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)

In Philolaus’ cosmology, the earth revolves around a central fire along with the other heavenly bodies, including a planet called the counter-earth which orbits below the earth. His theory can account for most astronomical phenomena. A common criticism of his theory since ancient times is that his counter-earth does no work in the system. Yet ancient sources say the planet was supposed to account for some lunar eclipses. A reconstruction of Philolaus’ cosmology shows how lunar eclipses occurring at (...) certain times of day cannot be explained by earth blocking the sun’s light. The counter-earth could explain these eclipses. (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)

The book is divided into four parts. Part 1 surveys biographical information and the complex philological and doxographical evidence that affect questions about authenticity. Part 2 provides an excellent overview of Philolaus's philosophy that is notable both for its clarity and mastery of the scholarly literature. The heart of the book comes in Part 3, which comprises the genuine fragments and testimonia with elaborate philological and philosophical commentary. The genuine texts are divided into seven groups: Basic Principles, Epistemology, Cosmogony, (...) Astronomy, Embryology and Medicine, Soul and Psychic Faculties, Miscellaneous. Huffman helpfully encapsulates the contemporary Greek philosophical theories on offer in each area of thought. Part 4 includes the Spurious and Doubtful Fragments and Testimonia, an important category given Huffman's rejection of fragments considered genuine by others. (shrink)

Presocratic philosophy, for all its diverse features, is united by the quest to understand the origin and nature of the world. The approach of the Pythagoreans to this quest is governed by their belief, probably based on studies of the numerical relations in musical harmony, that number or numerical structure plays a key role for explaining the world-order, the cosmos. It remains questionable to what extent the Pythagoreans, by positing number as an all-powerful explanatory concept, broke free from Presocratic ideas (...) that certain stuffs or material elements sufficed to account for the source and constitution of the world, but apparently number found such a universal application with them that Aristotle could summarize the Pythagorean position as ‘numbers…are the whole universe’ . Historians of Greek philosophy have generally accepted Aristotle's assessment. Of late, however, certain scholars have argued that the Pythagorean number doctrine is Aristotelian interpretation, unjustly foisted upon the Pythagoreans. Enlisted in support of their arguments are the fragments of Philolaus of Croton. Here we have the foremost representative of fifth-century Pythagoreanism, who states as his basic principles, not numbers exactly, but ‘limiters’ and ‘unlimiteds’, and who, it is argued, regards number solely as an epistemological aid for understanding the structure of reality. So Philolaus is called upon as a witness against Aristotle. The rationale goes something like this: Aristotle most likely had written sources for his knowledge of Pythagorean teachings; the only texts we know of with any certainty are Philolaus' book and the writings of Archytas; since Aristotle treats Archytas separately, he is mainly relying on Philolaus; because Philolaus does not expressly state that things are numbers, Aristotle's interpretation is wrong. (shrink)

In this paper, three problems that have hardly been noticed or even gone unnoticed in the available literature in the cosmology of Philolaus are addressed. They have to do with the interrelationships of the orbits of the Earth, the Sun, and the Moon around the Central Fire and all three of them constitute potentially insurmountable obstacles within the context of the Philolaic system. The first difficulty is Werner Ekschmitt’s claim that the Philolaic system cannot account for the length of (...) the day (νυχϑήμερον). It is shown that this problem can be solved with the help of the distinction between the synodic day and the sidereal day. The other two problems discussed in this paper are concerned with two hitherto unnoticed deficiencies in the explanation of lunar eclipses in the Philolaic system. The Philolaic system cannot account for long-lasting lunar eclipses and according to the internal logic of the system, during lunar eclipses the Moon enters the shadow of the Earth from the wrong side. It is almost unbelievable that nobody, from the Pythagoreans themselves up to recent authors, has noticed these two serious deficiencies, and especially the latter, in the cosmology of Philolaus the Pythagorean. (shrink)

L'A. étudie le concept de kosmos défini non pas comme entité cosmologique, mais comme entité structurée, dans le traité «Du Kosmos» et le traité «De la nature» de Philolaos de Croton. L'A. propose sa propre interprétation de la classification ontologique de Philolaos en trois classes d'objets: il s'agit en fait d'une ontologie bipartite composée d'une part des objets limitants et illimités, et d'autre part du kosmos constitué de ces deux principes.

