Plato’s forms, mathematics and astronomy
Plato’s forms, mathematics and astronomy

Author: Theokritos Kouremenos

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-05-22

Total Pages: 152

ISBN-13: 3110601486

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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.

Plato's Problem
Plato's Problem

Author: M. Panza

Publisher: Springer

Published: 2013-01-21

Total Pages: 289

ISBN-13: 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's Ghost
Plato's Ghost

Author: Jeremy Gray

Publisher: Princeton University Press

Published: 2008-09-02

Total Pages: 528

ISBN-13: 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.

Mathematical Plato
Mathematical Plato

Author: Roger Sworder

Publisher:

Published: 2013

Total Pages: 130

ISBN-13: 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

Explorations in Ancient and Modern Philosophy
Explorations in Ancient and Modern Philosophy

Author: M. F. Burnyeat

Publisher: Cambridge University Press

Published: 2012-06-14

Total Pages: 393

ISBN-13: 0521750725

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The first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.

The Mathematics of Plato's Academy
The Mathematics of Plato's Academy

Author: D. H. Fowler

Publisher: Oxford University Press, USA

Published: 1987

Total Pages: 442

ISBN-13:

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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.

Plato: A Very Short Introduction
Plato: A Very Short Introduction

Author: Julia Annas

Publisher: OUP Oxford

Published: 2003-02-13

Total Pages: 128

ISBN-13: 019157922X

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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.

The Great Philosopher
The Great Philosopher

Author: Mary Gow

Publisher: Enslow Publishing, LLC

Published: 2010-07-01

Total Pages: 132

ISBN-13: 9780766031197

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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.

Aristotle and Mathematics
Aristotle and Mathematics

Author: John J. Cleary

Publisher: BRILL

Published: 2016-06-21

Total Pages: 597

ISBN-13: 9004320903

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John Cleary here explores the role which the mathematical sciences play in Aristotle's philosophical thought, especially in his cosmology, metaphysics, and epistemology. He also thematizes the aporetic method by means of which he deals with philosophical questions about the foundations of mathematics. The first two chapters consider Plato's mathematical cosmology in the light of Aristotle's critical distinction between physics and mathematics. Subsequent chapters examine three basic aporiae about mathematical objects which Aristotle himself develops in his science of first philosophy. What emerges from this dialectical inquiry is a different conception of substance and of order in the universe, which gives priority to physics over mathematics as the cosmological science. Within this different world-view, we can better understand what we now call Aristotle's philosophy of mathematics.