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Author:
Publisher: Elsevier
ISBN: 0080930662
Category : Mathematics
Languages : en
Pages : 878
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Book Description
Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights
Author:
Publisher: Elsevier
ISBN: 0080930662
Category : Mathematics
Languages : en
Pages : 878
Get Book
Book Description
Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights
Author: Charles Parsons
Publisher: Harvard University Press
ISBN: 0674419502
Category : Philosophy
Languages : en
Pages : 364
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Book Description
In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.
Author: David Ballard
Publisher: American Mathematical Soc.
ISBN: 0821802933
Category : Mathematics
Languages : en
Pages : 135
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Book Description
This work proposes a major new extension of 'non' standard mathematics. Addressed to a general mathematical audience, the book is intended to be philosophically provocative. The model theory on which 'non' standard mathematics has been based is first reformulated within point set topology, which facilitates proofs and adds perspective. These topological techniques are then used to give new, uniform conservativity proofs for the various versions of 'non'standard mathematics proposed by Nelson, Hrbacek, and Kawai.The proofs allow for sharp comparison. Addressing broader issues, Ballard then argues that what is novel in these forms of 'non'standard mathematics is the introduction, however tentative, of relativity in one's mathematical environment. This hints at the possibility of a mathematical environment which is radically relativistic. The work's major and final feature is to present and prove conservative a version of 'non'standard mathematics which, for the first time, illustrates this full radical relativism. The book is entirely self-contained, with all necessary background in point set topology, model theory, 'non'standard analysis, and set theory provided in full.
Author: Zach Weber
Publisher: Cambridge University Press
ISBN: 1108999026
Category : Mathematics
Languages : en
Pages : 339
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Book Description
Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.
Author: Jaegwon Kim
Publisher: John Wiley & Sons
ISBN: 9781444308532
Category : Philosophy
Languages : en
Pages : 680
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Book Description
Fully extended and revised, A Companion to Metaphysics 2ndEdition includes a section of detailed review essays fromrenowned metaphysicians, and the addition of more than 30 newencyclopedic entries, taking the number of entries to over 300. Includes revisions to existing encyclopedic entries Features more than 30 all-new "A to Z" entries Offers a section of in-depth, essays from renownedmetaphysicians Provides the most complete and up-to-date reference guide forstudents and professionals alike
Author: Lynne Warren
Publisher: Routledge
ISBN: 1135205361
Category : Photography
Languages : en
Pages : 2042
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Book Description
The Encyclopedia of Twentieth-Century Photography explores the vast international scope of twentieth-century photography and explains that history with a wide-ranging, interdisciplinary manner. This unique approach covers the aesthetic history of photography as an evolving art and documentary form, while also recognizing it as a developing technology and cultural force. This Encyclopedia presents the important developments, movements, photographers, photographic institutions, and theoretical aspects of the field along with information about equipment, techniques, and practical applications of photography. To bring this history alive for the reader, the set is illustrated in black and white throughout, and each volume contains a color plate section. A useful glossary of terms is also included.
Author: Dov M. Gabbay
Publisher:
ISBN:
Category : Logic
Languages : en
Pages : 0
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Book Description
In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality.
Author: Edward Craig
Publisher:
ISBN: 9780415187107
Category : Philosophy
Languages : en
Pages : 890
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Book Description
Volume five of a ten volume set which provides full and detailed coverage of all aspects of philosophy, including information on how philosophy is practiced in different countries, who the most influential philosophers were, and what the basic concepts are.
Author: Ben-Ami Scharfstein
Publisher: SUNY Press
ISBN: 9780791413470
Category : Philosophy
Languages : en
Pages : 316
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Book Description
Scharfstein describes the extraordinary powers that have been attributed to language everywhere, and then looks at ineffability as it has appeared in the thought of the great philosophical cultures: India, China, Japan, and the West. He argues that there is something of our prosaic, everyday difficulty with words in the ineffable reality of the philosophers and theologians, just as there is something unformulable, and finally mysterious in the prosaic, everyday successes and failures of words.
Author: Marie-Jeanne Lesot
Publisher: Springer Nature
ISBN: 3030543412
Category : Technology & Engineering
Languages : en
Pages : 305
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Book Description
This book gathers cutting-edge papers in the area of Computational Intelligence, presented by specialists, and covering all major trends in the research community in order to provide readers with a rich primer. It presents an overview of various soft computing topics and approximate reasoning-based approaches, both from theoretical and applied perspectives. Numerous topics are covered: fundamentals aspects of fuzzy sets theory, reasoning approaches (interpolative, analogical, similarity-based), decision and optimization theory, fuzzy databases, soft machine learning, summarization, interpretability and XAI. Moreover, several application-based papers are included, e.g. on image processing, semantic web and intelligent tutoring systems. This book is dedicated to Bernadette Bouchon-Meunier in honor of her achievements in Computational Intelligence, which, throughout her career, have included profuse and diverse collaborations, both thematically and geographically.