We critically reconsider an old hypothesis of the role of the dekad in Pythagorean philosophy. Unlike Zhmud, we claim that: 1) the dekad did play a role in Philolaus’ astronomical system, and 2) Aristotle did not project Plato’s theory of the ten eidetic numbers onto the Pythagoreans. We claim that the dekad, as the τέλειος ἀριθμός, should be understood in Philolaus’ philosophy as completeness and the basis of counting in Greek – as in most other languages – in (...) a decimal system. Additionally, we argue that the number ten is not even a candidate for the τέλειος ἀριθμός in Plato’s philosophy. As a final result of our discussion, we compare and contrast Philolaus’, Plato’s, and Speusippus’ accounts of completeness in relation to numbers. (shrink)

This paper traces how the dualism of body and soul, cosmic and human, is bridged in philosophical and religious traditions through appeal to the notion of ‘breath’ (πνεῦμα). It pursues this project by way of a genealogy of pneumatic cosmology and anthropology, covering a wide range of sources, including the Pythagoreans of the fifth century BCE (in particular, Philolaus of Croton); the Stoics of the third and second centuries BCE (especially Posidonius); the Jews writing in Hellenistic Alexandria in the (...) first century BCE (Philo); and the Christians of the first century CE (the gospel writers and Paul). Starting from the early Pythagoreans, ‘breath’ and ‘breathing’ function to draw analogies between cosmogony and anthropogony – a notion ultimately rejected by Plato in the Timaeus and Aristotle in his cosmological works, but taken up by the Posidonius (perhaps following the early Stoa) and expanded into a rich and challenging corporeal metaphysics. Similarly, the Post-Hellenistic philosopher and biblical exegete Philo of Alexandria, who was deeply influenced by both Platonist and Stoic physics, approaches the cosmogony and anthropogony described in Genesis (1:1–3 and 1:7) through Platonist-Stoic philosophy, in his attempt to provide a philosophically rigorous explanation for why Moses employed certain terms or phrases when writing his book of creation. Finally, the chapter sees a determined shift in the direction of rejecting pneumatic cosmology for a revised pneumatic anthropogony in the writings of the New Testament: by appeal to the ‘Holy Spirit’ or ‘Holy Breath’ (πνεῦμα ἅγιον), early Christians effectively adapted the Stoic metaphysics of ‘breath’, with its notions of divine intelligence and bonding, to the prophetic and ecclesiastical project of building a Christian community conceived of as the ‘body of Christ’. Hence, the spiritual cosmogony of the Pythagoreans, Stoics, and Philo is effectively subordinated to the spiritual anthropogony that facilitates the construction of the Christian kosmopolis, only fully realised in the form of New Jerusalem, the ‘bride’ which, in tandem with the Holy Spirit, calls to the anointed. At the end of the Christian worldview, the kosmos of Greek philosophy is supplanted by the pneumatic kosmopolis. (shrink)

At Phaedo 86b7–c2 Simmias puts forward the theory that the soul is the attunement of bodily elements. Many scholars have claimed that this theory originates in the Pythagoreans, especially Philolaus. The claim is largely based on their reading of the Phaedo, since we have scarce doxographical evidence. In this paper I show that the dialogue in question does not constitute any evidence for the Pythagorean origin of Simmias’ attunement theory, and that it rather represents the theory as stemming from (...) a materialistic world view that had become widespread among people at that time. I also pursue the question how and why, then, the attunement theory was able to attract many people, by examining its relation to Socrates’ affinity argument. (shrink)

Since its publication in 1994, Richard McKirahan's _Philosophy Before Socrates_ has become the standard sourcebook in Presocratic philosophy. It provides a wide survey of Greek science, metaphysics, and moral and political philosophy, from their roots in myth to the philosophers and Sophists of the fifth century. A comprehensive selection of fragments and testimonia, translated by the author, is presented in the context of a thorough and accessible discussion. An introductory chapter deals with the sources of Presocratic and Sophistic texts and (...) the special problems of interpretation they present. In its second edition, this work has been updated and expanded to reflect important new discoveries and the most recent scholarship. Changes and additions have been made throughout, the most significant of which are found in the chapters on the Pythagoreans, Parmenides, Zeno, Anaxagoras, and Empedocles, and the new chapter on Philolaus. The translations of some passages have been revised, as have some interpretations and discussions. A new Appendix provides translations of three Hippocratic writings and the Derveni papyrus. (shrink)

