This book develops Tennant's Natural Logicist account of the foundations of the natural, rational, and real numbers. Tennant uses this framework to distinguish the logical from the intuitive aspects of the basic elements of arithmetic.
This book develops Tennant's Natural Logicist account of the foundations of the natural, rational, and real numbers. Tennant uses this framework to distinguish the logical from the intuitive aspects of the basic elements of arithmetic.
Neil Tennant is Arts & Sciences Distinguished Professor in Philosophy at The Ohio State University. He has previously held positions at the University of Edinburgh, the University of Stirling, and the Australian National University. He is the author of Anti-Realism and Logic: Truth as Eternal (1987), The Taming of The True (1997), Changes of Mind: An Essay on Rational Belief Revision (2012), and Core Logic (2017), all published by OUP.
Inhaltsangabe
* I Natural Logicism * 1: What is Natural Logicism? * 2: Before and after Frege * 3: After Gentzen * 4: Foundations after Gödel * 5: Logico-Genetic Theorizing * II Natural Logicism and the Naturals 65 * 6: Introduction, with Some Historical Background * 7: Denoting Numbers * 8: Exact Numerosity * 9: The Adequacy Condition Involving Schema N * 10: The Rules of Constructive Logicism * 11: Formal Results of Constructive Logicism * 12: Reflections on Counting * 13: Formal Results about the Inductively Defined Numerically Exact Quantifiers * III Natural Logicism and the Rationals * 14: What Would a Gifted Child Need in order to Grasp Fractions? The Case of Edwin * 15: Past Accounts of the Rationals as Ratios * 16: Mereology and Fraction Abstraction * 17: Taking Stock and Glimpsing Beyond * IV Natural Logicism and the Reals * 18: The Trend towards Arithmetization * 19: Resisting the Trend towards Arithmetization * 20: Impurities and Incompletenesses * 21: The Concept of Real Number * 22: Geometric Concepts and Axioms * 23: Bicimals * 24: Uncountability * 25: Back to Bicimals * Appendices 337 * A Proof of the Non-Compossibility Theorem * B Formal Proof of a Geometric Inference
* I Natural Logicism * 1: What is Natural Logicism? * 2: Before and after Frege * 3: After Gentzen * 4: Foundations after Gödel * 5: Logico-Genetic Theorizing * II Natural Logicism and the Naturals 65 * 6: Introduction, with Some Historical Background * 7: Denoting Numbers * 8: Exact Numerosity * 9: The Adequacy Condition Involving Schema N * 10: The Rules of Constructive Logicism * 11: Formal Results of Constructive Logicism * 12: Reflections on Counting * 13: Formal Results about the Inductively Defined Numerically Exact Quantifiers * III Natural Logicism and the Rationals * 14: What Would a Gifted Child Need in order to Grasp Fractions? The Case of Edwin * 15: Past Accounts of the Rationals as Ratios * 16: Mereology and Fraction Abstraction * 17: Taking Stock and Glimpsing Beyond * IV Natural Logicism and the Reals * 18: The Trend towards Arithmetization * 19: Resisting the Trend towards Arithmetization * 20: Impurities and Incompletenesses * 21: The Concept of Real Number * 22: Geometric Concepts and Axioms * 23: Bicimals * 24: Uncountability * 25: Back to Bicimals * Appendices 337 * A Proof of the Non-Compossibility Theorem * B Formal Proof of a Geometric Inference
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