Theokritos Kouremenos's Books

Aristotle on Mathematical Infinity

By: Theokritos Kouremenos,Aristotle

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Aristotle on Mathematical Infinity

By: Theokritos Kouremenos,Aristotle

Aristotle was the first not only to distinguish between potential and actual infinity but also to insist that potential infinity alone is enough for mathematics thus initiating an issue still central to the philosophy of mathematics. Modern scholarship, however, has attacked Aristotle's thesis because, according to the received doctrine, it does not square with Euclidean geometry and it also seems to contravene Aristotle's belief in the finitude of the physical universe. This monograph, the first thorough study of the issue, puts Aristotle's views on infinity in the proper perspective. Through a close study of the relevant Aristotelian passages it shows that the Stagirite's theory of infinity forms a well argued philosophical position which does not bear on his belief in a finite cosmos and does not undermine the Euclidean nature of geometry. The monograph draws a much more positive picture of Aristotle's views and reaffirms his disputed stature as a serious philosopher of mathematics. This innovative and stimulating contribution will be essential reading to a wide range of scholars, including classicists, philosophers of science and mathematics as well as historians of ideas.

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142

Publisher

Franz Steiner Verlag

Published Date

ISBN 10

3515068511

ISBN 13

9783515068512

Plato’s forms, mathematics and astronomy

By: Theokritos Kouremenos

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Plato’s forms, mathematics and astronomy

By: Theokritos Kouremenos

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.

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158

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110601869

ISBN 13

9783110601862

Plato’s forms, mathematics and astronomy

By: Theokritos Kouremenos

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Plato’s forms, mathematics and astronomy

By: Theokritos Kouremenos

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152

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110601486

ISBN 13

9783110601480

Aristotle's de Caelo Gamma

Introduction, Translation and Commentary

By: Theokritos Kouremenos

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Aristotle's de Caelo Gamma

Introduction, Translation and Commentary

By: Theokritos Kouremenos

This is the first full-scale commentary on Aristotle's de Caelo III to appear in recent decades. de Caelo III can serve as a good introduction to Aristotle's physics and its character. In it he answers some very general questions about the elements of all material things except celestial objects: how many these elements are, why they cannot be infinitely many but must be more than one, whether they are eternal or can be generated and decay, and, if the second, how. His discussion is often framed as a critique of rival theories, and he argues systematically against the geometrical theory of the elements in Plato's Timaeus, which adds greatly to the interest of the work. The commentary adduces many parallel passages from Aristotle's other works to round off the readers understanding, and the introduction offers a brief but comprehensive overview of the Aristotelian theory of the elements, which de Caelo III often takes for granted

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121

Publisher

Franz Steiner Verlag Wiesbaden gmbh

Published Date

ISBN 10

3515103368

ISBN 13

9783515103367

Aristotle on Mathematical Infinity

By: Theokritos Kouremenos,Aristotle

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Aristotle on Mathematical Infinity

By: Theokritos Kouremenos,Aristotle

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Page Count

142

Publisher

Franz Steiner Verlag

Published Date

ISBN 10

3515068511

ISBN 13

9783515068512

The Proportions in Aristotle's Phys. 7.5

By: Theokritos Kouremenos

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The Proportions in Aristotle's Phys. 7.5

By: Theokritos Kouremenos

In Phys. 8.10 and Cael. 1.7, 3.2 Aristotle establishes theses central to his physical theory by relying on proportions he sets out in Phys. 7.5 without, though, giving any clue as to their character or even their role in the argument he develops in Phys. 7. The author seeks to determine the nature of the problematic Phys. 7.5 proportions, which have been traditionally understood out of any context as Aristotle's flawed mathematical laws of motion, in the light of their applications in Phys. 8.10 and Cael. 1.7, 3.2. He argues that Aristotle conceived these proportions as purely mathematical assumptions which, though, do not compromise the arguments in Phys. 8.10 and Cael. 1.7, 3.2, for there is strong evidence that for Aristotle these arguments do not turn on any proportionality assumption. This is the first comprehensive study of the important arguments in which Aristotle makes use of the Phys. 7.5 proportions and sheds light on a rather neglected side of his physics.

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Page Count

144

Publisher

Obrake Books - (Obrake Cana

Published Date

ISBN 10

351508178X

ISBN 13

9783515081788

Plato's Forms, Mathematics and Astronomy

By: Theokritos Kouremenos

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Plato's Forms, Mathematics and Astronomy

By: Theokritos Kouremenos

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.

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Page Count

158

Published Date

ISBN 10

3110601915

ISBN 13

9783110601916

Book's by Theokritos Kouremenos

Aristotle on Mathematical Infinity

Aristotle on Mathematical Infinity

Plato’s forms, mathematics and astronomy

Plato’s forms, mathematics and astronomy

Plato’s forms, mathematics and astronomy

Plato’s forms, mathematics and astronomy

Aristotle's de Caelo Gamma

Aristotle's de Caelo Gamma

Aristotle on Mathematical Infinity

Aristotle on Mathematical Infinity

The Proportions in Aristotle's Phys. 7.5

The Proportions in Aristotle's Phys. 7.5

Plato's Forms, Mathematics and Astronomy

Plato's Forms, Mathematics and Astronomy

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