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 essay provides a comprehensive and detailed analysis of a cluster of Heraclitus’ fragments that revolve around an image of ‘musical’ harmony (B 8, 10, and 51 Diels-Kranz). The aim is to demonstrate that more numerous as well as more specific references to contemporary musical practice can be found in these fragments than is usually thought. In particular, it is argued that in his talk of cosmic harmonia Heraclitus might well know and exploit a musical sense of this word, namely, (...) that of ‘attunement’, which was already developing at his time from the primary meaning of ‘connection’ and ‘agreement’. Furthermore, it is shown that the investigation of musical patterns with which Heraclitus was clearly acquainted offered him a significant analogical ground for his reflection on the order and rationality of kosmos. He was not apparently interested in the numerical definition of musical patterns, and thus there is no need to assume any influence of earlier Pythagorean research on his theory of cosmic harmony: the other way round, this theory was likely food for thought for Philolaus. (shrink)

The essay explores the Pythagorean explanation of the origin of the Sun's light and warmth, particularly in the fragments of Philolaus. His cosmological notion of the Sun centers around the idea that the Sun is merely a medium between the Earth and the primal source of warmth and light.

Western philosophy begins with Thales, Anaximander, and Anaximenes. Or so we are told by Aristotle and many members of the later doxographical tradition. But a good case can be made that several centuries before the Milesian thinkers began their investigations, the poets of archaic Greece reflected on the limits of human intelligence and concluded that no mortal being could know the full and certain truth. Homer belittled the mental capacities of ‘creatures of a day’ and a series of poets of (...) the archaic period declared that mortals think only in terms of ‘what they meet with’ while failing to detect the larger cycles that make for success or failure. While Xenophanes embraced this pessimistic tradition, a number of early thinkers (Heraclitus, Parmenides, Empedocles, and Philolaus) expressed a more positive view of the powers of human intelligence, at least in those who heard and took to heart their novel philosophical teachings. (shrink)

This chapter contains sections titled: Criteria Used for the Concept of the Universal Some Conceptual Barriers to Early Grasp of the Universal Empedocles: Formulae for Compounds; Biological Forms; Type‐Identities across Cycles Philolaus: Genus, Species, and the Relation to Particulars Democritus: An Infinity of Atomic Types, Atomic Tokens Comments by Democritus on the Universal Democritus and Aristotle: Origins of the Type–Token Distinction Democritus and Plato Bibliography.

