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Author: Noson S. Yanofsky
Publisher: MIT Press
ISBN: 026252984X
Category : Science
Languages : en
Pages : 419
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Book Description
This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.
Author: Noson S. Yanofsky
Publisher: MIT Press
ISBN: 026252984X
Category : Science
Languages : en
Pages : 419
Get Book Here
Book Description
This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.
Author: Stewart Shapiro
Publisher: Routledge
ISBN: 1351886665
Category : Philosophy
Languages : en
Pages : 352
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Book Description
The International research Library of Philosophy collects in book form a wide range of important and influential essays in philosophy, drawn predominantly from English-language journals. Each volume in the library deals with a field of enquiry which has received significant attention in philosophy in the last 25 years and is edited by a philosopher noted in that field.
Author: Patrick Shaw
Publisher: Oxford University Press on Demand
ISBN: 9780192892805
Category : Philosophy
Languages : en
Pages : 260
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Book Description
A common-sense introduction to the everyday use of logic, this book explains some of the rules of good argument and some of the ways in which arguments can fail, drawing illustrations from a variety of contemporary and international sources. A wide range of thought-provoking examples and exercises make this a readable and stimulating guide for the student and general reader alike. Diagrams.
Author: Moshe Machover
Publisher: Cambridge University Press
ISBN: 9780521479981
Category : Mathematics
Languages : en
Pages : 304
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Book Description
This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.
Author: Bernard Barber
Publisher:
ISBN:
Category : Social Science
Languages : en
Pages : 208
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Book Description
Author: Eugenia Cheng
Publisher: Basic Books
ISBN: 154167250X
Category : Mathematics
Languages : en
Pages : 321
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Book Description
How both logical and emotional reasoning can help us live better in our post-truth world In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic -- for example, emotion -- is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.
Author: Graham Priest
Publisher: Oxford University Press
ISBN: 9780199254057
Category : Philosophy
Languages : en
Pages : 344
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Book Description
Graham Priest presents an expanded edition of his exploration of the nature and limits of thought. Embracing contradiction and challenging traditional logic, he engages with issues across philosophical borders, from the historical to the modern, Eastern to Western, continental to analytic.
Author: William Davies
Publisher: SAGE
ISBN: 152641161X
Category : Social Science
Languages : en
Pages : 249
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Book Description
Brilliant...explains how the rhetoric of competition has invaded almost every domain of our existence." —Evgeny Morozov, author of To Save Everything, Click Here" "In this fascinating book Davies inverts the conventional neoliberal practice of treating politics as if it were mere epiphenomenon of market theory, demonstrating that their version of economics is far better understood as the pursuit of politics by other means." —Professor Philip Mirowski, University of Notre Dame "A sparkling, original, and provocative analysis of neoliberalism. It offers a distinctive account of the diverse, sometimes contradictory, conventions and justifications that lend authority to the extension of the spirit of competitiveness to all spheres of social life...This book breaks new ground, offers new modes of critique, and points to post-neoliberal futures." —Professor Bob Jessop, University of Lancaster Since its intellectual inception in the 1930s and its political emergence in the 1970s, neo-liberalism has sought to disenchant politics by replacing it with economics. This agenda-setting text examines the efforts and failures of economic experts to make government and public life amenable to measurement, and to re-model society and state in terms of competition. In particular, it explores the practical use of economic techniques and conventions by policy-makers, politicians, regulators and judges and how these practices are being adapted to the perceived failings of the neoliberal model. By picking apart the defining contradiction that arises from the conflation of economics and politics, this book asks: to what extent can economics provide government legitimacy? Now with a new preface from the author and a foreword by Aditya Chakrabortty.
Author: Leon Chwistek
Publisher: Routledge
ISBN: 1317829840
Category : Philosophy
Languages : en
Pages : 406
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Book Description
This is Volume III of eight in a series on the Philosophy of Logic and Mathematics. Originally published in 1948, this book portrays an outline of logic and of the methodology of the exact sciences.
Author: Michael Shenefelt
Publisher: Columbia University Press
ISBN: 0231161050
Category : Philosophy
Languages : en
Pages : 352
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Book Description
While logical principles seem timeless, placeless, and eternal, their discovery is a story of personal accidents, political tragedies, and broad social change. If A, Then B begins with logic's emergence twenty-three centuries ago and tracks its expansion as a discipline ever since. It explores where our sense of logic comes from and what it really is a sense of. It also explains what drove human beings to start studying logic in the first place. Logic is more than the work of logicians alone. Its discoveries have survived only because logicians have also been able to find a willing audience, and audiences are a consequence of social forces affecting large numbers of people, quite apart from individual will. This study therefore treats politics, economics, technology, and geography as fundamental factors in generating an audience for logic--grounding the discipline's abstract principles in a compelling material narrative. The authors explain the turbulent times of the enigmatic Aristotle, the ancient Stoic Chrysippus, the medieval theologian Peter Abelard, and the modern thinkers René Descartes, David Hume, Jeremy Bentham, George Boole, Augustus De Morgan, John Stuart Mill, Gottlob Frege, Bertrand Russell, and Alan Turing. Examining a variety of mysteries, such as why so many branches of logic (syllogistic, Stoic, inductive, and symbolic) have arisen only in particular places and periods, If A, Then B is the first book to situate the history of logic within the movements of a larger social world. If A, Then B is the 2013 Gold Medal winner of Foreword Reviews' IndieFab Book of the Year Award for Philosophy.
