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Zusatztext The volume is a collection of papers by many of the most important people working in the contemporary philosophy of mathematics. It think it to be essential reading for all those interested in the area. Klappentext This comprehensive volume gives a panorama of the best current work in this lively field, through twenty specially written essays by the leading figures in the field. All essays deal with foundational issues, from the nature of mathematical knowledge and mathematical existence to logical consequence, abstraction, and the notions of set and natural number. The contributors also represent and criticize a variety of prominent approaches to the philosophy of mathematics, including platonism, realism, normalism, constructivism, and formalism. Zusammenfassung A collection of twenty essays which deal with foundational issues, from the nature of mathematical knowledge and mathematical existence to logical consequence, abstraction, and the notions of set and natural number. A variety of prominent approaches to the philosophy of mathematics are represented and criticized. Inhaltsverzeichnis Introduction. PART I: ONTOLOGY, MODELS, AND INDETERMINACY 1: Paul Benacerraf: What Mathematical Truth Could Not Be--1 2: Bob Hale: Iis Platonism Epistemologically Bankrupt? 3: Hartry Field: Do We Have a Determinate Conception of Finiteness and Natural Number? 4: Stewart Shapiro: Logical Consequence: Models and Modality 5: Charles Chihara: Tarski's Thesis and the Ontology of Mathematics PART II: MATHEMATICS, SCIENCE, AND METHOD 6: Penelope Maddy: Naturalizing Mathematical Methodology 7: John P. Burgess: Occam's Razor and Scientific Method 8: Geoffrey Hellman: Beyond Definitionism - But Not Too Far Beyond 9: Michael D. Resnik: Holistic Mathematics PART III: FINITISM AND INTUITIONISM 10: Charles Parsons: Finitism and Intuitive Knowledge 11: Karl-Georg Niebergall and Matthias Schirn: Hilbert's Finitism and the Notion of Infinity 12: Michael Detlefsen: Constructive Existence Claims PART IV: FREGE AND THE FOUNDATIONS OF ARITHMETIC 13: Crispin Wright: On the Harmless Impredicativity of N= (`Hume's Principle') 14: Michael Dummett: Neo-Fregeans: In Bad Company? 15: Crispin Wright: Response to Dummett 16: George Boolos and Richard G. Heck: Die Grundlagen der Arithmetik, 82-3 17: Richard G. Heck: The Finite and the Infinite in Frege's Grundgesetze der Arithmetik PART V: SETS, STRUCTURE, AND ABSTRACTION 18: W. W. Tait: Zermelo's Conception of Set Theory and Reflection Principles 19: Peter Simons: Structure and Abstraction 20: Kit Fine: The Limits of Abstraction Index ...
