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Mathematical Plato

Mathematical Plato
Author: Roger Sworder
Publisher:
Total Pages: 130
Release: 2013
Genre: Philosophy
ISBN: 9781597311380

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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


Plato's Ghost

Plato's Ghost
Author: Jeremy Gray
Publisher: Princeton University Press
Total Pages: 528
Release: 2008-09-02
Genre: Mathematics
ISBN: 1400829046

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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.


Numbers Rule

Numbers Rule
Author: George Szpiro
Publisher: Princeton University Press
Total Pages: 240
Release: 2020-11-03
Genre: History
ISBN: 0691209081

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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.


A History of Greek Mathematics

A History of Greek Mathematics
Author: Sir Thomas Little Heath
Publisher:
Total Pages: 470
Release: 1921
Genre: Mathematics
ISBN:

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Plato's Problem

Plato's Problem
Author: M. Panza
Publisher: Springer
Total Pages: 289
Release: 2013-01-21
Genre: Mathematics
ISBN: 1137298138

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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.


Plato and Pythagoreanism

Plato and Pythagoreanism
Author: Phillip Sidney Horky
Publisher: Oxford University Press
Total Pages: 328
Release: 2016
Genre: History
ISBN: 0190465700

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Was Plato a Pythagorean? Plato's students and earliest critics thought so, but later scholars have been more skeptical. Plato and Pythagoreanism reconsiders this question by arguing that a specific type of Pythagorean philosophy, called "mathematical" Pythagoreanism, played a profound role in Plato's philosophy.


Greek Mathematical Thought and the Origin of Algebra

Greek Mathematical Thought and the Origin of Algebra
Author: Jacob Klein
Publisher: Courier Corporation
Total Pages: 246
Release: 2013-04-22
Genre: Mathematics
ISBN: 0486319814

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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.


Imperial Plato

Imperial Plato
Author: Ryan Fowler
Publisher: Parmenides Publishing
Total Pages: 372
Release: 2016-12-29
Genre: Philosophy
ISBN: 1930972881

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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.


From the Beginning to Plato

From the Beginning to Plato
Author: C.C.W. Taylor
Publisher: Taylor & Francis
Total Pages: 521
Release: 2023-05-09
Genre: Philosophy
ISBN: 100094381X

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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.