, Narration and Knowledge, for further criticisms of the model. Hempel formalizes historical explanation as involving (a) statements of determining (initial and boundary) conditions for the event to be explained, and (b) statements of (...) general laws that imply that whenever events of the kind described in (a) occur, an event of the kind to be explained will take place. He admits that in practice historians rarely explain historical events in this way, but instead give only fragmentary "explanation sketches." Such sketches can, however, be "scientifically acceptable," providing it points to where "more specific statements" are to be found (351). An interesting aspect of the article is its "late" positivist, proto‑Kuhnian assertion that "the separation of 'pure description' and 'hypothetical generalization and theory construction' in empirical science is unwarranted" (356). But Hempel does not work out the wider implications of this important conclusion. It is also worth noting that he himself was not much interested in the philosophy of history; other authors took up his model and discussed it within that context. Usefully discussed by #Ricoeur, Time and Narrative, 1:112‑17. (shrink)

Patrick L. Miller - Archytas of Tarentum: Pythagorean, Philosopher, and Mathematician-King - Journal of the History of Philosophy 46:1 Journal of the History of Philosophy 46.1 165-166 Muse Search Journals This Journal Contents Reviewed by Patrick Lee Miller Duquesne University Carl Huffman, Archytas of Tarentum: Pythagorean, Philosopher, and Mathematician-King. Cambridge-New York: Cambridge University Press, 2005. Pp. xv + 665. Cloth, $180.00. Archytas of Tarentum has in some ages been considered a major philosopher. He was one of the three (...) most important early Pythagoreans—along with Philolaus and Pythagoras himself—and so his reputation has risen and fallen with the popularity of this movement. When Pythagoreanism captivated some Romans at the end of the Republic, they championed him as a native talent; much later, some medieval Europeans inflated him into one of the great wise men of the ancient world. But Pythagoreanism has ebbed in recent centuries, and Archytas is now known only to specialists in ancient philosophy, and even then only by acquaintance from a few passages of Plato and.. (shrink)

We argue that intelligible appeals to interlevel causes (top-down and bottom-up) can be understood, without remainder, as appeals to mechanistically mediated effects. Mechanistically mediated effects are hybrids of causal and constitutive relations, where the causal relations are exclusively intralevel. The idea of causation would have to stretch to the breaking point to accommodate interlevel causes. The notion of a mechanistically mediated effect is preferable because it can do all of the required work without appealing to mysterious interlevel causes. When interlevel (...) causes can be translated into mechanistically mediated effects, the posited relationship is intelligible and should raise no special philosophical objections. When they cannot, they are suspect. (shrink)

Like his fellow first-generation Peripatetic Theophrastus, Aristoxenus wrote an extraordinary number of works. Many concerned music; one on Socrates contained evidence independent of Plato and Xenophon. At least five concerned Pythagoreanism: The Life of Pythagoras, On Pythagoras and His Associates, On the Pythagorean Way of Life, Life of Archytas, and the Pythagorean Precepts. This last one, as Carl Huffman...

Not all models are explanatory. Some models are data summaries. Some models sketch explanations but leave crucial details unspecified or hidden behind filler terms. Some models are used to conjecture a how-possibly explanation without regard to whether it is a how-actually explanation. I use the Hodgkin and Huxley model of the action potential to illustrate these ways that models can be useful without explaining. I then use the subsequent development of the explanation of the action potential to show what is (...) required of an adequate mechanistic model. Mechanistic models are explanatory. (shrink)

Many areas of science develop by discovering mechanisms and role functions. Cummins' (1975) analysis of role functions-according to which an item's role function is a capacity of that item that appears in an analytic explanation of the capacity of some containing system-captures one important sense of "function" in the biological sciences and elsewhere. Here I synthesize Cummins' account with recent work on mechanisms and causal/mechanical explanation. The synthesis produces an analysis of specifically mechanistic role functions, one that uses the characteristic (...) active, spatial, temporal, and hierarchical organization of mechanisms to add precision and content to Cummins' original suggestion. This synthesis also shows why the discovery of role functions is a scientific achievement. Discovering a role function (i) contributes to the interlevel integration of multilevel mechanisms, and (ii) provides a unique, contextual variety of causal/mechanical explanation. (shrink)

The goal of this paper is to sketch and defend a new interpretation or 'theory' of objective chance, one that lets us be sure such chances exist and shows how they can play the roles we traditionally grant them. The account is 'Humean' in claiming that objective chances supervene on the totality of actual events, but does not imply or presuppose a Humean approach to other metaphysical issues such as laws or causation. Like Lewis (1994) I take the Principal Principle (...) (PP) to be the key to understanding objective chance. After describing the main features of Humean objective chance (HOC), I deduce the validity of PP for Humean chances, and end by exploring the limitations of Humean chance. (shrink)

The fundamental tenet of modern empiricism is the view that all non-analytic knowledge is based on experience. Let us call this thesis the principle of empiricism. [1] Contemporary logical empiricism has added [2] to it the maxim that a sentence makes a cognitively meaningful assertion, and thus can be said to be either true or false, only if it is either (1) analytic or self-contradictory or (2) capable, at least in principle, of experiential test. According to this so-called empiricist criterion (...) of cognitive meaning, or of cognitive significance, many of the formulations of traditional metaphysics and large parts of epistemology are devoid of cognitive significance--however rich some of them may be in non-cognitive import by virtue of their emotive appeal or the moral inspiration they offer. Similarly certain doctrines which have been, at one time or another, formulated within empirical science or its border disciplines are so contrived as to be incapable of test by any conceivable evidence; they are therefore qualified as pseudo- [p. 42:] hypotheses, which assert nothing, and which therefore have no explanatory or predictive force whatever. This verdict applies, for example, to the neo-vitalist speculations about entelechies or vital forces, and to the "telefinalist hypothesis" propounded by Lecomte du Noüy. (shrink)

One of the most significant political philosophers of the twentieth century, Carl Schmitt is a deeply controversial figure who has been labeled both Nazi sympathizer and modern-day Thomas Hobbes. First published in 1938, The Leviathan in the State Theory of Thomas Hobbes used the Enlightenment philosopher’s enduring symbol of the protective Leviathan to address the nature of modern statehood. A work that predicted the demise of the Third Reich and that still holds relevance in today’s security-obsessed society, this volume (...) will be essential reading for students and scholars of political science. “Carl Schmitt is surely the most controversial German political and legal philosopher of this century. . . . We deal with Schmitt, against all odds, because history stubbornly persists in proving many of his tenets right.”— Perspectives on Political Science “[A] significant contribution. . . . The relation between Hobbes and Schmitt is one of the most important questions surrounding Schmitt: it includes a distinct, though occasionally vacillating, personal identification as well as an association of ideas.”— Telos. (shrink)