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The Unity of Mathematics in Plato's Republic

The Unity of Mathematics in Plato's Republic PDF Author: Theokritos Kouremenos
Publisher: Franz Steiner Verlag Wiesbaden GmbH
ISBN: 9783515110761
Category : Mathematics
Languages : en
Pages : 141

Book Description
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.

The Unity of Mathematics in Plato's Republic

The Unity of Mathematics in Plato's Republic PDF Author: Theokritos Kouremenos
Publisher: Franz Steiner Verlag Wiesbaden GmbH
ISBN: 9783515110761
Category : Mathematics
Languages : en
Pages : 141
Book Description
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.

Plato: 'The Republic'

Plato: 'The Republic' PDF Author: Plato
Publisher: Cambridge University Press
ISBN: 9780521484435
Category : Philosophy
Languages : en
Pages : 444
Book Description
Presents the most important of the Socratic dialogues as if it were a conversation; deals with the creation of an ideal commonwealth and ranks as one of the earliest Utopian works.

Mathematics in Plato's Republic

Mathematics in Plato's Republic PDF Author: Sarah Broadie
Publisher:
ISBN: 9780874621952
Category : Mathematics, Greek
Languages : en
Pages :
Book Description
"A discussion of Plato's evaluation of mathematics as an intellectual discipline, and his reasons for training his philosopher-rulers to be mathematical experts"--

Plato’s forms, mathematics and astronomy

Plato’s forms, mathematics and astronomy PDF Author: Theokritos Kouremenos
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110601869
Category : Literary Criticism
Languages : en
Pages : 158
Book Description
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.

The Role of Mathematics in Plato's Republic

The Role of Mathematics in Plato's Republic PDF Author: Kevin Bryan Bedell
Publisher:
ISBN:
Category :
Languages : en
Pages : 140
Book Description


Greek Studies in the Philosophy and History of Science

Greek Studies in the Philosophy and History of Science PDF Author: P. Nicolacopoulos
Publisher: Springer Science & Business Media
ISBN: 9400920156
Category : Science
Languages : en
Pages : 439
Book Description
Our Greek colleagues, in Greece and abroad, must know (indeed they do know) how pleasant it is to recognize the renaissance of the philosophy of science among them with this fine collection. Classical and modern, technical and humane, historical and logical, admirably original and respectfully traditional, these essays will deserve close study by philosophical readers throughout the world. Classical scholars and historians of science likewise will be stimulated, and the historians of ancient as well as modern philosophers too. Reviewers might note one or more of the contributions as of special interest, or as subject to critical wrestling (that ancient tribute); we will simply congratulate Pantelis Nicolacopoulos for assembling the essays and presenting the book, and we thank the contributors for their works and for their happy agreement to let their writings appear in this book. R. S. C. xi INTRODUCTORY REMARKS Neither philosophy nor science is new to Greece, but philosophy of science is. There are broader (socio-historical) and more specific (academic) reasons that explain, to a satisfactory degree, both the under-development of philosophy and history of science in Greece until recently and its recent development to international standards. It is, perhaps, not easy to have in mind the fact that the modem Greek State is only 160 years old (during quite a period of which it was consider ably smaller than it is today, its present territory having been settled after World War II).

An Engagement with Plato's Republic

An Engagement with Plato's Republic PDF Author: Basil Mitchell
Publisher: Routledge
ISBN: 1351958976
Category : Philosophy
Languages : en
Pages : 190
Book Description
Outrageous, unfashionable, politically incorrect though many of Plato's opinions undoubtedly are, we should not just dismiss them as thoughts now unthinkable, but think through them, recognising the force of the arguments that led Plato to enunciate them and consider the counter-arguments he might have marshalled to meet contemporary objections. This book encourages today's students to engage in Plato's thought, grapple with Plato's arguments, and explore the relevance of his arguments in contemporary terms. A text only comes alive if we make it our own; Plato's great work The Republic, often reads as though it were addressing the problems of the day rather than those of ancient Athens. Treating The Republic as a whole and offering a comprehensive introduction to Plato's arguments, Mitchell and Lucas draw students into an exploration of the relevance of Plato's thought to our present ideas about politics, society and education, as well as the philosophy of mathematics, science and religion. The authors bring The Republic to life. The first chapters help the reader to make sense of the text, either in translation or the original Greek. Later chapters deal with the themes that Plato raises, treating Plato as a contemporary. Plato is inexhaustible: he speaks to many different people of different generations and from different backgrounds. The Republic is not just an ancient text: it never ceases to be relevant to contemporary concerns, and it demands fresh discussion in every age.

The Frontiers of Ancient Science

The Frontiers of Ancient Science PDF Author: Brooke Holmes
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110336332
Category : History
Languages : en
Pages : 775
Book Description
Our understanding of science, mathematics, and medicine today can be deeply enriched by studying the historical roots of these areas of inquiry in the ancient Near East and Mediterranean. The fields of ancient science and mathematics have in recent years witnessed remarkable growth. The present volume brings together contributions from more than thirty of the most important scholars working in these fields in the United States and Europe in honor of the eminent historian of ancient science and medicine Heinrich von Staden, Professor Emeritus of Classics and History of Science at the Institute of Advanced Study and William Lampson Professor Emeritus of Classics and Comparative Literature at Yale University. The papers range widely from Mesopotamia to Ancient Greece and Rome, from the first millennium B.C. to the early medieval period, and from mathematics to philosophy, mechanics to medicine, representing both a wide diversity of national traditions and the cutting edge of the international scholarly community.

Plato’s Republic

Plato’s Republic PDF Author: R C Cross
Publisher: Springer
ISBN: 1349028517
Category : Philosophy
Languages : en
Pages : 295
Book Description


The Bright and the Good

The Bright and the Good PDF Author: Audrey L. Anton
Publisher: Rowman & Littlefield
ISBN: 1786602385
Category : Philosophy
Languages : en
Pages : 288
Book Description
This book provides a contemporary overview of an age-old question in philosophy, namely the connection between intellectual and moral virtues. Ideal for courses in virtue ethics and virtue epistemology, the volume includes coverage of specific topics, such as vice, ignorance, hope, courage, patience, justice and mercy.