Friedman, Harvey M.
One Hundred Years of Russell's Paradox : Mathematics, Logic, Philosophy. - 1 online resource (672 pages) - De Gruyter Series in Logic and Its Applications Ser. ; v.6 . - De Gruyter Series in Logic and Its Applications Ser. .
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.
9783110199680
Liar paradox.
Paradox.
Electronic books.
BC199.P2O54 2004
165
One Hundred Years of Russell's Paradox : Mathematics, Logic, Philosophy. - 1 online resource (672 pages) - De Gruyter Series in Logic and Its Applications Ser. ; v.6 . - De Gruyter Series in Logic and Its Applications Ser. .
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.
9783110199680
Liar paradox.
Paradox.
Electronic books.
BC199.P2O54 2004
165