Download or read book Mathematics in Plato s Republic written by Sarah Broadie and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A discussion of Plato's evaluation of mathematics as an intellectual discipline, and his reasons for training his philosopher-rulers to be mathematical experts"--
Download or read book The Unity of Mathematics in Plato s Republic written by Theokritos Kouremenos and published by Franz Steiner Verlag Wiesbaden GmbH. This book was released on 2015 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A History of Greek Mathematics written by Sir Thomas Little Heath and published by Courier Corporation. This book was released on 1981-01-01 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1 of an authoritative two-volume set that covers the essentials of mathematics and includes every landmark innovation and every important figure. This volume features Euclid, Apollonius, others.
Download or read book Mathematical Plato written by Roger Sworder and published by . This book was released on 2013 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
Download or read book The Role of Mathematics in Plato s Republic written by Kevin Bryan Bedell and published by . This book was released on 1990 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
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.
Download or read book Plato s Republic An Introduction written by Sean McAleer and published by Open Book Publishers. This book was released on 2020-11-09 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: It 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.
Download or read book Plato Was Not a Mathematical Platonist written by Elaine Landry and published by Cambridge University Press. This book was released on 2023-01-31 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Republic written by By Plato and published by BookRix. This book was released on 2019-06-15 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Republic is a Socratic dialogue, written by Plato around 380 BCE, concerning the definition of justice, the order and character of the just city-state and the just man. The dramatic date of the dialogue has been much debated and though it must take place some time during the Peloponnesian War, "there would be jarring anachronisms if any of the candidate specific dates between 432 and 404 were assigned". It is Plato's best-known work and has proven to be one of the most intellectually and historically influential works of philosophy and political theory. In it, Socrates along with various Athenians and foreigners discuss the meaning of justice and examine whether or not the just man is happier than the unjust man by considering a series of different cities coming into existence "in speech", culminating in a city (Kallipolis) ruled by philosopher-kings; and by examining the nature of existing regimes. The participants also discuss the theory of forms, the immortality of the soul, and the roles of the philosopher and of poetry in society.
Download or read book Plato s Republic written by R C Cross and published by Springer. This book was released on 1979-01-01 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Plato s Philosophy of Mathematics written by Anders Wedberg and published by Praeger. This book was released on 1977 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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.
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.
Download or read book Plato s Republic written by Alain Badiou and published by John Wiley & Sons. This book was released on 2013-04-25 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plato's Republic is one of the most well-known and widely discussed texts in the history of philosophy, but how might we get to the heart of this work today, 2500 years after it was originally composed? Alain Badiou invents a new genre in order to breathe fresh life into Plato's text and restore its universality. Rather than producing yet another critical commentary, he has retranslated the work from the original Greek and, by making various changes, adapted it for our times. In this innovative reimagining of a classic text, Badiou has removed all references specific to ancient Greek society, from the endless exchanges about the moral courage of poets to those political considerations that were only of interest to the aristocratic elite. On the other hand, Badiou has expanded the range of cultural references: here philosophy is firing on all cylinders, and Socrates and his companions are joined by Beckett, Pessoa, Freud and Hegel. They demonstrate the enduring nature of true philosophy, always ready to move with the times. Moreover, Badiou the dramatist has made the Socratic dialogue a true oratorial contest: in his version of the Republic, the interlocutors have more in mind than merely agreeing with the Master. They stand up to him, put him on the spot and thereby show thought in motion. Through this work of writing, scholarship and philosophy, we are able, for the first time, to read a version of Plato's text which is alive, stimulating and directly relevant to our world today.
Download or read book Plato s Philosophy of Mathematics written by Paul Pritchard and published by . This book was released on 1995 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
