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  1. Pythagorean Geometry and Fundamental Constants.Michael A. Sherbon - manuscript
    The Cosmological Circle from ancient geometry, with its right triangles, and the ratios of the Pythagorean Table are found to be harmonically related to the fundamental physical constants. After a brief history of harmonic mathematics, harmonic values are calculated for the speed of light constant, gravitational constant, Planck's constant, and the inverse fine-structure constant. We then calculate the harmonic of electron mass and proton mass, showing the related Pythagorean/Cosmological Circle harmonics; and speculate on geometry and symmetry.
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  2. Averiguando a Filolao.Lucas - forthcoming - In D. S. (ed.), Uranie. Guelfe noir publisher.
    Averiguando la esboza de Filolao, tomando cuenta del recurso acesorio que hizo verodImilmente a datos observacionales.
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  3. Mathematical Explanation: A Pythagorean Proposal.Samuel Baron - forthcoming - British Journal for the Philosophy of Science.
    Mathematics appears to play an explanatory role in science. This, in turn, is thought to pave a way toward mathematical Platonism. A central challenge for mathematical Platonists, however, is to provide an account of how mathematical explanations work. I propose a property-based account: physical systems possess mathematical properties, which either guarantee the presence of other mathematical properties and, by extension, the physical states that possess them; or rule out other mathematical properties, and their associated physical states. I explain why Platonists (...)
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  4. 'Archytas: Author and Authenticator of Pythagoreanism'.Phillip Sidney Horky - forthcoming - In Constantinos Macris, Luc Brisson & Tiziano Dorandi (eds.), Pythagoras Redivivus: Studies on the Texts Attributed to Pythagoras and the Pythagoreans. 53757 Sankt Augustin, Germany:
    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 (...)
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  5. A Case Study in Arabic Doxography: Šahrastānī's Account of Pythagoras and Its Ismāʻīlī Background.Fedor Benevich - 2022 - In Andreas Lammer & Mareike Jas (eds.), Received Opinions: Doxography in Antiquity and the Islamic World. Brill.
  6. Solar Motion and Lunar Eclipses in Philolaus’ Cosmological System.Dirk L. Couprie - 2022 - Apeiron 55 (4):627-645.
    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 (...)
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  7. A Centralidade do Fogo na Cosmogonia do Pitagórico Filolau.Erick D' Luca - 2022 - Pólemos 11 (22):1-21.
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  8. Pythagoreans and Samnite Philosophers.Phillip Horky - 2022 - In David Konstan, Myrto Garani & Gretchen Reydams-Schils (eds.), The Oxford Handbook of Roman Philosophy. Oxford University Press, Usa.
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  9. Socratic Death Rattles : Pythagorean Hearing and Listening in Plato's Phaedo.Kris McLain & Anne-Marie Schultz - 2022 - In Jill Gordon (ed.), Hearing, Sound, and the Auditory in Ancient Greece. Indiana University Press.
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  10. Acheloios, Thales, and the Origin of Philosophy: A Response to the Neo-Marxians.Nicholas J. Molinari - 2022 - Oxford: Archaeopress.
    This book presents a new account of Thales based on the idea that Acheloios, a deity equated with water in the ancient Greek world and found in Miletos during Thales’ life, was the most important cultic deity influencing the thinker, profoundly shaping his philosophical worldview. In doing so, it also weighs in on the metaphysical and epistemological dichotomy that seemingly underlies all academia—the antithesis of the methodological postulate of Marxian dialectical materialism vis-à-vis the Platonic idea of fundamentally real transcendental forms. (...)
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  11. Pythagorean Women.Caterina Pell- - 2022 - Cambridge University Press.
    The Pythagorean women are a group of female philosophers who were followers of Pythagoras and are credited with authoring a series of letters and treatises. In both stages of the history of Pythagoreanism – namely, the fifth-century Pythagorean societies and the Hellenistic Pythagorean writings – the Pythagorean woman is viewed as an intellectual, a thinker, a teacher, and a philosopher. The purpose of this Element is to answer the question: what kind of philosopher is the Pythagorean woman? The traditional picture (...)
