The Unity Of Mathematics In Plato S Republic

Author : Theokritos Kouremenos
Publisher : Franz Steiner Verlag Wiesbaden GmbH
Page : 141 pages
File Size : 46,6 Mb
Release : 2015
Category : Mathematics
ISBN : 3515110763

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The Unity of Mathematics in Plato's Republic by Theokritos Kouremenos Pdf

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.

Author : Theokritos Kouremenos
Publisher : Walter de Gruyter GmbH & Co KG
Page : 158 pages
File Size : 50,5 Mb
Release : 2018-05-22
Category : Literary Criticism
ISBN : 9783110601862

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Plato’s forms, mathematics and astronomy by Theokritos Kouremenos Pdf

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.

Author : Necip Fikri Alican
Publisher : State University of New York Press
Page : 527 pages
File Size : 40,6 Mb
Release : 2021-10-01
Category : Philosophy
ISBN : 9781438485652

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One over Many by Necip Fikri Alican Pdf

Finalist for the 2022 PROSE Award in the Philosophy category presented by the Association of American Publishers One over Many is a groundbreaking interpretation of Plato's philosophical outlook, solving longstanding problems in the scholarly literature. Its originality and its strength consist in replacing the metaphysical dualism of the traditional interpretation with the paradigm of unitary pluralism: one world with a gradation of reality, including three different types of Forms, as well as the entire spectrum of sensible phenomena, with intermediate ontological constructs in between. The model thus combines a monism of worlds with a pluralism of things, positing a unitary reality of infinite possibilities through ontological stratification. This tightly integrated collection of essays, conceived and developed by the author in pursuit of corrective intervention in Plato’s metaphysics, combines his previously published work with newly drafted material for the present volume. The book replaces the standard view of Plato as a metaphysical dualist with a novel interpretation providing greater explanatory power through the paradigm of unitary pluralism in a single reality built on ontological diversity.

Author : Orestis Karatzoglou
Publisher : Walter de Gruyter GmbH & Co KG
Page : 200 pages
File Size : 53,7 Mb
Release : 2021-04-06
Category : History
ISBN : 9783110732450

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The Embodied Self in Plato by Orestis Karatzoglou Pdf

This book argues that, rather than being conceived merely as a hindrance, the body contributes constructively in the fashioning of a Platonic unified self. The Phaedo shows awareness that the indeterminacy inherent in the body infects the validity of any scientific argument but also provides the subject of inquiry with the ability to actualize, to the extent possible, the ideal self. The Republic locates bodily desires and needs in the tripartite soul. Achievement of maximal unity is dependent upon successful training of the rational part of the soul, but the earlier curriculum of Books 2 and 3, which aims at instilling a pre-reflectively virtuous disposition in the lower parts of the soul, is a prerequisite for the advanced studies of Republic 7. In the Timaeus, the world soul is fashioned out of Being, Sameness, and Difference: an examination of the Sophist and the Parmenides reveals that Difference is to be identified with the Timaeus’ Receptacle, the third ontological principle which emerges as the quasi-material component that provides each individual soul with the alloplastic capacity for psychological growth and alteration.

Author : Paul Pritchard
Publisher : Unknown
Page : 212 pages
File Size : 46,9 Mb
Release : 1995
Category : Philosophy
ISBN : UOM:39015051596719

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Plato's Philosophy of Mathematics by Paul Pritchard Pdf

Author : Andrew Payne
Publisher : Oxford University Press
Page : 249 pages
File Size : 54,6 Mb
Release : 2017
Category : Philosophy
ISBN : 9780198799023

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The Teleology of Action in Plato's Republic by Andrew Payne Pdf

In many discussions of ancient philosophy, teleology is acknowledged as an important theme. How do we act for a particular end or purpose? One common answer describes humans as acting with the intention of achieving a goal. A person selects particular actions with the thought that these actions will lead to that goal. Andrew Payne accepts that this is one good answer to our question but proposes that it is not the only one. In Plato's Republic, Socrates appeals to a different understanding of how humans act for the sake of ends as they live together in political communities and pursue knowledge. As they carry out activities that are necessary for human flourishing, their actions can produce unintended results that signal the full completion of human capacities. For example, performing the actions of a just individual can help promote the establishment of a just society as an unintended result. Such unintended results qualify as ends or purposes of human action. This volume fully explores this functional teleology of action in Plato's Republic.

Author : Laurence Bloom
Publisher : Lexington Books
Page : 273 pages
File Size : 47,5 Mb
Release : 2017-03-08
Category : Philosophy
ISBN : 9780739190241

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The Principle of Non-contradiction in Plato's Republic by Laurence Bloom Pdf

Plato’s formulation of the Principle of Non-contradiction (PNC) in Republic IV is the first full statement of the principle in western philosophy. His use of the principle might seem to suggest that he endorses the PNC. After all, how could one possibly deny so fundamental a principle—especially when it seems difficult to deny it without relying on it. However, the endorsement in the text is qualified. Socrates refers to the principle as one that he and his interlocutors will hypothesize and warns that if it should ever be shown to be false, all that follows from it will also be refuted. Scholars who have noticed this issue have tended to assume that the truth of the hypothesis in question can be guaranteed. Laurence Bloom argues against unthinkingly accepting this claim. He suggests that what emerges from the text is more sophisticated: Plato’s concession that the PNC is hypothetical is a textual clue pointing us to a complex philosophical argument that grounds the PNC, as well as the sort of reasoning it grounds, in form. Indeed, in framing the problem in this way, we can read the Republic as providing an extended argument for form. The argument for forms that emerges is complex and difficult. It is not and cannot be a normal, discursive argument. Indeed, the argument cannot even be one that assumes the PNC; if it did so, it would fall prey to a vicious circularity. Rather, the argument rests on the very possibility of our hypothesizing the PNC in the first place. Our ability to hypothesize the PNC—and perhaps our inability not to hypothesize it—is the linchpin. When we ask questions such as “to what objects does the PNC apply?” or “how is it possible that we apply the PNC?,” we are asking questions that lead us to the existence of form. The Principle of Non-contradiction in Plato’s Republic also explores the soul of the knower—the very entity to which and by which the principle is applied in the text—and its underlying unity.

