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Author : Theon (of Smyrna.)
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.:/5 (321 download)
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:
Author : Jeremy Gray
Publisher : Princeton University Press
ISBN 13 : 1400829046
Total Pages : 528 pages
Book Rating : 4.4/5 (8 download)
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.
Author : D. H. Fowler
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 442 pages
Book Rating : 4.3/5 (91 download)
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.
Author : Theokritos Kouremenos
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110601486
Total Pages : 158 pages
Book Rating : 4.1/5 (16 download)
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 158 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.
Author : George Szpiro
Publisher : Princeton University Press
ISBN 13 : 0691209081
Total Pages : 240 pages
Book Rating : 4.6/5 (912 download)
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.
Author : Roger Sworder
Publisher : Angelico Press / Sophia Perennis
ISBN 13 : 9781621385806
Total Pages : 130 pages
Book Rating : 4.3/5 (858 download)
Download or read book Mathematical Plato written by Roger Sworder and published by Angelico Press / Sophia Perennis. This book was released on 2013-10-30 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
Author : Jacob Klein
Publisher : Courier Corporation
ISBN 13 : 0486319814
Total Pages : 246 pages
Book Rating : 4.4/5 (863 download)
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.
Author : Thomas Little Heath
Publisher :
ISBN 13 :
Total Pages : 470 pages
Book Rating : 4.:/5 (89 download)
Download or read book A History of Greek Mathematics written by Thomas Little Heath and published by . This book was released on 1921 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: I. From Thales to Euclid.--II. From Aristarchus to Diophantus.
Author : Phillip Sidney Horky
Publisher : Oxford University Press
ISBN 13 : 0190465700
Total Pages : 328 pages
Book Rating : 4.1/5 (94 download)
Download or read book Plato and Pythagoreanism written by Phillip Sidney Horky and published by Oxford University Press. This book was released on 2016 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Julia Annas
Publisher : Sterling Publishing Company, Inc.
ISBN 13 : 9781402770524
Total Pages : 192 pages
Book Rating : 4.7/5 (75 download)
Download or read book Plato written by Julia Annas and published by Sterling Publishing Company, Inc.. This book was released on 2009 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Julia Annas provides an incisive exploration of the many-sided and elusive genius whose wide-ranging, bold, and influential ideas continue to challenge, provoke, and inspire us today"--Page 4 of cover.
Author : Mary Gow
Publisher : Enslow Publishing, LLC
ISBN 13 : 9780766031197
Total Pages : 132 pages
Book Rating : 4.0/5 (311 download)
Download or read book The Great Philosopher written by Mary Gow and published by Enslow Publishing, LLC. This book was released on 2010-07-01 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Follows the life and teachings of the philosopher Plato, one of the world's greatest thinkers, who in his writings taught us to question what we think we know.
Author : M. F. Burnyeat
Publisher : Cambridge University Press
ISBN 13 : 0521750725
Total Pages : 393 pages
Book Rating : 4.5/5 (217 download)
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.
Author : Ryan Fowler
Publisher : Parmenides Publishing
ISBN 13 : 1930972881
Total Pages : 372 pages
Book Rating : 4.9/5 (39 download)
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 372 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.
Author : M. Panza
Publisher : Springer
ISBN 13 : 1137298138
Total Pages : 289 pages
Book Rating : 4.1/5 (372 download)
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.
Author : C.C.W. Taylor
Publisher : Taylor & Francis
ISBN 13 : 100095059X
Total Pages : 526 pages
Book Rating : 4.0/5 (9 download)
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.
Author : Proclus
Publisher : Cambridge University Press
ISBN 13 : 0521845955
Total Pages : 218 pages
Book Rating : 4.5/5 (218 download)
Download or read book Commentary on Plato's Timaeus written by Proclus and published by Cambridge University Press. This book was released on 2007 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pythagorean harmonic theory, as well as questions about the way in which the World Soul knows both Forms and the visible reality that constitutes its body. This part of Proclus' Commentary is particularly responsive to the interpretive tradition that precedes it. As a result, this volume is especially significant for the study of the Platonic tradition from the earliest commentators onwards." --Book Jacket.
Author : Donna M. Altimari Adler
Publisher : BRILL
ISBN 13 : 900438992X
Total Pages : 654 pages
Book Rating : 4.0/5 (43 download)
Download or read book Plato’s Timaeus and the Missing Fourth Guest written by Donna M. Altimari Adler and published by BRILL. This book was released on 2019-12-02 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Plato's Timaeus and the Missing Fourth Guest, Donna M. Altimari Adler offers an original account of Plato's Timaeus from 35a-36d, yielding a new interpretation of the Timaeus scale and cosmic harmony imbedded in the text.