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  12. Dorota Dutsch, Pythagorean Women Philosophers: Between Belief and Suspicion. [REVIEW]Caterina Pellò - 2022 - Ancient Philosophy Today 4 (2):237-241.
    Ancient Philosophy Today, Volume 4, Issue 2, Page 237-241, October, 2022.
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  13. Irene Caiazzo, Constantinos Macris, and Aurélien Robert, Eds., Brill’s Companion to the Reception of Pythagoras and Pythagoreanism in the Middle Ages and the Renaissance. (Brill’s Companions to Classical Reception 24.) Leiden: Brill, 2022. Pp. Xv, 496; Color and Black-and-White Figures. $215. ISBN: 978-9-0043-7362-4. Table of Contents Available Online at Https://Brill.Com/View/Title/38721. [REVIEW]Meryem Sebti - 2022 - Speculum 97 (4):1169-1170.
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  14. Brill's Companion to the Reception of Pythagoras and Pythagoreanism in the Middle Ages and the Renaissance.Irene Caiazzo, Constantinos Macris & Aurélien Robert (eds.) - 2021 - Leiden ; Boston: Brill.
    For the first time, the reader can have a synoptic view of the reception of Pythagoras and Pythagoreanism in the Middle Ages and the Renaissance, East and West, in a multicultural perspective. All the major themes of Pythagoreanism are addressed, from mathematics, number philosophy and metaphysics to ethics and religious thought.
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  15. Woman Philosopher of the Pythagorean School About Human Nature and Upbringing.Feano of Croton, Mia of Croton, Melissa, Fintis of Spartan, Esara of Lucan & Ptolemais of Cyrene - 2021 - Філософія Освіти 27 (1):239-260.
    The article offers academic translation into Ukrainian of a number of works by Pythagorean woman philosophers, which reveal the problems of human nature and personality education. The focus is on such pseudo-epigraphs of ancient woman thinkers as two letters by Theano of Crotone, letters of Miya of Crotone and Melissa, as well as treatises by Fintys of Sparta "On a woman prudence", Aesara of Lucania "On human nature" and excerpts from Porphyry’s "Pythagorean music" which contain fragments of the works of (...)
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  16. Pitagorejczycy, albo pochwała metafizyki.Jerzy Gołosz - 2021 - Filozofia i Nauka. Studia Filozoficzne I Interdyscyplinarne 1 (9):251-276.
    This paper attempts to demonstrate that the conviction about the harmony and order of the world was a fundamental metaphysical principle of the Pythagoreans. This harmony and order were primarily sought in the structures of arithmetics, yet following the discovery of incommensurable magnitudes (irrational numbers, as we now call them), the Pythagoreans began to see geometrical structure as a fundamental part of the world. On the example of the Pythagoreans’ metaphysics and science, the paper shows the mutual relations between metaphysics (...)
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  17. Hilbert Arithmetic as a Pythagorean Arithmetic: Arithmetic as Transcendental.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (54):1-24.
    The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis of the world in a Pythagorean manner. Hilbert arithmetic unifies the foundations of mathematics (Peano arithmetic and set theory), foundations of physics (quantum mechanics and information), and philosophical transcendentalism (Husserl’s phenomenology) into a formal theory and mathematical structure literally following Husserl’s tracе of “philosophy as a rigorous science”. In the pathway to that objective, Hilbert arithmetic identifies by itself information related to finite sets and series and quantum (...)
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  18. The “Pythagorean” “Theorem” and the Rant of Racist and Civilizational Superiority – Part 2.C. K. Raju - 2021 - Arụmarụka 1 (2):76-105.
    Previously we saw that racist prejudice is supported by false history. The false history of the Greek origins of mathematics is reinforced by a bad philosophy of mathematics. There is no evidence for the existence of Euclid. The “Euclid” book does not contain a single axiomatic proof, as was exposed over a century ago. Such was never the intention of the actual author. The book was brazenly reinterpreted, since axiomatic proof was a church political requirement, and used in church rational (...)
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  19. Euclid” Must Fall: The “Pythagorean” “Theorem” and the Rant of Racist and Civilizational Superiority - Part 1.C. K. Raju - 2021 - Arụmarụka 1 (1):127-156.