The present essay will cross, inside the matter of the sources of the platonic thought, the suggestion of Damascius of Damascus, with the intention to draw clear understanding, unless in this particular point, of the relationship between the ancient pythagoreanism and the platonic philosophy. In this, the study of the matter of the dialectics of the limiters/unlimited one is central. The page 16c of the Philebus is the crucial point of this discussion: here Socrates introduces the theme of the unity/multiplicity (...) as a very beautiful hodos, a run that comes from a very distant point of departure: it’s a “gift of the gods” and a discovery of the ancient ones. The comparative study of these footsteps of the Philebus and the fragments of Philolaus, especially В 2, 3, 6 and 7 bring us to conclude that the presence in the pages of the Philebus of the theory of the limiter/unlimited be taken as a pre-platonic “discovery” of the more ancient pythagorean philosophy. (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)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Texts of Early Greek Philosophy: The Complete Fragments and Selected Testimonies of the Major Presocratics ed. by Daniel W. GrahamPhillip Sidney HorkyDaniel W. Graham, ed. and trans. The Texts of Early Greek Philosophy: The Complete Fragments and Selected Testimonies of the Major Presocratics. Parts 1 and 2. Cambridge: Cambridge University Press, 2010. xvii + 1020 pp. Cloth, $180; paper, $99.It has been nearly 30 years since Malcolm (...) Schofield revised and updated the first edition of the venerable translation of fragments of the Presocratic philosophers by J. E. Raven and G. S. Kirk, originally compiled in 1957 in the wake of the sixth and final edition of Diels-Kranz’s (DK) Die Fragmente der Vorsokratiker (Berlin 1951–52). And in the time since Kirk-Raven-Schofield’s second edition of The Presocratic Philosophers (KRS), in 1983, several translations of selected portions of the collected fragments of early Greek philosophy into English have appeared: Jonathan Barnes’ Early Greek Philosophy (London 1987), drawn from his revised edition of The Presocratic Philosophers (London 1982), Robin Waterfield’s The First Philosophers (Oxford 2000), and Richard McKirahan’s Philosophy Before Socrates (Indianapolis, Ind. 2011). Students of Presocratic philosophy and the early intellectual history of Greece have profited immensely from the contributions made by KRS, Barnes, Waterfield, and McKirahan. Yet none of these volumes, despite their intellectual courage, philosophical acumen, and deep learning, could provide what Diels and Kranz had given German audiences in the middle of the twentieth century: a bilingual translation of the complete fragments of and selected testimonia concerning those important intellectual antecedents of Plato (including the Sophists).On the eve of Professor Schofield’s retirement, then, Daniel W. Graham has produced a two-volume translation and commentary on the complete fragments and selected testimonies of the “major Presocratics.” It should be mentioned that this is not an easy or even enviable project. Presocratic studies has undergone a renaissance of sorts since the last edition of KRS in 1983, and new critical editions and translations into English of individual figures (J. Lesher’s Xenophanes of Colophon [Toronto 1992]; C. A. Huffman’s editions of Philolaus of Croton [Cambridge 1993] and Archytas of Tarentum [Cambridge 2005]; the editions of Anaxagoras by P. Curd [Toronto 2007] and D. Sider [Sankt Augustin 2005]; C. C. W. Taylor’s The Atomists: Leucippus and Democritus [Toronto 1999]; G. J. Pendrick’s Antiphon the Sophist [Cambridge 2002]); new editions of papyrus discoveries (A. Martin and O. Primavesi’s L’Empédocle de Strasbourg [Berlin 1999], incorporated into B. Inwood’s The Poem of Empedocles [Toronto 2001] and the long-awaited “official” text of The Derveni Papyrus by T. Kouremenos, G. Parássoglou, and K. Tsantsanoglou [Firenze 2006]); and major critical studies [End Page 149] of Presocratic philosophers and/or philosophy (too numerous to name here) have significantly modified the landscape of the study of early Greek philosophy. In the midst of this renaissance, one has seen the critical approaches used to evaluate Presocratic thought develop into a perfect storm, with a barrage of new approaches concerning historiography, interpretation, reception, and contextualization, now considered legitimate in the assessment and evaluation of those thorny and often obscure fragments of the early Greek speculators. Presocratic studies has become contested ground, and the idea of producing a two-volume set that might update, stabilize, and make DK accessible for an English-reading audience, despite the protestations of the few (xiii), must be considered nothing less than wholly welcome. Given his demonstrated comprehension of the field of Presocratic studies at large—he has produced two broad-ranging monographs, edited several general volumes, and offered many article-length contributions on early Greek philosophy—Graham would seem to be the perfect choice for the job.What remains to be seen, then, is whether the volumes as we have them rise to the challenge of the project. The results, I think, are mixed. I will first discuss those aspects of The Texts of Early Greek Philosophy that seem more successful and testify to the value that such a collection offers to educators and students alike. Then I will examine some areas where the volumes do not quite reach the heights promised by the... (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)

This chapter examines aspects of the Pythagorean tradition from the perspective of “spiritual guidance”. The only traces that remain of the initial period of Pythagoreanism are the acousmata and a handful of authentic fragments of Philolaus of Croton. The chapter focuses on the Golden Verses, a short poem dating back to the Hellenistic period that constitutes the most complete and impressive illustration of spiritual guidance in a Pythagorean milieu. The chapter analyzes that despite the chronological distance that separates the (...) Golden Verses from the acousmata, what is at issue in both cases is the practice of the Pythagorean way of life, that gives guidance all its meaning. What emerges from the testimonies dealing with the Pythagoreans is that their way of life was practiced in a community, or the Pythagorean society or sect. (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)

