One Hundred Years of Russell´s Paradox : : Mathematics, Logic, Philosophy / / ed. by Godehard Link.

• Superior document: Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014
• MitwirkendeR: Bell, John L.,; Blau, Ulrich,; Cantini, Andrea,; Feferman, Solomon,; Field, Hartry,; Friedman, Harvey M.,; Friedman, Sy D.,; Friedman, Sy-David ,; Griffin, Nicholas,; Hauser, Kai,; Hazen, Allen P.,; Hellman, Geoffrey,; Hürter, Tobias,; Irvine, Andrew D.,; Jäger, Gerhard,; Landini, Gregory,; Lavine, Shaughan,; Link, Godehard,; Linsky, Bernard,; McCarty, David Charles,; McGee, Vann,; Mycielski, Jan,; Mycielsky, Jan,; Niebergall, Karl-Georg,; Peckhaus, Volker,; Probst, Dieter,; Rathjen, Michael,; Rodriguez-Consuegra, Francisco,; Rodríguez-Consuegra, Francisco,; Rouilhan, Philippe,; Schuster, Peter,; Schwichtenberg, Helmut,; Sturm, Holger,; Thomas, Robert S. D.,; Visser, Albert,; Wehmeier, Kai F.,; Woodin, W. Hugh,; de Rouilhan, Philippe,
• HerausgeberIn: Link, Godehard,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2008]; ©2004
• Year of Publication: 2008
• Language: English
• Series: De Gruyter Series in Logic and Its Applications , 6
• Physical Description: 1 online resource (662 p.)

Die in diesem Band zusammengefassten Beiträge stellen die wesentlichen Forschungsergebnisse der internationalen Münchner Konferenz "100 Jahre Russell-Paradoxon" im Jahr 2001 dar, auf der an die Entdeckung des berühmten Russell Paradoxons vor 100 Jahren erinnert wurde. Die 31 Beiträge und der Einführungsessay des Herausgebers wurden alle - bis auf zwei Ausnahmen - ursprünglich für diesen Band verfasst.

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.

Table of Contents

Frontmatter -- Table of Contents -- Introduction. Bertrand Russell—The Invention of -- Mathematical Philosophy -- Set Theory after Russell: The Journey Back to -- Eden -- A Way Out -- Completeness and Iteration in Modern Set -- Theory -- Was sind und was sollen (neue) Axiome? -- Iterating Σ Operations in Admissible Set Theory -- without Foundation: A Further Aspect of Metapredicative Mahlo -- Typical Ambiguity: Trying to Have Your Cake and Eat -- It Too -- Is ZF Finitistically Reducible? -- Inconsistency in the Real World -- Predicativity, Circularity, and -- Anti-Foundation -- Russell’s Paradox and Diagonalization in a -- Constructive Context -- Constructive Solutions of Continuous -- Equations -- Russell’s Paradox in Consistent Fragments of -- Frege’s Grundgesetze der Arithmetik -- On a Russellian Paradox about Propositions and -- Truth -- The Consistency of the Naive Theory of -- Properties -- The Significance of the Largest and Smallest -- Numbers for the Oldest Paradoxes -- The Prehistory of Russell’s Paradox -- Logicism’s ‘Insolubilia’ and Their Solution by -- Russell’s Substitutional Theory -- Substitution and Types: Russell’s Intermediate -- Theory -- Propositional Ontology and Logical Atomism -- Classes of Classes and Classes of Functions in -- Principia Mathematica -- A “Constructive” Proper Extension of Ramified Type -- Theory (The Logic of Principia Mathematica, Second Edition, Appendix -- B) -- Russell on Method -- Paradoxes in Göttingen -- David Hilbert and Paul du Bois-Reymond: Limits and -- Ideals -- Russell’s Paradox and Hilbert’s (much Forgotten) -- View of Set Theory -- Objectivity: The Justification for -- Extrapolation -- Russell’s Absolutism vs. (?) Structuralism -- Mathematicians and Mathematical Objects -- Russell’s Paradox and Our Conception of Properties, -- or: Why Semantics Is no Proper Guide to the Nature of Properties -- The Many Lives of Ebenezer Wilkes Smith -- What Makes Expressions Meaningful? A Reflection on -- Contexts and Actions -- Backmatter