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)

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)

Archytas of Tarentum, a contemporary and associate of Plato, was a famous Pythagorean, mathematician, and statesman of Tarentum. Although his works are lost and most of the fragments attributed to him were composed in later eras, they nevertheless contain valuable information about his thought. In particular, the fragments of On Law and Justice are likely based on a work by the early Peripatetic biographer Aristoxenus of Tarentum. The fragments touch on key themes of early Greek ethics, (...) including: written and unwritten laws; freedom and self-sufficiency; moderation of the emotions and cultivation of virtues; equality and the competence of the majority to participate in government; criticism of “rule by an individual”; a theory of the ideal “mixed constitution”; distributive and corrective justice and punishment, and of the rule of law. The fragments also contain one of the only positive accounts of democracy in ancient Greek philosophy. (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...

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)

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.

In his Exhortation to Philosophy (Protrepticus), the Neoplatonic philosopher Iamblichus famously preserves material culled from lost works of ancient philosophy, including dialogues of Aristotle. He also preserves a work entitled On Wisdom and ascribed to the Pythagorean philosopher Archytas of Tarentum, who was a friend and challenger of Plato. The text On Wisdom is a later Hellenistic production, probably written in the 1st century BCE, but it presents an important piece in the puzzle of reconstructing Pythagoreanism for the (...) Hellenistic and Post-Hellenistic periods. On Wisdom provides ps-Archytas' views on the nature, pursuit, and purposes of philosophy, as well as the division of the parts of knowledge. This article presents the first complete modern translation into English and analysis of this work, whilst also explaining the precise ways in which its first critic, Iamblichus, appropriates its content to Neoplatonic theories. (shrink)

This article explores in greater depth the historiographical traditions concerning Herennius Pontius, a Samnite wisdom-practitioner who is said by the Peripatetic Aristoxenus of Tarentum to have been an interlocutor of the philosophers Archytas of Tarentum and Plato of Athens. Specifically, it argues that extant speeches attributed to Herennius Pontius in the writings of Cassius Dio and Appian preserve a philosophy of “extreme proportional benefaction” among unequals. Greek theories of ethics among unequals such as those of Aristotle and (...) Archytas of Tarentum, which aim for moderation, can be distinguished from that attributed to Herennius Pontius, which is circumstantial and stipulates extreme responses to extremes. Romans, in particular Appius Claudius Caecus and Sulla, celebrate and espouse proverbial wisdom strikingly similar to the theory of “extreme proportional benefaction” associated with Herennius Pontius, and in contrast to Greek ethics of moderation. Such comparisons suggest that starting in the late fourth century BCE, Romans and Samnites may have held shared ideological principles, as defined against Greek cultural paradigms. (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)

THE surviving century of epigrams by this tedious writer was edited with a commentary by J. Geffcken in 1896, and they were included in A. Veniero's Poeti de l'Antol. Pal. and A. Olivieri's Epigrammatisti Gr. d. Magna Grecia , but the inquirer who is not content with Geffcken's explanations or with his frequent silences will rarely find satisfaction in Veniero, and Olivieri's comments are almost exclusively translated from Geffcken. I have not a great deal to offer by way of supplement, (...) but as a preliminary it may be worth while to consider the five epigrams which have been held to throw light on the poet's date, and first A.P. 6. 334, on which the authorities rely with varying degrees of confidence for placing his birth in or before 315 B.C. (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 explores the historical roots of biopolitics by investigating the structural homology between the supremely virtuous king discussed in Aristotle’s Politics and the sovereign living law advanced in On Law and Justice, accepted here as authored by Archytas of Tarentum. Archytas’s sovereign incarnates a divine law in order to ground the written law of the city and to constitute the way of life proper to the citizenry. The identity of life and law in his person exempts (...) this sovereign from the written laws he grounds just as Aristotle’s king cannot be subjected to law because he is a law unto himself. Despite this homology, Archytas’s sovereign exemplifies a highly determinate way of life fully constituted by law while an analysis of Aristotle’s king reveals a double determination of the virtuous exemplar as both sovereign and exile. This double determination both exhibits and complicates the logic of exclusion that, for Agamben, makes Western politics biopolitical from its inception. (shrink)