In the twenty-fourth aporia of Theophrastus' Metaphysics, there appears an important, if ‘bafflingly elliptical’, ascription to Plato and the ‘Pythagoreans’ of a theory of reduction to the first principles via ‘imitation’. Very little attention has been paid to the idea of Platonic and ‘Pythagorean’ reduction through the operation of ‘imitation’ as presented by Theophrastus in his Metaphysics. This article interrogates the concepts of ‘reduction’ and ‘imitation’ as described in the extant fragments of Theophrastus’ writings – with special attention to his (...) Metaphysics – in an attempt to make sense of how, precisely, Theophrastus characterizes the metaphysical systems of Plato and the ‘Pythagoreans’. A fuller examination of Aporia 24 produces important new understandings of the nature of the Early Academy in the mid fourth century B.C.E. Specifically, by ascribing the concept of reduction via ‘imitation’ to Plato and the ‘Pythagoreans’, Theophrastus is actually describing theories about the structure of the universe held by an important Platonist competitor and the contemporary head of the Academy in Athens, Xenocrates of Chalcedon (396/5–314/13 B.C.E.), who (a) took it upon himself to establish a Platonic doctrine that could be associated with his master’s writings and (b) coordinated that doctrine with the philosophical precepts of the Pythagoreans. As a consequence, we are prompted to question Aristotle’s famous ascription of a theory of ‘imitation’ to the metaphysics of the genuine contemporary or recently deceased Pythagoreans (such as Philolaus of Croton or Archytas of Tarentum) and consider how Xenocrates’ writings on Plato and the ‘Pythagoreans’ might be informing both Theophrastus’ and Aristotle’s descriptions of the Platonic and Pythagorean philosophical system(s). (shrink)

In his discussion of the ethics of suicide Plato alludes to more than one traditional injunction against it:indicates a fairly general acceptance of its wickedness. Cebes has heard the Pythagorean Philolaus, among others, saying that suicide was immoral, but has gathered no satisfactory explanation as to why this should be so. One reason, impressive, but, Socrates admits, difficult is to be found.

Introduction: The poetic topos of the doctrine of transmigration -- Genealogy of the doctrine of transmigration -- Beyond mysticism and science : symbolism and philosophical magic -- The emergence of mystic cults and the immortal soul -- Philolaus and the question of pythagorean harmony -- The alleged critique of Pythagoras by Parmenides -- Between the earth and the sky : on the pythagorean divine -- The pythagorean bios and the doctrine of transmigration -- The path of the event -- (...) The path of remembrance or return -- The platonic rupture : writing and difference -- Plotinus : the ascent of the soul toward the one -- Plotinus as neoplatonic mystic : letter to Flaccus -- Epilogue: The fate of the doctrine of transmigration. (shrink)

