**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.

**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.

**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.

**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"--

**Author**: Elaine Landry

**Publisher:** Cambridge University Press

**ISBN:** 1009313800

**Category : **Philosophy

**Languages : **en

**Pages : **103

**Book Description**
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.

**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.

**Author**: Theokritos Kouremenos

**Publisher:**
**ISBN:** 9783515110778

**Category : **
**Languages : **en

**Pages : **
**Book Description**

**Author**: Michalis Sialaros

**Publisher:** Walter de Gruyter GmbH & Co KG

**ISBN:** 3110565951

**Category : **History

**Languages : **en

**Pages : **401

**Book Description**
This volume brings together a number of leading scholars working in the field of ancient Greek mathematics to present their latest research. In their respective area of specialization, all contributors offer stimulating approaches to questions of historical and historiographical ‘revolutions’ and ‘continuity’. Taken together, they provide a powerful lens for evaluating the applicability of Thomas Kuhn’s ideas on ‘scientific revolutions’ to the discipline of ancient Greek mathematics. Besides the latest historiographical studies on ‘geometrical algebra’ and ‘premodern algebra’, the reader will find here some papers which offer new insights into the controversial relationship between Greek and pre-Hellenic mathematical practices. Some other contributions place emphasis on the other edge of the historical spectrum, by exploring historical lines of ‘continuity’ between ancient Greek, Byzantine and post-Hellenic mathematics. The terminology employed by Greek mathematicians, along with various non-textual and material elements, is another topic which some of the essays in the volume explore. Finally, the last three articles focus on a traditionally rich source on ancient Greek mathematics; namely the works of Plato and Aristotle.

**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).

**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.

**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.