Author : Robert Sherrick Brumbaugh
Publisher : Unknown
Page : 96 pages
File Size : 43,5 Mb
Release : 1942
Category : Mathematics, Greek
ISBN : OSU:32435005988597

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The Role of Mathematics in Plato's Dialectic ... by Robert Sherrick Brumbaugh Pdf

Author : Plato
Publisher : Unknown
Page : 408 pages
File Size : 47,5 Mb
Release : 1894
Category : Political science
ISBN : UOMDLP:afx0245:0002.001

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Plato's Republic by Plato Pdf

Author : Plato
Publisher : The Floating Press
Page : 720 pages
File Size : 41,7 Mb
Release : 2009-01-01
Category : Philosophy
ISBN : 9781775413660

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The Republic by Plato Pdf

The Republic is Plato's most famous work and one of the seminal texts of Western philosophy and politics. The characters in this Socratic dialogue - including Socrates himself - discuss whether the just or unjust man is happier. They are the philosopher-kings of imagined cities and they also discuss the nature of philosophy and the soul among other things.

Author : Carolina Araújo
Publisher : Bloomsbury Publishing
Page : 265 pages
File Size : 43,8 Mb
Release : 2022-12-01
Category : Philosophy
ISBN : 9781350257054

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Cooperative Flourishing in Plato’s 'Republic' by Carolina Araújo Pdf

In this pathbreaking interpretation of Plato's foundational text of political philosophy, Carolina Araújo reveals how the Republic remains ripe for an interpretation grounded in notions of cooperation, flourishing and justice relevant to the diversity of contemporary life. Plato's Republic has the Greek name of Politeia that Araújo translates as “the way of life of the citizens,” not “the State” or “the form of government” as it more traditionally rendered. Plato's treatise, Politeia, depicts the rich array of patterns emerging from human interaction and enquires into the best amongst them. Cooperative Flourishing in Plato's Republic returns to these important questions about society – how to live with a vast diversity of personalities, with different interests and abilities, all of them trying to flourish – and asks how best can we share our environment? With rigorous philosophical analysis of the Greek text, accompanied by original translations of the most important passages, Araújo upends mainstream scholarship to progress Socrates' “bottom-up” view of politics and rejects previous readings of the Republic as a proto-totalitarian text, psychological study or lengthy analogy. By defending a theory of Platonic justice that is rooted in cooperative flourishing, the public education of all citizens and the contribution of philosophers to political life, “the beautiful city”, which Plato called Kallipolis, emerges as a hopeful possibility.

Author : Theon (of Smyrna.),Christos Toulis
Publisher : Unknown
Page : 200 pages
File Size : 45,7 Mb
Release : 1979
Category : Astronomy, Greek
ISBN : UCSC:32106008441393

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Mathematics Useful for Understanding Plato by Theon (of Smyrna.),Christos Toulis Pdf

Author : Lizhen Ji,Athanase Papadopoulos,Sumio Yamada
Publisher : Springer
Page : 647 pages
File Size : 51,8 Mb
Release : 2017-10-03
Category : Mathematics
ISBN : 9783319600390

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From Riemann to Differential Geometry and Relativity by Lizhen Ji,Athanase Papadopoulos,Sumio Yamada Pdf

This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.

Author : M. F. Burnyeat
Publisher : Cambridge University Press
Page : 393 pages
File Size : 52,5 Mb
Release : 2012-06-14
Category : History
ISBN : 9780521750721

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Explorations in Ancient and Modern Philosophy by M. F. Burnyeat Pdf

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

Author : Constance Meinwald
Publisher : Routledge
Page : 286 pages
File Size : 49,8 Mb
Release : 2016-05-05
Category : Philosophy
ISBN : 9781136184420

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Plato by Constance Meinwald Pdf

In this engaging introduction, Constance Meinwald shows how Plato has shaped the landscape of Western philosophy. She provides much-needed historical context, and helps readers grapple with Plato’s distinctive use of highly crafted literary masterpieces for philosophical purposes. Meinwald examines some of Plato’s most famous discussions of human questions, concerning erōs, the capacities and immortality of our psyche, human excellence and the good life, and Plato’s controversial ideas about culture, society, and political organization. She shows how Plato makes a sketch of his theory of Forms foundational in this work, and she offers illuminating readings of texts concerned with the development of the theory and its relationship to Greek science and mathematics. Throughout, Meinwald draws expertly on Plato’s dialogues to present a lively and accessible picture of his philosophy. Including a chronology, glossary of terms, and suggestions for further reading, Plato is an ideal introduction to arguably the greatest of all Western philosophers, and is essential reading for students of ancient philosophy and classics.