In his essay Thinking Colours and/or Machines Kittler hints at a key point in the emergence of modern European culture: the point at which ‘letters and numbers no longer coincide’. In this essay - first published in 2003 as Zahl und Ziffer - Kittler traces the split between numerals and numbers in sweeping historical detail. This is part of a much larger project, the aim of which is to think about technology, history and culture anew by considering the ways in (...) which ‘letters, numbers, images and tones’ have been differentiated and re-integrated by developing notation systems and media technologies. In this present essay, Kittler is concerned specifically with the question of number. His argument is that numbers and numerals have not always stood apart. In Old Hebrew and even nursery rhymes, for example, numbers are in fact words. This might seem like a banal observation, but for Kittler it is crucial as historically, mathematics proper only developed ‘in cultures in which numbers are present as numerals’, a development which entailed the transformation of numbers from signifiers (‘a matter of hearing’) into signifieds (‘a matter of reading and writing’) and which rested on the emergence of storage and transmission media that Kittler calls ‘the media of mathematics’. This connection between media and mathematics is explored through a wide range of philosophical sources: Plato, Philolaus, Aristotle and Aquinas, to name but a few. Kittler is fascinated by the inscription technologies that make mathematics possible, and which at the same time structure cultural forms as well as our bodily experience of them. As he puts it in a programmatic aside, ‘media studies only make sense’ if they focus on how ‘media make senses.’ Hence his focus on the Greek phonetic alphabet: for Kittler, its superiority has less to do with its ability to reproduce the spoken words of any language, than with the fact that at one point it was used to handle language, music, and mathematics - that is, one and the same set of signs was used to encode letters, tones and numbers. This, however, was not an abstract undertaking but developed in constant feedback with specific instruments or media, especially the lyre and the bow. It was here that fundamental concepts such as logoi were first developed that were subsequently distorted, misunderstood and deprived of their musico-technical origins by philosophers such as Aristotle. Kittler’s essay is thus also part of a larger cultural project, indebted in particular to Martin Heidegger, whose aim it is to ferret out the different, as yet unrevealed beginning of occidental culture. Moreover, while it was necessary for the evolution of modern mathematics that numbers receive a notation system of their own that will allow for ratios and decimals, among others, it is obvious that Kittler sees the computer (as first envisaged in Alan Turing’s mathematical modelling) as a return of universal alphabet that operates in constant feedback with a medium that shapes our senses: ‘In the Greek alphabet our senses were present - and thanks to Turing they are so once again.’. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS Galileo: For Copemicanism and for the Church. By ANNIBALE FANTOLI. Translated by George V. Coyne, S.J. Studi Galileiani Vol. 3. Vatican City: Vatican Observatory Publications, 1994. Distributed by the University of Notre Dame Press, Notre Dame, Indiana. Pp. xix+ 540. $21.95 (paper). This exhaustive treatment of Galileo and his relationship to the Church was first published in Italian by the Vatican Observatory in 1993 as Vol. 2 (...) of its Studi Galileiani series, bearing the title Galileo: Per il Copemicanesimo e per la Chiesa. So excellent was the study that Father George Coyne, the director of the Vatican Observatory, took it on himself personally to translate the volume into English. Although not a member of the Galileo Commission set up by Pope John Paul II to review the Galileo case, as were Coyne and myself, Fantoli has admirably complemented the work of the Commission and his book surely belongs in the Studi Galileiani collection. A former Jesuit with degrees in mathematics and physics, Fantoli began the book more than twenty-five years ago when he was preparing a course on Galileo at Sophia University in Tokyo. His intention was to show that for Galileo it was never a question of choosing between Copernicanism and the Church, and that the saddest drama of his life was being faced with an injunction that forced him to befor the Church and against Copemicanism. The subtitle of his book proclaims Galileo's true intentions, despite his failure to convince others that this was what his life was all about. A great strength of Fantoli's treatment is its documentation, which abounds in excerpts from Galileo's writings and his correspondence as found in the National Edition of his works and also in citations from new materials that have been uncovered by the Galileo Commission. Thanks to Coyne, all of these texts, many of which were hitherto available only in Latin or Italian, can now be easily accessed in English translation. Another strength of Fantoli's work is that he has kept abreast of Galileo literature over the years and thus is able to offer scholarly critiques of authors whose works exhibit a bias against the Church. Especially welcome are his careful discussions of the positions of earlier writers such as Giorgio de Santillana, Ludovico Geymonat, and Stillman Drake, as well as those of more recent authors, Mario Biagioli, Maurice Finocchiaro, Pietro Redondi, William R. Shea, and Richard S. Westfall. The book is a tour de force and there is little to criticize in it. Unfortunately, however, a typesetting error at its very beginning might create 317 318 BOOK REVIEWS the wrong impression and throw off prospective readers. About six lines of text were omitted at the bottom of page 9. To remedy this the following words should be inserted between the end of page 9 and the beginning of page 10: confused with the Sun) which had heen worked out by Philolaus (about 475 B.C.) within the context of the Pythagorean school.9 In a further modification of this theory the central fire as well as the hypothesis of an anti-earth were done away with, which left the earth at the center of the universe. To offset this addition, the last six lines on the bottom of page 10 should be deleted, for these lines are repeated at the top of page 11. Otherwise, with this change, the exposition reads correctly. The remaining typographical errors are few and in no case do they affect the sense. After a brief introduction in which he presents the astronomical concepts necessary for understanding the details of the Copernican debate, Fantoli divides his treatment into seven chapters. The first two of these are devoted to Galileo's early life and teaching at the Universities of Pisa and Padua, his perfection of the telescope, and the beginnings of the controversies about the earth's motion that were provoked by his telescopic discoveries, The next three chapters then take up the scriptural arguments in detail, Galileo's battle with the Jesuits over the comets of 1618 and his The Assayer of 1623, and his resumption of the Copernican program with the publication of his Dialogue... (shrink)

This volume, the twenty-seventh year of published proceedings, contains papers and commentaries presented to the Boston Area Colloquium in Ancient Philosophy during academic year 2010-11. The papers treat thinkers ranging from Philolaus, Plato and Aristotle, to Plotinus.

