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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. A New Type of Neutrosophic Set in Pythagorean Fuzzy Environment and Applications to Multi-criteria Decision Making.Mahmut Can Bozyigit, Florentin Smarandache, Murat Olgun & Mehmet Unver - 2023 - International Journal of Neutrosophic Science 20 (2):107-134.
    In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by (...)
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  5. Ethical Issues Related to the Predominant Weltbild: The Pythagorean vs. The Post-Einstein Age.Renate C.-Z.-Quehenberger - 2023 - In Raffaela Giovagnoli & Robert Lowe (eds.), The Logic of Social Practices II. Springer Nature Switzerland. pp. 115-146.
    For ancient pre-Socratic societies the living pattern of the Universe was—according to Plato—also the blueprint for the organizational structures within a society. Divine order and equilibrium were the universal principles and the theoretical construct governing nature around us and the entire cosmos. The old Theory of Everything (ToE) as it was mathematically conceptualized by Pythagoras and visualized by Plato—in the 5 synonymous regular forms—epitomized the principle of harmony. With the recent rediscovery of Plato’s 5th element we are able to understand (...)
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  6. Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns by Arkady Plotnitsky (review).Noam Cohen - 2023 - Review of Metaphysics 77 (2):359-361.
    In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns by Arkady PlotnitskyNoam CohenPLOTNITSKY, Arkady. Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns. Cham: Springer, 2023. xvi + 294 pp. Cloth, $109.99The limits of thought in its relations to reality have defined Western philosophical inquiry from its very beginnings. The shocking discovery of the incommensurables in Greek mathematics (...)
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  7. A Epistemologia Numérica de Filolau.Erick D'Luca - 2023 - Cadernos: Coleção Do Encontro Nacional de Pesquisa Na Graduação Em Filosofia da Universidade de Brasília.
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  8. The Pythagorean method in the Philebus.Alexandre Losev - 2023 - Philosophia: E-Journal for Philosophy and Culture 30:207-228.
    The well-known connection between the extant fragments of Philolaus and Plato’s Philebus is examined in its methodological aspect. By drawing on more texts, it is shown that Plato was aware of an explanatory scheme that can be attributed to Pythagoreanism. His attempt to modify it is also outlined, which sets the historical-philosophical perspective.
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  9. Donne Pitagoriche (VI-IV secolo a.C.).Caterina Pellò - 2023 - Archivio Delle Filosofe.
  10. 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.
  11. 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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  12. A Centralidade do Fogo na Cosmogonia do Pitagórico Filolau.Erick D' Luca - 2022 - Pólemos 11 (22):1-21.
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  13. Pitagora e il pitagorismo.Nuccio D'Anna - 2022 - Roma: Edizioni Arkeios.
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  14. Pythagoreans and Samnite philosophers.Phillip Horky - 2022 - In David Konstan, Myrto Garani & Gretchen Reydams-Schils (eds.), The Oxford Handbook of Roman Philosophy. New York: Oxford University Press, Usa.
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  15. 'Italic Pythagoreanism in the Hellenistic Age'.Phillip Horky - 2022 - In David Konstan, Myrto Garani & Gretchen Reydams-Schils (eds.), The Oxford Handbook of Roman Philosophy. New York: Oxford University Press, Usa. pp. 3-26.
    This chapter pursues an understanding of what Cicero thought 'Italic' philosophy to be, and proceeds to develop a broader account of how Cicero's version compares with the surviving textual evidence and testimonia from the Hellenistic period of the philosophy of the 'Italic' philosophers, including the Lucanians 'Ocellus', 'Eccelus', and 'Aresas/Aesara', and the Rudian Ennius. Special focus is placed on their theories of cosmology, psychology, and law. Collocation of 'Italic' with 'Pythagorean' philosophy of this era aids in building a more comprehensive (...)
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  16. 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. Bloomington, Indiana: Indiana University Press.
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  17. 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. Bloomington, Indiana: Indiana University Press.
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  18. 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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  19. 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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  20. 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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  21. 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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  22. 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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  23. The World-Soul as the Principal of Unity in the Pythagorean Philosophy: Monad.Aynur Çinar - 2021 - Cumhuriyet İlahiyat Dergisi 25 (2):695-711.
    Pythagoras and Pythagoreanism have a different position in the ancient philosophy tradition. The reason for this is the eclectical structure of Pythagoreanism which has syncretized from Orphism, Indian and Egyptian religions with philosophy. Orphism of these religions is especially important for affecting Pythagoreanism the most and giving to the ancient Greek religion a mystical content. Orphism which is a mystery cult is based on Orpheus, the poet, who sometimes is identified with Pythagoras in philosophy and the history of religions. Orpheus, (...)
