The Philosophy of Mathematics Today

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.

Review from previous edition essential reading for all those interested in the area. Graham Priest, Studia Logica