Download or read book Mathematics Useful for Understanding Plato written by Theon (of Smyrna.) and published by . This book was released on 1979 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numbers Rule written by George Szpiro and published by Princeton University Press. This book was released on 2020-11-03 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author takes the general reader on a tour of the mathematical puzzles and paradoxes inherent in voting systems, such as the Alabama Paradox, in which an increase in the number of seats in the Congress could actually lead to a reduced number of representatives for a state, and the Condorcet Paradox, which demonstrates that the winner of elections featuring more than two candidates does not necessarily reflect majority preferences. Szpiro takes a roughly chronological approach to the topic, traveling from ancient Greece to the present and, in addition to offering explanations of the various mathematical conundrums of elections and voting, also offers biographical details on the mathematicians and other thinkers who thought about them, including Plato, Pliny the Younger, Pierre Simon Laplace, Thomas Jefferson, John von Neumann, and Kenneth Arrow.
Download or read book Plato s Ghost written by Jeremy Gray and published by Princeton University Press. This book was released on 2008-09-02 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
Download or read book Mathematical Plato written by Roger Sworder and published by . This book was released on 2013 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plato is the first scientist whose work we still possess. He is our first writer to interpret the natural world mathematically, and also the first theorist of mathematics in the natural sciences. As no one else before or after, he set out why we should suppose a link between nature and mathematics, a link that has never been stronger than it is today. Mathematical Plato examines how Plato organized and justified the principles, terms, and methods of our mathematical, natural science. "Roger Sworder deserves our gratitude for drawing attention to the significance of mathematics in Plato's thought and writings. He lays the principal discussions out before us with clarity. He also presents Plato as a theorist of nature: of physics and not just metaphysics, to use Aristotle's distinction. Not all readers, we should admit, will be equally convinced of the usefulness of Plato's science for today, but they will all be led more deeply into Plato's vision of reality."--ANDREW DAVISON, Westcott House, Cambridge "Here is Plato for an anti-Platonic age. The author gives careful attention to some of the most important passages in the Platonic dialogues and offers new solutions to some of Plato's most famous mathematical puzzles. He then considers the implications of these penetrating studies for the philosophy of science, and the natural sciences especially. This is a book that revivifies the core themes of Platonism and restores science to worship. It shows Roger Sworder to be one of the foremost students of Plato writing today, and places him in the noble tradition of Thomas Taylor."--RODNEY BLACKHIRST, author of Primordial Alchemy and Modern Religion: Essays on Traditional Cosmology
Download or read book Plato s forms mathematics and astronomy written by Theokritos Kouremenos and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-05-22 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plato’s view that mathematics paves the way for his philosophy of forms is well known. This book attempts to flesh out the relationship between mathematics and philosophy as Plato conceived them by proposing that in his view, although it is philosophy that came up with the concept of beings, which he calls forms, and highlighted their importance, first to natural philosophy and then to ethics, the things that do qualify as beings are inchoately revealed by mathematics as the raw materials that must be further processed by philosophy (mathematicians, to use Plato’s simile in the Euthedemus, do not invent the theorems they prove but discover beings and, like hunters who must hand over what they catch to chefs if it is going to turn into something useful, they must hand over their discoveries to philosophers). Even those forms that do not bear names of mathematical objects, such as the famous forms of beauty and goodness, are in fact forms of mathematical objects. The first chapter is an attempt to defend this thesis. The second argues that for Plato philosophy’s crucial task of investigating the exfoliation of the forms into the sensible world, including the sphere of human private and public life, is already foreshadowed in one of its branches, astronomy.
Download or read book Plato s Problem written by M. Panza and published by Springer. This book was released on 2013-01-21 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.
Download or read book The Mathematics of Plato s Academy written by D. H. Fowler and published by Oxford University Press, USA. This book was released on 1987 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a reinterpretation of early Greek mathematics, one of the most tantalizing intellectual subjects of the last 2,000 years. The first part offers several new interpretations of the idea of ratio in early Greek mathematics and illustrates them in detailed discussion of several texts. Part Two discusses the historical context of the subject--what we know of Plato's academy during his lifetime, the origin of our text of Euclid's Elements, and what we know of early Greek numerical practice. The book finishes with an account of the theory of continued fractions and its history since the 17th century.
Download or read book Explorations in Ancient and Modern Philosophy written by M. F. Burnyeat and published by Cambridge University Press. This book was released on 2012-06-14 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.
Download or read book A history of Greek mathematics written by Thomas Little Heath and published by Dalcassian Publishing Company. This book was released on 1921-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Greek Mathematical Thought and the Origin of Algebra written by Jacob Klein and published by Courier Corporation. This book was released on 2013-04-22 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th-16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. 1968 edition. Bibliography.