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  24. 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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  25. Lacan and the Pythagoreans: a note on the background to Lacan’s Seminar VIII.John Gale - 2021 - Vestigia 3 (1):81-99.
    This article endeavours to provide the context to a digression in Lacan’s Seminar viii concerning the Pythagoreans, within the Vorlage of the history of ancient medicine. This shows the philosophical and historical richness that lies behind the Lacanian corpus, while illustrating the manifold pitfalls that await the uncritical reader who may take Lacan’s text merely at face value. First, the author suggests that Lacan’s investigation into the meaning of ἔρως and desire in Plato’s Symposium, cannot be separated from Platonism as (...)
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  26. 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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  27. 'Archytas: Author and Authenticator of Pythagoreanism'.Phillip Sidney Horky - 2021 - In Constantinos Macris, Luc Brisson & Tiziano Dorandi (eds.), Pythagoras Redivivus: Studies on the Texts Attributed to Pythagoras and the Pythagoreans. Academia – ein Verlag in der Nomos Verlagsgesellschaft. pp. 141-76.
    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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  28. 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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  29. 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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  30. 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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  31. 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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  32. 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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  33. Pitagora, il padre di tutti i teoremi.Umberto Bottazzini - 2020 - Bologna: Il mulino.
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  34. On Law and Justice Attributed to Archytas of Tarentum.Johnson Monte & P. S. Horky - 2020 - In David Conan Wolfsdorf (ed.), Early Greek Ethics. Oxford: Oxford University Press. 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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  35. Cosmos in the Ancient World.Phillip Sidney Horky (ed.) - 2019 - New York: 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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  36. Cosmic Spiritualism among the Pythagoreans, Stoics, Jews, and Early Christians.Phillip Sidney Horky - 2019 - In Cosmos in the Ancient World. New York: Cambridge University Press. 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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  37. When did Kosmos become the Kosmos?Phillip Sidney Horky - 2019 - In Cosmos in the Ancient World. New York: Cambridge University Press. 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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  38. Pitagora e l'Egitto: le arti sapienti per la tutela della vita.Francesco Lopez - 2019 - Pisa: Pisa University Press.
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  39. 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.
  40. Pseudo-Archytas and the categories.Myrto Hatzimichali - 2018 - In Jenny Bryan, Robert Wardy & James Warren (eds.), Authors and Authorities in Ancient Philosophy. Cambridge: Cambridge University Press.
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  41. Aristoxenus of Tarentum: The Pythagorean Precepts : An Edition of and Commentary on the Fragments with an Introduction.Carl A. Huffman (ed.) - 2018 - Cambridge: Cambridge University Press.
    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 (...)
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  42. Pythagoras.Alicia Klepeis - 2018 - Hallandale, FL: Mitchell Lane Publishers.
    Mathematician. Philosopher. World traveler. Pythagoras was an intelligent and curious scholar and teacher. While he¿s best-known for the Pythagorean theorem, he shared ideas about numbers, animals, and many other areas of knowledge with his students. Since none of his writings were left behind, it¿s not always easy for historians to know what¿s true about Pythagoras and what may be legendary. What does seem apparent is that he was a vegetarian but not a trendy dresser. Some people saw him as godlike. (...)
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  43. 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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  44. 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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  45. The Metaphysics of the Pythagorean Theorem by Robert Hahn.Jean Rioux - 2018 - Review of Metaphysics 72 (2):383-385.
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  46. Iamblichus' response to Aristotle's and Pseudo-Archytas' theories of time.Sergey Trostyanskiy - 2018 - In Sotiris Mitralexis & Marcin Podbielski (eds.), Christian and Islamic philosophies of time. Wilmington, Delaware: Vernon Press.
  47. Pythagore juste et parfait: philosophie ou ésotérisme?Michel Weber - 2018 - [Mazy]: Les Éditions Chromatika.
    Quel est le secret de Pythagore? On pourrait avancer que, par défi nition, s'il y a secret, il est caché et n’est pas dévoilable, ou ne sera pas dévoilé. Le vrai secret est celui dont on ne soupçonne même pas l’existence. On peut toutefois approcher tangentiellement le coeur du pythagorisme à partir d’un idéal qui a traversé les âges.
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  48. 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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  49. The Pythagorean World: Why Mathematics Is Unreasonably Effective In Physics.Jane McDonnell - 2017 - Cham: Imprint: Palgrave Macmillan.
    This book explores the persistence of Pythagorean ideas in theoretical physics. It shows that the Pythagorean position is both philosophically deep and scientifically interesting. However, it does not endorse pure Pythagoreanism; rather, it defends the thesis that mind and mathematical structure are the grounds of reality. The book begins by examining Wigner's paper on the unreasonable effectiveness of mathematics in the natural sciences. It argues that, whilst many issues surrounding the applicability of mathematics disappear upon examination, there are some core (...)
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  50. 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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