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Iamblichus: On the General Science of Mathematics

Iamblichus: On the General Science of Mathematics PDF Author: John Dillon
Publisher: Bloomsbury Academic
ISBN: 9781350194847
Category : Mathematics
Languages : en
Pages : 176

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Book Description
On the General Science of Mathematics is the third of four surviving works out of ten by Iamblichus (c. 245 CE–early 320s) on the Pythagoreans. He thought the Pythagoreans had treated mathematics as essential for drawing the human soul upwards to higher realms described by Plato, and downwards to understand the physical cosmos, the products of arts and crafts and the order required for an ethical life. His Pythagorean treatises use edited quotation to re-tell the history of philosophy, presenting Plato and Aristotle as passing on the ideas invented by Pythagoras and his early followers. Although his quotations tend to come instead from Plato and later Pythagoreanising Platonists, this re-interpretation had a huge impact on the Neoplatonist commentators in Athens. Iamblichus' cleverness, if not to the same extent his re-interpretation, was appreciated by the commentators in Alexandria.

Iamblichus: On the General Science of Mathematics

Iamblichus: On the General Science of Mathematics PDF Author: John Dillon
Publisher: Bloomsbury Academic
ISBN: 9781350194847
Category : Mathematics
Languages : en
Pages : 176

View

Book Description
On the General Science of Mathematics is the third of four surviving works out of ten by Iamblichus (c. 245 CE–early 320s) on the Pythagoreans. He thought the Pythagoreans had treated mathematics as essential for drawing the human soul upwards to higher realms described by Plato, and downwards to understand the physical cosmos, the products of arts and crafts and the order required for an ethical life. His Pythagorean treatises use edited quotation to re-tell the history of philosophy, presenting Plato and Aristotle as passing on the ideas invented by Pythagoras and his early followers. Although his quotations tend to come instead from Plato and later Pythagoreanising Platonists, this re-interpretation had a huge impact on the Neoplatonist commentators in Athens. Iamblichus' cleverness, if not to the same extent his re-interpretation, was appreciated by the commentators in Alexandria.

Iamblichus: On the General Science of Mathematics

Iamblichus: On the General Science of Mathematics PDF Author: John Dillon
Publisher: Bloomsbury Publishing
ISBN: 1350127671
Category : Mathematics
Languages : en
Pages : 176

View

Book Description
On the General Science of Mathematics is the third of four surviving works out of ten by Iamblichus (c. 245 CE–early 320s) on the Pythagoreans. He thought the Pythagoreans had treated mathematics as essential for drawing the human soul upwards to higher realms described by Plato, and downwards to understand the physical cosmos, the products of arts and crafts and the order required for an ethical life. His Pythagorean treatises use edited quotation to re-tell the history of philosophy, presenting Plato and Aristotle as passing on the ideas invented by Pythagoras and his early followers. Although his quotations tend to come instead from Plato and later Pythagoreanising Platonists, this re-interpretation had a huge impact on the Neoplatonist commentators in Athens. Iamblichus' cleverness, if not to the same extent his re-interpretation, was appreciated by the commentators in Alexandria.

Descartes’s Mathematical Thought

Descartes’s Mathematical Thought PDF Author: C. Sasaki
Publisher: Springer Science & Business Media
ISBN: 9781402017469
Category : Mathematics
Languages : en
Pages : 526

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Book Description
Covering both the history of mathematics and of philosophy, Descartes's Mathematical Thought reconstructs the intellectual career of Descartes most comprehensively and originally in a global perspective including the history of early modern China and Japan. Especially, it shows what the concept of "mathesis universalis" meant before and during the period of Descartes and how it influenced the young Descartes. In fact, it was the most fundamental mathematical discipline during the seventeenth century, and for Descartes a key notion which may have led to his novel mathematics of algebraic analysis.

Science Writing in Greco-Roman Antiquity

Science Writing in Greco-Roman Antiquity PDF Author: Liba Taub
Publisher: Cambridge University Press
ISBN: 0521113709
Category : History
Languages : en
Pages : 211

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Book Description
This book explores how science and mathematics were communicated in antiquity in a wide variety of texts, including poetry, letters and biographies.