    To eliminate racist prejudices, it is necessary to identify the root cause of racism. American slavery preceded racism, and it was closely associated with genocide. Accordingly, we seek the unique cause of the unique event of genocide + slavery. This was initially justified by religious prejudice, rather than colour prejudice. This religious justification was weakened when many Blacks converted to Christianity, after the trans-Atlantic slave trade. The curse of Kam, using quick visual cues to characterize Blacks as inferior Christians, was (...)
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  20. Armonia, concordia e politica in Eraclito e nei pitagorici.Diego Garcia Rincon - 2021 - Eirene. Studia Graeca Et Latina 1 (57):93-118.
    This paper examines the relation between Pythagorean and Heraclitean political views. I argue that for Pythagoras, Heraclitus, and Archytas the cosmological and musical notions of harmony (ἁρμονία) and the related notion of concord (ὁμόνοια) have an intrinsic political significance. These thinkers variously reflect upon political harmony and concord, and agree that a crucial condition for it is law (νόμος), which according to Pythagoras and Heraclitus has a divine origin. I begin with the Heraclitean fragments 22 B51, 54, 72, and 114 (...)
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  21. Upbringing and Education of Children in Context Letters of Pythagorean Woman Philosophers.Vitalii Turenko - 2021 - Філософія Освіти 27 (1):228-238.
    The article reveals in detail the understanding of raising children in the context of two pseudo-epigraphic letters of Pythagorean wonan thinkers – Theano and Myia of Crotone. Based on these letters, it was found that pedagogical issues were important in general for the whole Pythagorean tradition. In fact, we can say that this early Greek philosophical school was the first to systematically and comprehensively approach the problem of upbringing and education in ancient society. It is hypothesized that this topic is (...)
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  22. On Law and Justice Attributed to Archytas of Tarentum.Johnson Monte & P. S. Horky - 2020 - In David Wolfsdorf (ed.), Early Greek Ethics. Oxford: pp. 455-490.
    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 (...)
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  23. Cosmic Spiritualism Among the Pythagoreans, Stoics, Jews, and Early Christians.Phillip Sidney Horky - 2019 - In Cosmos in the Ancient World. Cambridge, UK: pp. 270-94.
    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 (...)
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  24. When Did Kosmos Become the Kosmos?Phillip Sidney Horky - 2019 - In Cosmos in the Ancient World. Cambridge: pp. 22-41.
    When did kosmos come to mean *the* kosmos, in the sense of ‘world-order’? I venture a new answer by examining later evidence often underutilised or dismissed by scholars. Two late doxographical accounts in which Pythagoras is said to be first to call the heavens kosmos (in the anonymous Life of Pythagoras and the fragments of Favorinus) exhibit heurematographical tendencies that place their claims in a dialectic with the early Peripatetics about the first discoverers of the mathematical structure of the universe. (...)
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  25. Cosmos in the Ancient World.Phillip Sidney Horky (ed.) - 2019 - Cambridge University Press.
    How did the ancient Greeks and Romans conceptualise order? This book answers that question by analysing the formative concept of kosmos in ancient literature, philosophy, science, art, and religion. This concept encouraged the Greeks and Romans to develop theories to explain core aspects of human life, including nature, beauty, society, politics, the individual, and what lies beyond human experience. Hence, Greek kosmos, and its Latin correlate mundus, are subjects of profound reflection by a wide range of important ancient figures, including (...)
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  26. The Papyrological Tradition on Pythagoras and the Pythagoreans.Leonid Zhmud - 2019 - In Christian Vassallo (ed.), Presocratics and Papyrological Tradition: A Philosophical Reappraisal of the Sources.Proceedings of the International Workshop Held at the University of Trier. De Gruyter. pp. 111-146.
  27. Empedocles’ Emulation of Anaxagoras and Pythagoras.Dmitri Panchenko - 2018 - Apeiron 51 (4):453-457.
    Journal Name: Apeiron Issue: Ahead of print.
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  28. The Lives of Pythagoras: A Proposal for Reading Pythagorean Metempsychosis.Caterina Pellò - 2018 - Rhizomata 6 (2):135-156.
