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Author: Godehard Link
Publisher: Walter de Gruyter
ISBN: 3110174383
Category : Mathematics
Languages : en
Pages : 672
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Book Description
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.
Author: Godehard Link
Publisher: Walter de Gruyter
ISBN: 3110174383
Category : Mathematics
Languages : en
Pages : 672
Get Book Here
Book Description
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.
Author: Godehard Link
Publisher: Walter de Gruyter
ISBN: 3110199688
Category : Mathematics
Languages : en
Pages : 673
Get Book Here
Book Description
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.
Author: Alfred North Whitehead
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 688
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Book Description
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: Nicholas Griffin
Publisher: Routledge
ISBN: 1135893144
Category : Philosophy
Languages : en
Pages : 456
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Book Description
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.
Author: Chi Tat Chong
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311038129X
Category : Mathematics
Languages : en
Pages : 409
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Book Description
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.
Author: Thomas Drucker
Publisher: Springer Science & Business Media
ISBN: 0817647694
Category : Mathematics
Languages : en
Pages : 218
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Book Description
This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.
Author: Bertrand Russell
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 565
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Book Description
Author: Michael B. Katz
Publisher: Russell Sage Foundation
ISBN: 1610443314
Category : Social Science
Languages : en
Pages : 369
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Book Description
American society today is hardly recognizable from what it was a century ago. Integrated schools, an information economy, and independently successful women are just a few of the remarkable changes that have occurred over just a few generations. Still, the country today is influenced by many of the same factors that revolutionized life in the late nineteenth century—immigration, globalization, technology, and shifting social norms—and is plagued by many of the same problems—economic, social, and racial inequality. One Nation Divisible, a sweeping history of twentieth-century American life by Michael B. Katz and Mark J. Stern, weaves together information from the latest census with a century's worth of data to show how trends in American life have changed while inequality and diversity have endured. One Nation Divisible examines all aspects of work, family, and social life to paint a broad picture of the American experience over the long arc of the twentieth century. Katz and Stern track the transformations of the U.S. workforce, from the farm to the factory to the office tower. Technological advances at the beginning and end of the twentieth century altered the demand for work, causing large population movements between regions. These labor market shifts fed both the explosive growth of cities at the dawn of the industrial age and the sprawling suburbanization of today. One Nation Divisible also discusses how the norms of growing up and growing old have shifted. Whereas the typical life course once involved early marriage and living with large, extended families, Americans today commonly take years before marrying or settling on a career path, and often live in non-traditional households. Katz and Stern examine the growing influence of government on trends in American life, showing how new laws have contributed to more diverse neighborhoods and schools, and increased opportunities for minorities, women, and the elderly. One Nation Divisible also explores the abiding economic paradox in American life: while many individuals are able to climb the financial ladder, inequality of income and wealth remains pervasive throughout society. The last hundred years have been marked by incredible transformations in American society. Great advances in civil rights have been tempered significantly by rising economic inequality. One Nation Divisible provides a compelling new analysis of the issues that continue to divide this country and the powerful role of government in both mitigating and exacerbating them. A Volume in the Russell Sage Foundation Census Series
Author: John P. Burgess
Publisher: Princeton University Press
ISBN: 9780691122311
Category : Mathematics
Languages : en
Pages : 276
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Book Description
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.
