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One Hundred Years of Russell's Paradox :  Mathematics, Logic, Philosophy - Link Godehard

One Hundred Years of Russell's Paradox

Mathematics, Logic, Philosophy

By: Link Godehard (Editor)

Hardcover Published: 26th July 2004
ISBN: 9783110174380
Number Of Pages: 671
For Ages: 22+ years old

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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 thereby to the well-established body of mathematical philosophy initiated to a large extent by Russell's work.

Industry Reviews

"This is an important collection. The new research presented in this one book is roughly equivalent to a year's worth of articles in an important journal. The overall quality is impressive."
Kevin C. Klement in: The Review of Modern Logic 1-2/2007/2008

"This is a well-done celebration of an important incident in the history of mathematics."
P.Schmitt in: Monatshefte fur Mathematik 1/2006

Introduction : Bertrand Russell - the invention of mathematical philosophyp. 1
Set theory after Russell : the journey back to Edenp. 29
A way outp. 49
Completeness and iteration in modern set theoryp. 85
Was sind und was sollen (neue) Axiome?p. 93
Iterating [Sigma] operations in admissible set theory without foundation : a further aspect of metapredicative Mahlop. 119
Typical ambiguity : trying to have your cake and eat it toop. 135
Is ZF finitistically reducible?p. 153
Inconsistency in the real worldp. 181
Predicativity, circularity, and anti-foundationp. 191
Russell's paradox and diagonalization in a constructive contextp. 221
Constructive solutions of continuous equationsp. 227
Russell's paradox in consistent fragments of Frege's Grundgesetze der Arithmetikp. 247
On a Russellian paradox about propositions and truthp. 259
The consistency of the naive theory of propertiesp. 285
The significance of the largest and smallest numbers for the oldest paradoxesp. 311
The prehistory of Russell's paradoxp. 349
Logicism's 'insolubilia' and their solution by Russell's substitutional theoryp. 373
Substitution and types : Russell's intermediate theoryp. 401
Propositional ontology and logical atomismp. 417
Classes of classes and classes of functions in Principia Mathematicap. 435
A "constructive" proper extension of ramified type theory (the logic of Principia Mathematica, second edition, appendix B)p. 449
Russell on methodp. 481
Paradoxes in Gottingenp. 501
David Hilbert and Paul du Bois-Reymond : limits and idealsp. 517
Russell's paradox and Hilbert's (much forgotten) view of set theoryp. 533
Objectivity : the justification for extrapolationp. 549
Russell's absolutism vs. (?) structuralismp. 561
Mathematicians and mathematical objectsp. 577
Russell's paradox and our conception of properties, or : why semantics is no proper guide to the nature of propertiesp. 591
The many lives of Ebenezer Wilkes Smithp. 611
What makes expressions meaningful? : a reflection on contexts and actionsp. 625
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783110174380
ISBN-10: 3110174383
Series: de Gruyter Logic and Its Applications
Audience: General
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 671
Published: 26th July 2004
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 3.66
Weight (kg): 1.11