    According to Dicaearchus, metempsychosis was the best known among Pythagoras’ teachings. In this paper, I investigate two features of Pythagorean metempsychosis: its non-retributive character and its epistemological value. I argue that the Pythagoreans did not conceive of reincarnation as a punishment for the wicked and a reward for the virtuous, but rather as a way to gain experience, knowledge and therefore wisdom. This reading enables us to throw light on the puzzling list of Pythagoras’ past lives, which includes Aethalides son (...)
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  29. The Metaphysics of the Pythagorean Theorem by Robert Hahn.Jean Rioux - 2018 - Review of Metaphysics 72 (2):383-385.
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  30. PYTHAGOREANISM - (G.) Cornelli, (R.) McKirahan, (C.) Macris (Edd.) On Pythagoreanism. (Studia Praesocratica 5.) Pp. Xx + 532, Figs. Berlin and Boston: De Gruyter, 2013. Cased, €109.95, US$154. ISBN: 978-3-11-031845-6. [REVIEW]Giulia De Cesaris - 2017 - The Classical Review 67 (1):16-18.
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  31. Wigner’s Puzzle and the Pythagorean Heuristic.Jane McDonnell - 2017 - Synthese 194 (8):2931-2948.
    It is argued that mathematics is unreasonably effective in fundamental physics, that this is genuinely mysterious, and that it is best explained by a version of Pythagorean metaphysics. It is shown how this can be reconciled with the fact that mathematics is not always effective in real world applications. The thesis is that physical structure approaches isomorphism with a highly symmetric mathematical structure at very high energy levels, such as would have existed in the early universe. As the universe cooled, (...)
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  32. L’Harmonie des Sirènes, du Pythagorisme Ancien À Platon_ _, Written by Viltanioti Irini-Fotini.André Motte - 2017 - International Journal of the Platonic Tradition 11 (2):217-219.
  33. On Being Reminded of Heraclitus by the Motifs in Plato’s Phaedo.Catherine Rowett - 2017 - In Enrica Fantino, Ulrike Muss, Charlotte Schubert & Kurt Sier (eds.), Heraklit Im Kontext. De Gruyter. pp. 373-414.
    In this paper I argue that we can better understand Plato’s Phaedo, if we don’t concentrate solely on the hints of Pythagoreanism among the characters and their doctrines, as though that were the principal key to the dialogue’s dialec- tical targets. I suggest that the dialogue is intended to make us think of the meta-physics of at least one other Presocratic predecessor, besides any Pythagorean influence (which may be much less than has been thought). Not least among the thinkers of (...)
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  34. Heraclitus on Pythagoras.Leonid Zhmud - 2017 - In Charlotte Schubert, Ulrike Muss, Kurt Sier & Enrica Fantino (eds.), Heraklit Im Kontext. De Gruyter. pp. 171-186.
  35. Kepler: Analogies in the Search for the Law of Refraction.Carlos Alberto Cardona - 2016 - Studies in History and Philosophy of Science Part A 59:22-35.
    This paper examines the methodology used by Kepler to discover a quantitative law of refraction. The aim is to argue that this methodology follows a heuristic method based on the following two Pythagorean principles: (1) sameness is made known by sameness, and (2) harmony arises from establishing a limit to what is unlimited. We will analyse some of the author's proposed analogies to find the aforementioned law and argue that the investigation's heuristic pursues such principles.
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  36. David Sider and Dirk Obbink , Doctrine and Doxography: Studies on Heraclitus and Pythagoras.Patricia Curd - 2016 - Rhizomata 4 (2):276-287.
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  37. Visa to Heaven: Orpheus, Pythagoras, and Immortality.Alex V. Halapsis - 2016 - ScienceRise 25 (8):60-65.
    The article deals with the doctrines of Orpheus and Pythagoras about the immortality of the soul in the context of the birth of philosophy in ancient Greece. Orpheus demonstrated the closeness of heavenly (divine) and earthly (human) worlds, and Pythagoras mathematically proved their fundamental identity. Greek philosophy was “an investment in the afterlife future”, being the product of the mystical (Orpheus) and rationalist (Pythagoras) theology.
