Intro -- Preface -- Table of Contents -- Introduction. Bertrand Russell-The Invention of Mathematical Philosophy -- Set Theory after Russell: The Journey Back to Eden -- AWay Out -- Completeness and Iteration in Modern Set Theory -- Iterating -- 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 RealWorld -- 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 -- 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 EbenezerWilkes Smith -- What Makes Expressions Meaningful? A Reflection on Contexts and Actions.

List of Contributors.

The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.