Paradoxes and Inconsistent Mathematics

Paradoxes and Inconsistent Mathematics PDF

Author: Zach Weber

Publisher: Cambridge University Press

Published: 2021-10-21

Total Pages: 339

ISBN-13: 1108999026

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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.

Courtly Contradictions

Courtly Contradictions PDF

Author: Sarah Kay

Publisher: Stanford University Press

Published: 2001

Total Pages: 412

ISBN-13: 9780804730792

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Where does courtly literature come from? What is the meaning of courtly love? What is the relation between religious and secular culture in the Middle Ages, and why does it matter? This book addresses these questions by way of contradiction, which is central both to medieval logic and to most modern protocols of reading.

Contradictions

Contradictions PDF

Author: Elena Ficara

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-08-20

Total Pages: 232

ISBN-13: 3110340828

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The papers in this volume present some of the most recent results of the work about contradictions in philosophical logic and metaphysics; examine the history of contradiction in crucial phases of philosophical thought; consider the relevance of contradictions for political and philosophical actuality. From this consideration a common question emerges: the question of the irreducibility, reality and productive force of (some) contradictions.

Beyond the Limits of Thought

Beyond the Limits of Thought PDF

Author: Graham Priest

Publisher: Oxford University Press

Published: 2002

Total Pages: 344

ISBN-13: 9780199254057

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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.

The Outer Limits of Reason

The Outer Limits of Reason PDF

Author: Noson S. Yanofsky

Publisher: MIT Press

Published: 2016-11-04

Total Pages: 419

ISBN-13: 026252984X

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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.

Contradiction Set Free

Contradiction Set Free PDF

Author: Hermann Levin Goldschmidt

Publisher: Bloomsbury Publishing

Published: 2020-01-23

Total Pages: 168

ISBN-13: 1350079804

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First published in in 1976, Hermann Levin Goldschmidt's Contradiction Set Free, (Freiheit für den Widerspruch), reflects the push to explore new forms of critical thinking that gained momentum in the decade between Theodor Adorno's Negative Dialectics of 1966 and Paul Feyerabend's Against Method in 1975. The book articulates Goldschmidt's reclamation of an epistemologically critical position that acknowledges the deep underlying link between the modes of production of knowledge and the social and political life they produce. In signalling a breakout from the academic rut and its repressive hold, Goldschmidt pointed beyond the ossified methods of a philosophical discourse whose oppressive consequences could no longer be ignored.Contradiction Set Free makes available for the first time in English a pivotal work by one of the great critical thinkers of the 20th century.

The Contradictions of Jazz

The Contradictions of Jazz PDF

Author: Paul Rinzler

Publisher: Scarecrow Press

Published: 2008-10-16

Total Pages: 226

ISBN-13: 0810862158

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In The Contradictions of Jazz, Paul Rinzler takes a new approach to jazz aesthetics and theory by exploring four pairs of opposites present in jazz: individualism and interconnectedness, assertion and openness, freedom and responsibility, and creativity and tradition. By themselves, these eight values speak volumes about the meaning of jazz and its significance. Understanding how these opposites coexist in jazz leads to an exploration of the connections linking jazz with the experiential and existential, which contrast with the connections between composition and science. Rinzler explains the various concepts, including either/or and dialectic thinking, and then examines the pairs of opposites individually, describing their position and presence in jazz. He then demonstrates how the larger meaning of these contradictory opposites depends on ideas from the philosophies of phenomenology and existentialism. Rinzler considers the opposites inherent in the product and process of jazz, as well as mistakes and the challenge of perfection, presenting these values in light of the contradictions inherent in jazz. With a full bibliography and an index, The Contradictions of Jazz is a fascinating read for fans and scholars of jazz history and aesthetics.