The Philosophy Of The Infinite
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Infinity And The Mind
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Author : Rudy Rucker
language : en
Publisher: Bantam Books
Release Date : 1983-01-01
Infinity And The Mind written by Rudy Rucker and has been published by Bantam Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-01 with Philosophy categories.
The book contains popular expositions (accessible to readers with no more than a high school mathematics background) on the mathematical theory of infinity, and a number of related topics. These include G?del's incompleteness theorems and their relationship to concepts of artificial intelligence and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical. There is a brief account of the author's personal contact with Kurt G?del.An appendix contains one of the few popular expositions on set theory research on what are known as "strong axioms of infinity."
Philosophical Perspectives On Infinity
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Author : Graham Oppy
language : en
Publisher: Cambridge University Press
Release Date : 2006-04-03
Philosophical Perspectives On Infinity written by Graham Oppy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-03 with Philosophy categories.
This book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the nature of part/whole relations, mathematical theories of the infinite, and infinite regression and principles of sufficient reason.
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.
Georg Cantor
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Author : Joseph Warren Dauben
language : en
Publisher: Princeton University Press
Release Date : 1990
Georg Cantor written by Joseph Warren Dauben and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Biography & Autobiography categories.
One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now a vital component of elementary school curricula. Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradoxes in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by recurring attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.
The Philosophy Of The Infinite
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Author : Emanuel Swedenborg
language : en
Publisher:
Release Date : 1848
The Philosophy Of The Infinite written by Emanuel Swedenborg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1848 with Infinite categories.
The Philosophy Of The Infinite Translated By James John Garth Wilkinson Copied From The London Edition Etc
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Author : Emanuel Swedenborg
language : en
Publisher:
Release Date : 1848
The Philosophy Of The Infinite Translated By James John Garth Wilkinson Copied From The London Edition Etc written by Emanuel Swedenborg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1848 with categories.
The Philosophy Of The Infinite
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Author : Henry Calderwood (philosophe).)
language : en
Publisher:
Release Date : 1854
The Philosophy Of The Infinite written by Henry Calderwood (philosophe).) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1854 with Infinite categories.
The Philosophy Of The Infinite
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Author : Henry Calderwood
language : en
Publisher:
Release Date : 1854
The Philosophy Of The Infinite written by Henry Calderwood and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1854 with Infinite categories.
Understanding The Infinite
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Author : Shaughan Lavine
language : en
Publisher: Harvard University Press
Release Date : 1994
Understanding The Infinite written by Shaughan Lavine 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 1994 with Mathematics categories.
How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge.
The Philosophy Of Set Theory
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Author : Mary Tiles
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
The Philosophy Of Set Theory written by Mary Tiles and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
A century ago, Georg Cantor demonstrated the possibility of a series of transfinite infinite numbers. His methods, unorthodox for the time, enabled him to derive theorems that established a mathematical reality for a hierarchy of infinities. Cantor's innovation was opposed, and ignored, by the establishment; years later, the value of his work was recognized and appreciated as a landmark in mathematical thought, forming the beginning of set theory and the foundation for most of contemporary mathematics. As Cantor's sometime collaborator, David Hilbert, remarked, "No one will drive us from the paradise that Cantor has created." This volume offers a guided tour of modern mathematics' Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory; logical objects and logical types; and independence results and the universe of sets. She concludes with views of the constructs and reality of mathematical structure. Philosophers with only a basic grounding in mathematics, as well as mathematicians who have taken only an introductory course in philosophy, will find an abundance of intriguing topics in this text, which is appropriate for undergraduate-and graduate-level courses.