Aristotle On Mathematical Infinity

Author : Theokritos Kouremenos,Aristotle
Publisher : Franz Steiner Verlag
Page : 142 pages
File Size : 43,9 Mb
Release : 1995
Category : History
ISBN : 3515068511

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Aristotle on Mathematical Infinity by Theokritos Kouremenos,Aristotle Pdf

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.

Author : Theokritos Kouremenos,David E.. Hahm
Publisher : Unknown
Page : 306 pages
File Size : 46,9 Mb
Release : 1995
Category : Electronic
ISBN : OCLC:35563412

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Aristotle on Mathematical Infinity by Theokritos Kouremenos,David E.. Hahm Pdf

Author : A. W. Moore
Publisher : Psychology Press
Page : 294 pages
File Size : 40,7 Mb
Release : 1990
Category : Philosophy
ISBN : 9780415070485

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The Infinite by A. W. Moore Pdf

This historical study of the infinite covers all its aspects from the mathematical to the mystical. Anyone who has ever pondered the limitlessness of space and time, or the endlessness of numbers, or the perfection of God will recognize the special fascination of the subject. Beginning with an entertaining account of the main paradoxes of the infinite, including those of Zeno, A.W. Moore traces the history of the topic from Aristotle to Kant, Hegel, Cantor, and Wittgenstein.

Author : Anthony C. Patton
Publisher : Algora Publishing
Page : 200 pages
File Size : 47,5 Mb
Release : 2018-07-01
Category : Philosophy
ISBN : 9781628943412

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The End of Infinity by Anthony C. Patton Pdf

Author : Emanuele Gambetta
Publisher : Gangemi Editore spa
Page : 167 pages
File Size : 42,8 Mb
Release : 2021-01-03T00:00:00+01:00
Category : Philosophy
ISBN : 9788849244427

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Philosophy of the Infinite by Emanuele Gambetta Pdf

Infinity is a fascinating subject. What do we mean when we use the concept of infinity? What did the ancient Greeks mean? What do modern mathematicians mean when they use infinity in their calculations? What are the debates of contemporary philosophers of mathematics regarding the infinite? This book, starting from Aristotle and Plato, tries to retrace the steps that led to contemporary conceptions of infinity. The book also deals with the first mathematical problem of the twentieth century on Hilbert's list with no solution that has correlations with the concept of infinity. Is the mathematical universe unique or do we have infinite parallel universes with different truths? This is a question related to the concept of infinity and the book tries to answer it. The goal of this book is to make the mathematics of infinity accessible by showing the most incredible mathematical results of the last century and deepening the themes of contemporary debates in mathematics and philosophy regarding infinity. EMANUELE GAMBETTA obtained his PHD in philosophy of mathematics from the Scuola Normale Superiore with cum laude mark. He was a visiting research student at the university of Barcelona where he participated in the seminars of the set theory center. He has been a visiting graduate student in many universities around the world. Infinity is a fascinating subject. What do we mean when we use the concept of infinity? What did the ancient Greeks mean? What do modern mathematicians mean when they use infinity in their calculations? What are the debates of contemporary philosophers of mathematics regarding the infinite? This book, starting from Aristotle and Plato, tries to retrace the steps that led to contemporary conceptions of infinity. The book also deals with the first mathematical problem of the twentieth century on Hilbert's list with no solution that has correlations with the concept of infinity. Is the mathematical universe unique or do we have infinite parallel universes with different truths? This is a question related to the concept of infinity and the book tries to answer it. The goal of this book is to make the mathematics of infinity accessible by showing the most incredible mathematical results of the last century and deepening the themes of contemporary debates in mathematics and philosophy regarding infinity. EMANUELE GAMBETTA obtained his PHD in philosophy of mathematics from the Scuola Normale Superiore with cum laude mark. He was a visiting research student at the university of Barcelona where he participated in the seminars of the set theory center. He has been a visiting graduate student in many universities around the world. Infinity is a fascinating subject. What do we mean when we use the concept of infinity? What did the ancient Greeks mean? What do modern mathematicians mean when they use infinity in their calculations? What are the debates of contemporary philosophers of mathematics regarding the infinite? This book, starting from Aristotle and Plato, tries to retrace the steps that led to contemporary conceptions of infinity. The book also deals with the first mathematical problem of the twentieth century on Hilbert's list with no solution that has correlations with the concept of infinity. Is the mathematical universe unique or do we have infinite parallel universes with different truths? This is a question related to the concept of infinity and the book tries to answer it. The goal of this book is to make the mathematics of infinity accessible by showing the most incredible mathematical results of the last century and deepening the themes of contemporary debates in mathematics and philosophy regarding infinity. EMANUELE GAMBETTA obtained his PHD in philosophy of mathematics from the Scuola Normale Superiore with cum laude mark. He was a visiting research student at the university of Barcelona where he participated in the seminars of the set theory center. He has been a visiting graduate student in many universities around the world.

Author : John J. Cleary
Publisher : BRILL
Page : 597 pages
File Size : 51,5 Mb
Release : 2016-06-21
Category : Philosophy
ISBN : 9789004320901

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Aristotle and Mathematics by John J. Cleary Pdf

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.