Plato and Pythagoreanism

Plato and Pythagoreanism PDF Author: Phillip Sidney Horky
Publisher: Oxford University Press
ISBN: 0190465700
Category : History
Languages : en
Pages : 328

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Book Description
Was Plato a Pythagorean? Plato's students and earliest critics thought so, but scholars since the nineteenth century have been more skeptical. With this probing study, Phillip Sidney Horky argues that a specific type of Pythagorean philosophy, called mathematical Pythagoreanism, exercised a decisive influence on fundamental aspects of Plato's philosophy. The progenitor of mathematical Pythagoreanism was the infamous Pythagorean heretic and political revolutionary Hippasus of Metapontum, a student of Pythagoras who is credited with experiments in harmonics that led to innovations in mathematics. The innovations of Hippasus and other mathematical Pythagoreans, including Empedocles of Agrigentum, Epicharmus of Syracuse, Philolaus of Croton, and Archytas of Tarentum, presented philosophers like Plato with novel ways to reconcile empirical knowledge with abstract mathematical theories. Plato and Pythagoreanism demonstrates how mathematical Pythagoreanism established many of the fundamental philosophical questions Plato dealt with in his central dialogues, including Cratylus, Phaedo, Republic, Timaeus, and Philebus. In the process, it also illuminates the historical significance of the mathematical Pythagoreans, a group whose influence on the development of philosophical and scientific methods has been obscured since late antiquity. The picture that results is one in which Plato inherits mathematical Pythagorean method only to transform it into a powerful philosophical argument about the essential relationships between the cosmos and the human being.

Platonisms

Platonisms PDF Author: Kevin Corrigan
Publisher: BRILL
ISBN: 9004158413
Category : Philosophy
Languages : en
Pages : 292

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Book Description
By questioning the modern categories of Plato and Platonism, this book offers new ways of reading the Platonic dialogues and the many traditions that resonate in them from Antiquity to Post-Modernity.

The Poetics of Phantasia

The Poetics of Phantasia PDF Author: Anne Sheppard
Publisher: A&C Black
ISBN: 1472509218
Category : Philosophy
Languages : en
Pages : 256

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Book Description
With a thorough examination of ancient views of literary and artistic realism, allegory and symbolism, The Poetics of Phantasia brings together a study of the ways in which the concept of imagination (phantasia in Greek) was used in ancient aesthetics and literary theory. The Greeks and Romans tended to think of the production of works of art in terms of imitation, either of the world around us or of a transcendent ideal world, rather than in terms of originality and creativity. Study of the way phantasia is used in ancient writing about literature and art reveals important features of the ancient approach to the arts and in doing so will also shed light on modern concepts of imagination and the literary and artistic differences between realism and allegory. Covering a range of literary and philosophical material from the beginnings of Greek literature down to the Neoplatonist philosophers of late antiquity, The Poetics of Phantasia discusses three discrete senses of imagination in ancient thought. Firstly, phantasia as visualization is explored: when a writer 'brings before his eyes' what he is describing and enables his audience or reader to visualise it likewise. The second theory of phantasia is that which is capable not only of conveying images from sense-perception but also of receiving images from intellectual and supra-intellectual faculties in the soul, and thus helping people grasp mathematical, metaphysical or even mystical concepts. Finally, phantasia is seen as a creative power which can conjure up an image that points beyond itself and to express ideas outside our everyday experience.

Pythagoras Revived

Pythagoras Revived PDF Author: Dominic J. O'Meara
Publisher: Clarendon Press
ISBN: 0191519804
Category : Philosophy
Languages : en
Pages : 264

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Book Description
The Pythagorean idea that number is the key to understanding reality inspired Neoplatonist philosophers in the fourth and fifth centuries to develop theories in physics and metaphysics based on mathematical models. The theories produced by this revived interest in Pythagoreanism were to become influential in medieval and early modern philosophy, and this book makes use of some newly-discovered evidence to examine for the first time the development of those theories.

A New History of Greek Mathematics

A New History of Greek Mathematics PDF Author: Reviel Netz
Publisher: Cambridge University Press
ISBN: 1108991912
Category : Philosophy
Languages : en
Pages : 541

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Book Description
The ancient Greeks played a fundamental role in the history of mathematics and their ideas were reused and developed in subsequent periods all the way down to the scientific revolution and beyond. In this, the first complete history for a century. Reviel Netz offers a panoramic view of the rise and influence of Greek mathematics and its significance in world history. He explores the Near Eastern antecedents and the social and intellectual developments underlying the subject's beginnings in Greece in the fifth century BCE. He leads the reader through the proofs and arguments of key figures like Archytas, Euclid and Archimedes, and considers the totality of the Greek mathematical achievement which also includes, in addition to pure mathematics, such applied fields as optics, music, mechanics and, above all, astronomy. This is the story not only of a major historical development, but of some of the finest mathematics ever created.

Cause and Explanation in Ancient Greek Thought

Cause and Explanation in Ancient Greek Thought PDF Author: R. J. Hankinson
Publisher: Oxford University Press
ISBN: 0199246564
Category : Philosophy
Languages : en
Pages : 516

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Book Description
This work traces the history of ancient Greek thought about causation and explanation. It examines ways in which they dealt with questions about how and why things happen, about the constitution and structure of things, laws of nature, and more.

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