Read and Download eBook Full
Author: Sarah Broadie
Publisher:
Published: 2020
Total Pages: 0
ISBN-13: 9780874621952
DOWNLOAD EBOOK"A discussion of Plato's evaluation of mathematics as an intellectual discipline, and his reasons for training his philosopher-rulers to be mathematical experts"--
Author: Theokritos Kouremenos
Publisher: Franz Steiner Verlag Wiesbaden GmbH
Published: 2015
Total Pages: 141
ISBN-13: 9783515110761
DOWNLOAD EBOOKIn 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.
Author: Sir Thomas Little Heath
Publisher:
Published: 1921
Total Pages: 470
ISBN-13:
DOWNLOAD EBOOKAuthor: Kevin Bryan Bedell
Publisher:
Published: 1990
Total Pages: 140
ISBN-13:
DOWNLOAD EBOOKAuthor: George Szpiro
Publisher: Princeton University Press
Published: 2020-11-03
Total Pages: 240
ISBN-13: 0691209081
DOWNLOAD EBOOKThe 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: Theokritos Kouremenos
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2018-05-22
Total Pages: 152
ISBN-13: 3110601486
DOWNLOAD EBOOKPlato’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: M. F. Burnyeat
Publisher: Cambridge University Press
Published: 2012-06-14
Total Pages: 393
ISBN-13: 0521750725
DOWNLOAD EBOOKThe first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.
Author: Elaine Landry
Publisher: Cambridge University Press
Published: 2023-01-31
Total Pages: 103
ISBN-13: 1009313800
DOWNLOAD EBOOKThis 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.
Author: Sean McAleer
Publisher: Open Book Publishers
Published: 2020-11-09
Total Pages: 233
ISBN-13: 1800640560
DOWNLOAD EBOOKIt is an excellent book – highly intelligent, interesting and original. Expressing high philosophy in a readable form without trivialising it is a very difficult task and McAleer manages the task admirably. Plato is, yet again, intensely topical in the chaotic and confused world in which we are now living. Philip Allott, Professor Emeritus of International Public Law at Cambridge University This book is a lucid and accessible companion to Plato’s Republic, throwing light upon the text’s arguments and main themes, placing them in the wider context of the text’s structure. In its illumination of the philosophical ideas underpinning the work, it provides readers with an understanding and appreciation of the complexity and literary artistry of Plato’s Republic. McAleer not only unpacks the key overarching questions of the text – What is justice? And Is a just life happier than an unjust life? – but also highlights some fascinating, overlooked passages which contribute to our understanding of Plato’s philosophical thought. Plato’s 'Republic': An Introduction offers a rigorous and thought-provoking analysis of the text, helping readers navigate one of the world’s most influential works of philosophy and political theory. With its approachable tone and clear presentation, it constitutes a welcome contribution to the field, and will be an indispensable resource for philosophy students and teachers, as well as general readers new to, or returning to, the text.
Author: Anders Wedberg
Publisher: Praeger
Published: 1977
Total Pages: 168
ISBN-13:
DOWNLOAD EBOOK