Author : Ian Stewart
Publisher : Oxford University Press
Page : 144 pages
File Size : 45,7 Mb
Release : 2017-03-13
Category : Mathematics
ISBN : 9780191071515

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Infinity: A Very Short Introduction by Ian Stewart Pdf

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals. In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Author : Thomas Heath
Publisher : Routledge
Page : 374 pages
File Size : 51,8 Mb
Release : 2015-08-14
Category : Philosophy
ISBN : 9781317380597

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Mathematics in Aristotle by Thomas Heath Pdf

Originally published in 1949. This meticulously researched book presents a comprehensive outline and discussion of Aristotle’s mathematics with the author's translations of the greek. To Aristotle, mathematics was one of the three theoretical sciences, the others being theology and the philosophy of nature (physics). Arranged thematically, this book considers his thinking in relation to the other sciences and looks into such specifics as squaring of the circle, syllogism, parallels, incommensurability of the diagonal, angles, universal proof, gnomons, infinity, agelessness of the universe, surface of water, meteorology, metaphysics and mechanics such as levers, rudders, wedges, wheels and inertia. The last few short chapters address ‘problems’ that Aristotle posed but couldn’t answer, related ethics issues and a summary of some short treatises that only briefly touch on mathematics.

Author : A. W. Moore
Publisher : Dartmouth Publishing Company
Page : 488 pages
File Size : 52,6 Mb
Release : 1993
Category : Mathematics
ISBN : UOM:39015029074484

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Infinity by A. W. Moore Pdf

Author : Stewart Shapiro,Geoffrey Hellman
Publisher : Oxford University Press
Page : 320 pages
File Size : 40,6 Mb
Release : 2020-12-01
Category : Philosophy
ISBN : 9780192537492

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The History of Continua by Stewart Shapiro,Geoffrey Hellman Pdf

Mathematical and philosophical thought about continuity has changed considerably over the ages. Aristotle insisted that continuous substances are not composed of points, and that they can only be divided into parts potentially. There is something viscous about the continuous. It is a unified whole. This is in stark contrast with the prevailing contemporary account, which takes a continuum to be composed of an uncountably infinite set of points. This vlume presents a collective study of key ideas and debates within this history. The opening chapters focus on the ancient world, covering the pre-Socratics, Plato, Aristotle, and Alexander. The treatment of the medieval period focuses on a (relatively) recently discovered manuscript, by Bradwardine, and its relation to medieval views before, during, and after Bradwardine's time. In the so-called early modern period, mathematicians developed the calculus and, with that, the rise of infinitesimal techniques, thus transforming the notion of continuity. The main figures treated here include Galileo, Cavalieri, Leibniz, and Kant. In the early party of the nineteenth century, Bolzano was one of the first important mathematicians and philosophers to insist that continua are composed of points, and he made a heroic attempt to come to grips with the underlying issues concerning the infinite. The two figures most responsible for the contemporary orthodoxy regarding continuity are Cantor and Dedekind. Each is treated in an article, investigating their precursors and influences in both mathematics and philosophy. A new chapter then provides a lucid analysis of the work of the mathematician Paul Du Bois-Reymond, to argue for a constructive account of continuity, in opposition to the dominant Dedekind-Cantor account. This leads to consideration of the contributions of Weyl, Brouwer, and Peirce, who once dubbed the notion of continuity "the master-key which . . . unlocks the arcana of philosophy". And we see that later in the twentieth century Whitehead presented a point-free, or gunky, account of continuity, showing how to recover points as a kind of "extensive abstraction". The final four chapters each focus on a more or less contemporary take on continuity that is outside the Dedekind-Cantor hegemony: a predicative approach, accounts that do not take continua to be composed of points, constructive approaches, and non-Archimedean accounts that make essential use of infinitesimals.

Author : M. Huemer
Publisher : Springer
Page : 275 pages
File Size : 51,8 Mb
Release : 2016-05-23
Category : Philosophy
ISBN : 9781137560872

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Approaching Infinity by M. Huemer Pdf

Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes.

Author : Michael Heller,W. Hugh Woodin
Publisher : Cambridge University Press
Page : 0 pages
File Size : 45,6 Mb
Release : 2014-01-02
Category : Mathematics
ISBN : 1107685486

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Infinity by Michael Heller,W. Hugh Woodin Pdf

"The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite." - David Hilbert This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world‐renowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than displaying a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: Can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity.

Author : Saburou Saitoh
Publisher : Scientific Research Publishing, Inc. USA
Page : 333 pages
File Size : 49,7 Mb
Release : 2021-11-29
Category : Antiques & Collectibles
ISBN : 9781649972255

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Division by Zero Calculus—History and Development by Saburou Saitoh Pdf

This is based on the record of how I have been discovering and pioneering a new world by breaking the first of the Ten Commandments of Mathematics, which has been 2300 years since Aristotle and must not be divided by zero. I am involved in the basic issues of humankind involved in mathematical physics, philosophy, and worldview. What is eternity and what is infinity? What is the significance of human existence?

Author : J. Franklin
Publisher : Springer
Page : 308 pages
File Size : 43,9 Mb
Release : 2014-04-09
Category : Mathematics
ISBN : 9781137400734

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An Aristotelian Realist Philosophy of Mathematics by J. Franklin Pdf

Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

Author : Paolo Zellini
Publisher : Penguin Global
Page : 212 pages
File Size : 43,7 Mb
Release : 2005
Category : Mathematics
ISBN : STANFORD:36105114563237

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A Brief History of Infinity by Paolo Zellini Pdf

In A Brief History of Infinity, the infinite in all its forms - viewed from the perspective of mathematicians, philosophers, and theologians - is explored, as Zellini strives to explain this fundamental principle. What is the difference between trueand false infinity? How might we explain away the puzzle of Zeno's paradox? And how is the concept of infinity helping us as we wrestle with the fundamental uncertainties of the quantum world? Paolo Zellini shows that the concept of the infinite is a multifaceted one, and eloquently demonstrates the manner in which humanity has attempted to comprehend that concept for millenia.