1. There is a commonly held endoxon that idealism did not exist and could not exist before Plato, since the «Presocratics» did not yet distinguish between the material and the ideal etc. This preconception is based on the misleading conception of «Presocratics» as physicalists and the simplistic evolutionist scheme of Aristotle’s Metaph. A. In fact, religious and idealist metaphysics are attested in different archaic traditions before Plato, whereas «simple» physical theories of elements of the Milesian type did not exist before (...) the 6th century B.C. scientific revolution. 2. Those who deny the existence of idealism in Greek philosophy commonly refer to Myles F. Burnyeat. We will argue against this article on the following grounds: a) it is based on a selective and incomplete data from early Greek philosophy, b) Burnyeat understands by «idealism» subjective idealism and anti-realism. But Greek idealism as a rule is a form of objective idealism and has nothing to do with anti-realism. The two basic forms are: dualstic idealism and monistic idealism. 3. We will argue against modern naturalist interpretations of the Pythagorean first principles by Huffmann and others. Both in the table of opposites and in Philolaus πέρας καὶ ἄπειρον denote self-subsistent mathematical essences, ‘out of which’ physical bodies are composed. It is impossible to interpret “the limit and the unlimited” as physical bodies themselves or as properties of physical bodies. 4. We will argue for the Pythagorean origin of the 5th centu-ry graffiti on bones’ plates from Olbia. According to this early table of oppo-site, the body is ψεῦδος, i.e., an illusion. 5. The Zeller-Burnet interpretation of Parmenides B3 is grammatically impossible. The fragment states the identity of νοεῖν καὶ εἶναι, i.e., affirms mental nature of Being.6.The basic opposition of Parmenides’ Aletheia exactly corresponds to the basic opposition of doxa. Light is the active and thinking element, night is the «heavy», dense, corporeal substance. Sine light corresponds to Being, night corresponds to non-Being. The philosophy of Parmenides is a radical form of immaterialism and idealistic monism. (shrink)

The relationship between philosophy and medicine in antiquity has been extensively discussed by commentators and scholars. The objective of this article was to determine if it is possible to assert that the Hippocratic treatise De prisca Medicina is a criticism directed at Philolaus and, if possible, in what terms it could be stated. With this in mind, the work concentrates on the characterization of the position of the opponent of the author of said treatise in DM § 1. 15-21. (...) Particular emphasis will be placed on the terms “hypothesis” and “principle”. Thus, from four possible proposed interpretations of the first of these terms, namely: a proposition postulated but not affirmed sharply, a proposition whose veracity is supposed, a proposition that must be proved, and an object put to discussion or a purpose, the criticisms that could be at stake in DM in each of these will be outlined and then contrasted with the doctrine of the Pythagorean philosopher that can be reconstructed from the fragments attributed to him as authentic, as well as some testimonies about his medical and epistemological approaches. Finally, it was stated by way of conclusion that the Hippocratic treatise that is thematized in it can be, in various ways, conceived as a criticism of Philolaus. However, it is necessary to emphasize that this inquisition on this subject is not intended to be conclusive; rather, it seeks to provide relevant elements to this debate. (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)

Allusions to a cosmogony contained in a Vedic hymn present striking analogies to a cosmogony attributed to the Pythagoreans by Aristotle, Simplicius and Stobaeus. The aim of the paper is to evaluate the extent to which they are similar and to which their differences respond to different cultural premises.

Ancient Greek music was purely or predominantly melodic; and in such music subtleties of intonation count for much. If our sources of information about the intervals used in Greek music are not always easy to interpret, they are at any rate fairly voluminous. On the one hand we have Aristoxenus, by whom musical intervals were regarded spatially and combined and subdivided by the processes of addition and subtraction; for him the octave consisted of six tones, and the tone was exactly (...) divisible into fractions such as the half and quarter, so that the fourth was equal to two tones and a half, the fifth to three tones and a half, and so on. On the other hand we have preserved for us in Ptolemy's Harmonics the computations of a number of mathematicians, who realized correctly that intervals could only be expressed as ratios , that the octave was less than the sum of six whole tones and that this tone could not be divided into equal parts. These authorities are Archytas, the Pythagorean of the early fourth century, Eratosthenes , Didymus and Ptolemy himself . To these we must add the scale of Plato's Timaeus and, closely related to it, the computations of the pseudo-Philolaus and of Boethius himself . Aristoxenus is less easy to understand than the mathematicians because of the unscientific nature of his postulates. His importance, however, is very great, not only from his comparatively early date but because he claims to champion the direct musical consciousness against the scientific approach of some of his predecessors and contemporaries. (shrink)