Scholars and editors of Hellenistic epigram have often discounted the authenticity of dialectal variance attested in the manuscript tradition, either privileging the dialectal variant that conforms to the predominant dialect in the epigram or even choosing to change attested dialect forms to produce a uniform coloring. This article argues that the addresses to earth at lines 2 and 10 of Leonidas of Tarentum Anth. Pal. 7.440 = Gow/page, HE 11 were originally Doric. I show that there are paleographic as (...) well as literary grounds for the reading. In particular, the presence of Doric forms at these two points in the epigram evoke the language of tragic lament. The findings of this article have potentially significant implications for the editing of dialectal mixture in the Greek Anthology. (shrink)

THE surviving century of epigrams by this tedious writer was edited with a commentary by J. Geffcken in 1896, and they were included in A. Veniero's Poeti de l'Antol. Pal. and A. Olivieri's Epigrammatisti Gr. d. Magna Grecia, but the inquirer who is not content with Geffcken's explanations or with his frequent silences will rarely find satisfaction in Veniero, and Olivieri's comments are almost exclusively translated from Geffcken. I have not a great deal to offer by way of supplement, but (...) as a preliminary it may be worth while to consider the five epigrams which have been held to throw light on the poet's date, and first A.P. 6. 334, on which the authorities rely with varying degrees of confidence for placing his birth in or before 315 B.C. (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 lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Explorations in Ancient and Modern Philosophy by Myles F. BurnyeatAllison Piñeros Glasscock and Elizabeth C. Shaw and Staff*BURNYEAT, Myles F. Explorations in Ancient and Modern Philosophy, vol. 4. Cambridge: Cambridge University Press, 2022. xii + 395 pp. Cloth, $120.00The eleven essays in this collection were originally published while Burnyeat was at All Souls College, Oxford (1996–2006) and during his subsequent retirement. Like volume 3 of the same series, (...) the collection was published posthumously, with editorial work undertaken by Carol Atack, Malcolm Schofield, and David Sedley. Part I contains seven essays on topics in ontology and epistemology; part II contains four essays on physics and optics. The figures examined include the usual suspects—Plato and Aristotle (plus an appearance by Aquinas)—but Burnyeat also draws our attention to some less appreciated accomplices to the ancient philosophical project: the Platonist commentator Numenius of Apamea, the Pythagorean Archytas of Tarentum, and Anaxarchus of Abdera, a follower of Democritus. The result is a collection that showcases one of Burnyeat's greatest strengths: his ability to identify the clues left for us in ancient texts and to produce from them compelling and exquisitely detailed accounts of what ancient philosophers were thinking and why.One of the final papers of the volume illustrates Burnyeat's detective acumen. "Archytas and optics" starts from the following question: Why is optics absent from the mathematical curriculum Plato sketches in the Republic? Burnyeat hypothesizes that if mathematical optics existed when the Republic was written, Plato likely excised it from the curriculum on the grounds that the discipline would lead the student to focus on visible things and their appearances. The bulk of the paper is devoted to establishing the antecedent of this conditional. Burnyeat argues that mathematical optics did exist at the time of the Republic's writing, and he posits the noncanonical Pythagorean Archytas as its founder. To recognize the significance of this lacuna in the Republic's curriculum and to provide a persuasive identification of the founder of an entire discipline is already to make a substantial contribution to scholarship. But how Burnyeat arrives at his central conclusion is equally impressive. He takes the reader on a tour of Aristotle, Plato, and Iamblichus, fragment 4 of Archytas, and the Apologia of Apuleius (whom readers might better recognize as the novelist responsible for The Golden [End Page 345] Ass). The result is not only an answer to the paper's central question, but a deeper understanding of the broader intellectual network in which canonical figures like Plato and Aristotle operated.No fragment is too small to catch Burnyeat's notice, nor is any line in a manuscript too faint. Part I of the collection includes Burnyeat's famous paper "Kinēsis vs. energeia: a much-read passage in (but not of) Aristotle's Metaphysics." The central argument is that Metaphysics 9.6.1048b18–35 is out of place. It was written by Aristotle for a different context and should not be printed in book 9. Because this article is so well known, I will not dwell on the details of the argument, but once again Burnyeat's methodology is worthy of comment. The first part of the paper offers a careful examination of the Metaphysics's manuscript tradition that attends both to what is present and to what is absent. For example, we learn that the focus passage is missing from an entire branch of the tradition, which Burnyeat suggests is the result of a learned excision. Later, Burnyeat develops a psychological sketch of the scribe of manuscript Ab beginning from the observation that a faint line is drawn through part of the focus passage. He argues that the scribe's motivation is not disapproval of the passage's contents but a desire to keep his text and commentary in sync. Observations like these provide the foundation for Burnyeat's thesis about the philosophical import of the focus passage, and they demonstrate that the physical record can be just as vital to reconstructions of ancient philosophy as the words that the record preserves.Occasionally, Burnyeat offers more direct admonitions to his readers about how to approach ancient philosophy. A key lesson... (shrink)

