Plato Was Not A Mathematical Platonist
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Plato Was Not A Mathematical Platonist
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Author : Elaine Landry
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-31
Plato Was Not A Mathematical Platonist written by Elaine Landry and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-31 with Philosophy categories.
This Element shows that Plato keeps a clear distinction between mathematical and metaphysical realism and the knife he uses to slice the difference is method. The philosopher's dialectical method requires that we tether the truth of hypotheses to existing metaphysical objects. The mathematician's hypothetical method, by contrast, takes hypotheses as if they were first principles, so no metaphysical account of their truth is needed. Thus, we come to Plato's methodological as-if realism: in mathematics, we treat our hypotheses as if they were first principles, and, consequently, our objects as if they existed, and we do this for the purpose of solving problems. Taking the road suggested by Plato's Republic, this Element shows that methodological commitments to mathematical objects are made in light of mathematical practice; foundational considerations; and, mathematical applicability. This title is also available as Open Access on Cambridge Core.
Mathematical Plato
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Author : Roger Sworder
language : en
Publisher: Angelico Press / Sophia Perennis
Release Date : 2013-10-30
Mathematical Plato written by Roger Sworder and has been published by Angelico Press / Sophia Perennis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-30 with categories.
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 Problem
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Author : M. Panza
language : en
Publisher: Springer
Release Date : 2013-01-21
Plato S Problem written by M. Panza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-21 with Mathematics categories.
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 Forms Mathematics And Astronomy
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Author : Theokritos Kouremenos
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-05-22
Plato S Forms Mathematics And Astronomy written by Theokritos Kouremenos and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-22 with Literary Criticism categories.
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 Philosophy Of Mathematics
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Author : Paul Pritchard
language : en
Publisher:
Release Date : 1995
Plato S Philosophy Of Mathematics written by Paul Pritchard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Philosophy categories.
An Introduction To Plato S Republic
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Author : Julia Annas
language : en
Publisher:
Release Date : 1985
An Introduction To Plato S Republic written by Julia Annas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Plato S Mathematical Imagination
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Author : Robert Sherrick Brumbaugh
language : en
Publisher: Bloomington : Indiana University Press
Release Date : 1954
Plato S Mathematical Imagination written by Robert Sherrick Brumbaugh and has been published by Bloomington : Indiana University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954 with Mathematics categories.
Was Plato A Mathematical Platonist
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Author : Hera Sharon Arsen
language : en
Publisher:
Release Date : 2009
Was Plato A Mathematical Platonist written by Hera Sharon Arsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Explorations In Ancient And Modern Philosophy
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Author : M. F. Burnyeat
language : en
Publisher: Cambridge University Press
Release Date : 2012-06-14
Explorations In Ancient And Modern Philosophy written by M. F. Burnyeat and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-14 with History categories.
The first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.
The Unity Of Mathematics In Plato S Republic
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Author : Theokritos Kouremenos
language : en
Publisher: Franz Steiner Verlag Wiesbaden GmbH
Release Date : 2015
The Unity Of Mathematics In Plato S Republic written by Theokritos Kouremenos and has been published by Franz Steiner Verlag Wiesbaden GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
In his Republic Plato considers grasping the unity of mathematics as the ultimate goal of the mathematical studies in which the future philosopher-rulers must engage before they turn to philosophy. How the unity of mathematics is supposed to be understood is not explained, however. This book argues that Plato conceives of the unity of mathematics in terms of the mutually benefiting links between its branches, just as he conceives of the unity of the state outlined in the Republic in terms of the common benefit for all citizens. Evidence for this view is provided by a discussion of his conception of astronomy as a propedeutic to philosophy, which can be best understood as hinting at a historically possible link between fourth-century-BC astronomy and solid geometry. The monograph also includes a detailed discussion of two well-known stories about Plato: not only he motivated Greek mathematicians to solve a difficult problem in solid geometry with his interpretation of a Delphic oracle given to the inhabitants of the island of Delos but he also posed the question which led to the development of the astronomical theory of homocentric spheres. It is argued that these stories are best understood as fictional episodes in Plato's life, constructed from passages in his works.