Aristotle On Mathematical Infinity
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Aristotle On Mathematical Infinity
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Author : Theokritos Kouremenos
language : en
Publisher: Franz Steiner Verlag
Release Date : 1995
Aristotle On Mathematical Infinity written by Theokritos Kouremenos and has been published by Franz Steiner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with History categories.
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.
Aristotle On Mathematical Infinity
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Author : Theokritos Kouremenos
language : en
Publisher:
Release Date : 1995
Aristotle On Mathematical Infinity written by Theokritos Kouremenos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Mathematics In Aristotle
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Author : Thomas Heath
language : en
Publisher: St. Augustine's Press
Release Date : 1998
Mathematics In Aristotle written by Thomas Heath and has been published by St. Augustine's Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics, Ancient categories.
This is a detailed exposition of Aristotelian mathematics and mathematical terminology. It contains clear translations of all the most important passages on mathematics in the writings of Aristotle, together with explanatory notes and commentary by Heath. Particularly interesting are the discussions of hypothesis and related terms, of Zeno's paradox, and of the relation of mathematics to other sciences. The book includes a comprehensive index of the passages translated.
Infinity In Early Modern Philosophy
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Author : Ohad Nachtomy
language : en
Publisher: Springer
Release Date : 2018-08-31
Infinity In Early Modern Philosophy written by Ohad Nachtomy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-31 with Philosophy categories.
This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity (before early modern thought) up through Kant. Readers will learn about the place of infinity in the writings of key early modern thinkers. The contributors profile the work of Descartes, Spinoza, Leibniz, and Kant. Debates over infinity significantly influenced philosophical discussion regarding the human condition and the extent and limits of human knowledge. Questions about the infinity of space, for instance, helped lead to the introduction of a heliocentric solar system as well as the discovery of calculus. This volume offers readers an insightful look into all this and more. It provides a broad perspective that will help advance the present state of knowledge on this important but often overlooked topic.
Aristotle And Mathematics
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Author : John J. Cleary
language : en
Publisher: BRILL
Release Date : 2016-06-21
Aristotle And Mathematics written by John J. Cleary and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-21 with Philosophy categories.
John Cleary here explores the role which the mathematical sciences play in Aristotle's philosophical thought, especially in his cosmology, metaphysics, and epistemology. He also thematizes the aporetic method by means of which he deals with philosophical questions about the foundations of mathematics. The first two chapters consider Plato's mathematical cosmology in the light of Aristotle's critical distinction between physics and mathematics. Subsequent chapters examine three basic aporiae about mathematical objects which Aristotle himself develops in his science of first philosophy. What emerges from this dialectical inquiry is a different conception of substance and of order in the universe, which gives priority to physics over mathematics as the cosmological science. Within this different world-view, we can better understand what we now call Aristotle's philosophy of mathematics.
Aristotle And Mathematics
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Author : John J. Cleary
language : en
Publisher: BRILL
Release Date : 1995
Aristotle And Mathematics written by John J. Cleary and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Philosophy categories.
This book examines Aristotle's critical reaction to the mathematical cosmology of Plato's Academy, and traces the aporetic method by which he developed his own cosmological and metaphysical views, which underpin his philosophy of mathematics.
The Infinite
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Author : A.W. Moore
language : en
Publisher: Routledge
Release Date : 2018-10-09
The Infinite written by A.W. Moore and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-09 with Philosophy categories.
We are all captivated and puzzled by the infinite, in its many varied guises; by the endlessness of space and time; by the thought that between any two points in space, however close, there is always another; by the fact that numbers go on forever; and by the idea of an all-knowing, all-powerful God. In this acclaimed introduction to the infinite, A. W. Moore takes us on a journey back to early Greek thought about the infinite, from its inception to Aristotle. He then examines medieval and early modern conceptions of the infinite, including a brief history of the calculus, before turning to Kant and post-Kantian ideas. He also gives an account of Cantor’s remarkable discovery that some infinities are bigger than others. In the second part of the book, Moore develops his own views, drawing on technical advances in the mathematics of the infinite, including the celebrated theorems of Skolem and Gödel, and deriving inspiration from Wittgenstein. He concludes this part with a discussion of death and human finitude. For this third edition Moore has added a new part, ‘Infinity superseded’, which contains two new chapters refining his own ideas through a re-examination of the ideas of Spinoza, Hegel, and Nietzsche. This new part is heavily influenced by the work of Deleuze. Also new for the third edition are: a technical appendix on still unresolved questions about different infinite sizes; an expanded glossary; and updated references and further reading. The Infinite, Third Edition is ideal reading for anyone interested in an engaging and historically informed account of this fascinating topic, whether from a philosophical point of view, a mathematical point of view, or a religious point of view.
Naming Infinity
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Author : Loren Graham
language : en
Publisher: Harvard University Press
Release Date : 2009-03-31
Naming Infinity written by Loren Graham and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-31 with Science categories.
In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.
The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics
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Author : John L. Bell
language : en
Publisher: Springer Nature
Release Date : 2019-09-09
The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics written by John L. Bell and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
Paradoxes Of The Infinite Routledge Revivals
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Author : Bernard Bolzano
language : en
Publisher: Routledge
Release Date : 2014-03-18
Paradoxes Of The Infinite Routledge Revivals written by Bernard Bolzano and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-18 with Philosophy categories.
Paradoxes of the Infinite presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19th century: Dr Bernard Bolzano’s Paradoxien. This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.