The main source of Archytas, fr. 1 Diels-Kranz is Porphyr. in Ptol. harmon. p. 56,5–57,27 Düring; there is also an extensive quotation of its initial part in Nicomachus, Introd. Arithm. p. 6,16–7,5 Hoche. In recent years both the text and the interpretation of this fragment, whose authenticity was questioned by W. Burkert, have been re-examined, and a good deal of progress has been made especially by paying more attention to the nature of Nicomachus' quotation and its context.

The solution attributed to Archytas for the problem of doubling the cube is a landmark of the pre-Euclidean mathematics. This paper offers textual arguments for a new reading of the text of Archytas’ solution for doubling the cube, and an approach to the solution which fits closely with the new reading. The paper also reviews modern attempts to explain the text, which are as complicated as the original, and its connections with some xvi-century mathematical results, without any documented (...) relation to Archytas’ doubling the cube. (shrink)

Intent upon harmonizing doctrines of their predecessors, some Neoplatonic commentators are faced with a problem of resolving doctrinal discrepancies so as to restore the συµφωνία in the history of philosophy. This article considers a particular example of this attempt ats harmonization: how Simplicius reconciles Aristotle's Categories with the Neopythagorean doctrine of the Pseudo-Archytas. The chronological inversion introduced by the counterfeiter produces remarkable effects on the late Platonic doctrine about general terms, to the extent that a commentator such as Simplicius (...) works to reduce the dissonance between Archytas' and Aristotle's words. This paper has three aims: to restore the general grid that Simplicius uses for reading and commenting on Archytas through Aristotle; to identify the exegetical strategies aimed at a doctrinal reconciliation; to consider a specific case, provided by the doctrine of weight, which engenders a new physical theory by Simplicius. (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 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)

This article aims to shed light on certain aspects of Iamblichus’ theory of time that have not been sufficiently examined to date in the scholarly literature. As of today, there are a mere handful of scholarly works tackling Iamblichus’ solutions to the paradoxes of time in particular, and his contribution to the developments of the Neoplatonic theory of the subject more generally. This article attempts to redress the lack of literature on this topic by examining Iamblichus’ response to Aristotle’s and (...) Pseudo-Archytas’ theories of time. It begins with a brief survey of the philosophical developments that led to and were formative for Iamblichus’ philosophical explorations of the area in question. Then it moves on to provide a detailed account of Iamblichus’ own unique and puzzling theory of time. The author applies the method of comparative analysis, scrutinizing Iamblichus’ solution to the paradoxes of time against the backdrop of Aristotle’s and Pseudo-Archytas’ theories. The author identifies firm scholarly grounds for doing so from within the tradition of Iamblichus studies initiated by the ground-breaking research of Shmuel Sambursky and Salomon Pines and continued, inter alia, in the subtly nuanced analysis of Richard Sorabji and John Dillon. The author concludes that Iamblichus successfully resolved the paradoxes of time and that his conception lent itself to a more effective highlighting of the ordering function of time. (shrink)