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  38. Number and Reality: Sources of Scientific Knowledge.Alex V. Halapsis - 2016 - ScienceRise 23 (6):59-64.
    Pythagoras’s number doctrine had a great effect on the development of science. Number – the key to the highest reality, and such approach allowed Pythagoras to transform mathematics from craft into science, which continues implementation of its project of “digitization of being”. Pythagoras's project underwent considerable transformation, but it only means that the plan in knowledge is often far from result.
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  39. Der Philosophiebegriff Im Florentinischen Renaissanceplatonismus Zwischen Pythagoreismus Und Aristotelismus.Jens Lemanski - 2016 - Archiv für Begriffsgeschichte 58:27-65.
    The paper examines the definitions of the concept ›philosophy‹ resp. ›the philosopher‹ in Florentine renaissance Platonism, namely Marsilio Ficino and his scholar Francesco di Zanobi Cattani da Diacceto. Following Socrates and Pythagoras, Ficino distinguishes between mundane philosophy and divine sapientia. In contrast to his teacher, Diacceto's Aristotelism rejects the Pythagoreanism and connects philosophy with sapientia. In order to show how the differences between Ficino and Diacceto emerge, three more contemporaries are taken into consideration: Christoforo Landino, Angelo Poliziano and Giovanni Pico (...)
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  40. Plato and Pythagoreanism by Phillip Sidney Horky.Gabriele Cornelli - 2015 - American Journal of Philology 136 (2):353-357.
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  41. Wegetarianizm a Ofiara Ze Zwierząt W Starożytności – Pomiędzy Postulatem a Praktyką.Katarzyna Kleczkowska - 2015 - Przeglad Filozoficzny - Nowa Seria 94.
    The article concerns on the topic of vegetarianism in the context of the importance of animal sacrifice in ancient Greece and Rome. In the first part the author analyses the function of animal sacrifice in ancient world, focusing on the religious and social meaning of eating the meat offered to gods on an altar. In the second part she presents the figures of vegetarians, who had to face the problem of obligatory character of sacrifice. The author focuses especially on the (...)
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  42. How Musical Was Heraclitus’ Harmony? A Reassessment of 22 B 8, 10, 51 DK.Maria Michela Sassi - 2015 - Rhizomata 3 (1).
    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, (...)
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  43. Plato and Pythagoreanism by Phillip Horky. [REVIEW]Eugenio Benitez - 2014 - Review of Metaphysics 68 (2):429-431.
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  44. Concept of ‘Rebirth’ in Pythagorean and Upanishadic Philosophy.Shakuntala Gawde - 2014 - Dhimahi 5:149-167.
  45. A History of Pythagoreanism.Carl A. Huffman (ed.) - 2014 - Cambridge University Press.
    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, (...)
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  46. Plato and Pythagoreanism, by Phillip Sidney Horky.Richard McKirahan - 2014 - Ancient Philosophy 34 (2):415-418.
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  47. Phillip Sidney Horky. Plato and Pythagoreanism. Oxford: Oxford University Press, 2013. Pp. 320. £47.99. [REVIEW]Joseph G. Miller - 2014 - Hopos: The Journal of the International Society for the History of Philosophy of Science 4 (2):391-393.
  48. Pythagoras and the Creation of Knowledge.Jose R. Parada-Daza & Miguel I. Parada-Contzen - 2014 - Open Journal of Philosophy 4 (1):68-74.
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  49. Plato and Pythagoreanism by Phillip Sidney Horky.Federico M. Petrucci - 2014 - Journal of the History of Philosophy 52 (4):837-838.
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  50. The Pythagorean Society and Politics.Catherine Rowett - 2014 - In Carl Huffman (ed.), A History of Pythagoreanism. Cambridge University Press. pp. 112-130.
    Pythagoreans dominated the political scene in southern Italy for nearly a century in the late 6th to 5th century BC. What was the secret of their political success and can their political, social and economic policies be assessed in the customary terms with which historians try to analyse ancient societies? I argue that they cannot, and that the Pythagorean approach to politics was sui generis, and successful because it was based on ideas, not force or popular demagogy.
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