The Philosophy of Mathematics Today

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