This article aims to shed light on certain aspects of Iamblichus’ theory of time that have not been sufficiently examined to date in the scholarly literature. As of today, there are a mere handful of scholarly works tackling Iamblichus’ solutions to the paradoxes of time in particular, and his contribution to the developments of the Neoplatonic theory of the subject more generally. This article attempts to redress the lack of literature on this topic by examining Iamblichus’ response to Aristotle’s and (...) Pseudo-Archytas’ theories of time. It begins with a brief survey of the philosophical developments that led to and were formative for Iamblichus’ philosophical explorations of the area in question. Then it moves on to provide a detailed account of Iamblichus’ own unique and puzzling theory of time. The author applies the method of comparative analysis, scrutinizing Iamblichus’ solution to the paradoxes of time against the backdrop of Aristotle’s and Pseudo-Archytas’ theories. The author identifies firm scholarly grounds for doing so from within the tradition of Iamblichus studies initiated by the ground-breaking research of Shmuel Sambursky and Salomon Pines and continued, inter alia, in the subtly nuanced analysis of Richard Sorabji and John Dillon. The author concludes that Iamblichus successfully resolved the paradoxes of time and that his conception lent itself to a more effective highlighting of the ordering function of time. (shrink)

AëtiusPlacita1.3.8, in the chapterOn Principles, provides a systematic overview of Pythagorean thought, which can be instructively compared with ps.-ArchytasOn Principles, provided both fragments of the latter are kept together.

The figure of the cordial host of the Academy, who invited the most gifted mathematicians and cultivated pure research, whose keen intellect was able if not to solve the particular problem then at least to show the method for its solution: this figure is quite familiar to students of Greek science. But was the Academy as such a center of scientific research, and did Plato really set for mathematicians and astronomers the problems they should study and methods they should use? (...) Our sources tell about Plato's friendship or at least acquaintance with many brilliant mathematicians of his day (Theodorus, Archytas, Theaetetus), but they were never his pupils, rather vice versa -- he learned much from them and actively used this knowledge in developing his philosophy. There is no reliable evidence that Eudoxus, Menaechmus, Dinostratus, Theudius, and others, whom many scholars unite into the group of so-called "Academic mathematicians," ever were his pupils or close associates. Our analysis of the relevant passages (Eratosthenes' Platonicus, Sosigenes ap. Simplicius, Proclus' "Catalogue of geometers", and Philodemus' "History of the Academy", etc.) shows that the very tendency of portraying Plato as the architect of science goes back to the early Academy and is born out of interpretations of his dialogues. (shrink)

I present a systematic interpretation of the foundational purpose of constructions in ancient Greek geometry. I argue that Greek geometers were committed to an operationalist foundational program, according to which all of mathematics—including its entire ontology and epistemology—is based entirely on concrete physical constructions. On this reading, key foundational aspects of Greek geometry are analogous to core tenets of 20th-century operationalist/positivist/constructivist/intuitionist philosophy of science and mathematics. Operationalism provides coherent answers to a range of traditional philosophical problems regarding classical mathematics, such (...) as the epistemic warrant and generality of diagrammatic reasoning, superposition, and the relation between constructivism and proof by contradiction. Alleged logical flaws in Euclid can be interpreted as sound operationalist reasoning. Operationalism also provides a compelling philosophical motivation for the otherwise inexplicable Greek obsession with cube duplication, angle trisection, and circle quadrature. Operationalism makes coherent sense of numerous specific choices made in this tradition, and suggests new interpretations of several solutions to these problems. In particular, I argue that: Archytas’s cube duplication was originally a single-motion machine; Diocles’s cissoid was originally traced by a linkage device; Greek conic section theory was thoroughly constructive, based on the conic compass; in a few cases, string-based constructions of conic sections were used instead; pointwise constructions of curves were rejected in foundational contexts by Greek mathematicians, with good reason. Operationalism enables us to view the classical geometrical tradition as a more unified and philosophically aware enterprise than has hitherto been recognised. (shrink)