One Hundred Years of Russell's Paradox
One Hundred Years of Russell's Paradox

Author: Godehard Link

Publisher: Walter de Gruyter

Published: 2004

Total Pages: 672

ISBN-13: 3110174383

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The papers collected in this volume represent the main body of research arising from the International Munich Centenary Conference in 2001, which commemorated the discovery of the famous Russell Paradox a hundred years ago. The 31 contributions and the introductory essay by the editor were (with two exceptions) all originally written for the volume. The volume serves a twofold purpose, historical and systematic. One focus is on Bertrand Russell's logic and logical philosophy, taking into account the rich sources of the Russell Archives, many of which have become available only recently. The second equally important aim is to present original research in the broad range of foundational studies that draws on both current conceptions and recent technical advances in the above-mentioned fields. The volume contributes therefore, to the well-established body of mathematical philosophy initiated to a large extent by Russell's work.

One Hundred Years of Russell ́s Paradox
One Hundred Years of Russell ́s Paradox

Author: Godehard Link

Publisher: Walter de Gruyter

Published: 2008-08-22

Total Pages: 673

ISBN-13: 3110199688

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The papers collected in this volume represent the main body of research arising from the International Munich Centenary Conference in 2001, which commemorated the discovery of the famous Russell Paradox a hundred years ago. The 31 contributions and the introductory essay by the editor were (with two exceptions) all originally written for the volume. The volume serves a twofold purpose, historical and systematic. One focus is on Bertrand Russell's logic and logical philosophy, taking into account the rich sources of the Russell Archives, many of which have become available only recently. The second equally important aim is to present original research in the broad range of foundational studies that draws on both current conceptions and recent technical advances in the above-mentioned fields. The volume contributes therefore, to the well-established body of mathematical philosophy initiated to a large extent by Russell's work.

The Outer Limits of Reason
The Outer Limits of Reason

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.

Exploring Theological Paradoxes
Exploring Theological Paradoxes

Author: Cyril Orji

Publisher: Taylor & Francis

Published: 2022-08-31

Total Pages: 208

ISBN-13: 1000640388

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This book focuses on the question of theological paradox, exploring what it means and its place in theological method from a Christian perspective. Just as paradoxes are unavoidable in logic and mathematics, paradoxes are inevitable in religious and theological discourses. The chapters in this volume examine a number of cases, including the ‘Red Heifer paradox’, the ‘liar paradox’, and the ‘paradox of omnipotence’, and attention is given to Christian doctrines such as the Trinity and the Incarnation. Arguing for a renewed understanding and appreciation of the role of paradox, this study will be of interest to scholars of theology and the philosophy of religion.

Recursion Theory
Recursion Theory

Author: Chi Tat Chong

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2015-08-17

Total Pages: 409

ISBN-13: 311038129X

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This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory. The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.

Russell vs. Meinong
Russell vs. Meinong

Author: Nicholas Griffin

Publisher: Routledge

Published: 2008-11-19

Total Pages: 456

ISBN-13: 1135893144

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A century after ‘On Denoting’ was published, the debate it initiated continues to rage. On the one hand, there is a mass of new historical scholarship, about both Russell and Meinong, which has not circulated very far beyond specialist scholars. On the other hand, there are continuing problems and controversies concerning contemporary Russellian and Meinongian theories, many of them involving issues that simply did not occur to the original protagonists. This work provides an overview of the latest historical scholarship on the two philosophers as well as detailed accounts of some of the problems facing the current incarnations of their theories.

Fixing Frege
Fixing Frege

Author: John P. Burgess

Publisher: Princeton University Press

Published: 2005-07-25

Total Pages: 276

ISBN-13: 9780691122311

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Gottlob Frege's attempt to found mathematics on a grand logical system came to grief when Bertrand Russell discovered a contradiction in it. This book surveys consistent restrictions in both the old and new versions of Frege's system, determining just how much of mathematics can be reconstructed in each.

Frege
Frege

Author: Michael Dummett

Publisher: Harvard University Press

Published: 1991

Total Pages: 364

ISBN-13: 9780674319356

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No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.