Download or read book Platonism and Anti Platonism in Mathematics written by Mark Balaguer and published by . This book was released on 2001 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible. (Philosophy)
Download or read book Plato A Very Short Introduction written by Julia Annas and published by OUP Oxford. This book was released on 2003-02-13 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lively and accessible introduction to Plato focuses on the philosophy and argument of his writings, drawing the reader into Plato's way of doing philosophy, and the general themes of his thinking. This is not a book to leave the reader standing in the outer court of introduction and background information, but leads directly into Plato's argument. It looks at Plato as a thinker grappling with philosophical problems in a variety of ways, rather than a philosopher with a fully worked-out system. It includes a brief account of Plato's life and the various interpretations that have been drawn from the sparse remains of information. It stresses the importance of the founding of the Academy and the conception of philosophy as a subject. Julia Annas discusses Plato's style of writing: his use of the dialogue form, his use of what we today call fiction, and his philosophical transformation of myths. She also looks at his discussions of love and philosophy, his attitude to women, and to homosexual love, explores Plato's claim that virtue is sufficient for happiness, and touches on his arguments for the immortality of the soul and his ideas about the nature of the universe. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Download or read book Creating Modern Probability written by Jan von Plato and published by Cambridge University Press. This book was released on 1998-01-12 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author charts the history and development of modern probability theory.
Download or read book From the Beginning to Plato written by C.C.W. Taylor and published by Taylor & Francis. This book was released on 2023-05-09 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume in the series traces the development of philosophy over two-and-a-half centuries, from Thales at the beginning of the sixth century BC to the death of Plato in 347 BC.
Download or read book Imperial Plato written by Ryan Fowler and published by Parmenides Publishing. This book was released on 2016-12-29 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imperial Plato presents new translations of three introductions to Plato's thought from the second half of the second century CE: the Introduction to Plato by Albinus of Smyrna, Dissertation 11 of Maximus of Tyre, and On Plato and his Teaching by Apuleius of Madaurus. These three presentations of Plato's ideas-one a Greek dialectic introduction with a suggested reading order for Plato's dialogues, another a Greek speech in the sophistic style of the time, and one a lengthy doxological study in Latin-are examples by three distinct authors using divergent methods of the assorted ways in which Plato and Platonism were understood and discussed during the revival of Hellenism and Greek Philosophy, and the period of the Roman Empire often referred to as the Second Sophistic.
Download or read book Plato the Teacher written by William H. F. Altman and published by Lexington Books. This book was released on 2012-02-16 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this unique and important book, William Altman shines a light on the pedagogical technique of the playful Plato, especially his ability to create living discourses that directly address the student. Reviving an ancient concern with reconstructing the order in which Plato intended his dialogues to be taught as opposed to determining the order in which he wrote them, Altman breaks with traditional methods by reading Plato’s dialogues as a multiplex but coherent curriculum in which the Allegory of the Cave occupies the central place. His reading of Plato's Republic challenges the true philosopher to choose the life of justice exemplified by Socrates and Cicero by going back down into the Cave of political life for the sake of the greater Good.
Download or read book Mathematical Theologies written by David Albertson and published by . This book was released on 2014 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: The writings of theologians Thierry of Chartres (d. 1157) and Nicholas of Cusa (d. 1464) represent a lost history of momentous encounters between Christianity and Pythagorean ideas before the Renaissance. Their robust Christian Neopythagoreanism reconceived the Trinity and the Incarnation within the framework of Greek number theory, challenging our contemporary assumptions about the relation of religion and modern science. David Albertson surveys the slow formation of theologies of the divine One from the Old Academy through ancient Neoplatonism into the Middle Ages. Against this backdrop, Thierry of Chartres's writings stand out as the first authentic retrieval of Neopythagoreanism within western Christianity. By reading Boethius and Augustine against the grain, Thierry reactivated a suppressed potential in ancient Christian traditions that harmonized the divine Word with notions of divine Number. Despite achieving fame during his lifetime, Thierry's ideas remained well outside the medieval mainstream. Three centuries later Nicholas of Cusa rediscovered anonymous fragments of Thierry and his medieval readers, and drew on them liberally in his early works. Yet tensions among this collection of sources forced Cusanus to reconcile their competing understandings of Word and Number. Over several decades Nicholas eventually learned how to articulate traditional Christian doctrines within a fully mathematized cosmology-anticipating the situation of modern Christian thought after the seventeenth century. Mathematical Theologies skillfully guides readers through the newest scholarship on Pythagoreanism, the school of Chartres, and Cusanus, while revising some of the categories that have separated those fields in the past.
