One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy (De Gruyter Series in Logic and Its Applications #6)

One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy (De Gruyter Series in Logic and Its Applications #6)

by Godehard Link
     
 

ISBN-10: 3110174383

ISBN-13: 9783110174380

Pub. Date: 07/26/2004

Publisher: De Gruyter

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

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Overview

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.

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Product Details

ISBN-13:
9783110174380
Publisher:
De Gruyter
Publication date:
07/26/2004
Series:
de Gruyter Series in Logic and Its Applications Series, #6
Pages:
674
Product dimensions:
6.14(w) x 9.21(h) x 1.44(d)
Age Range:
18 Years

Table of Contents

Introduction : Bertrand Russell - the invention of mathematical philosophy1
Set theory after Russell : the journey back to Eden29
A way out49
Completeness and iteration in modern set theory85
Was sind und was sollen (neue) Axiome?93
Iterating [Sigma] operations in admissible set theory without foundation : a further aspect of metapredicative Mahlo119
Typical ambiguity : trying to have your cake and eat it too135
Is ZF finitistically reducible?153
Inconsistency in the real world181
Predicativity, circularity, and anti-foundation191
Russell's paradox and diagonalization in a constructive context221
Constructive solutions of continuous equations227
Russell's paradox in consistent fragments of Frege's Grundgesetze der Arithmetik247
On a Russellian paradox about propositions and truth259
The consistency of the naive theory of properties285
The significance of the largest and smallest numbers for the oldest paradoxes311
The prehistory of Russell's paradox349
Logicism's 'insolubilia' and their solution by Russell's substitutional theory373
Substitution and types : Russell's intermediate theory401
Propositional ontology and logical atomism417
Classes of classes and classes of functions in Principia Mathematica435
A "constructive" proper extension of ramified type theory (the logic of Principia Mathematica, second edition, appendix B)449
Russell on method481
Paradoxes in Gottingen501
David Hilbert and Paul du Bois-Reymond : limits and ideals517
Russell's paradox and Hilbert's (much forgotten) view of set theory533
Objectivity : the justification for extrapolation549
Russell's absolutism vs. (?) structuralism561
Mathematicians and mathematical objects577
Russell's paradox and our conception of properties, or : why semantics is no proper guide to the nature of properties591
The many lives of Ebenezer Wilkes Smith611
What makes expressions meaningful? : a reflection on contexts and actions625

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