The Philosophy of Mathematics Today

by Matthias Schirn

Overview

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.

Product Details

ISBN-13:	9780199262625
Publisher:	Oxford University Press, USA
Publication date:	05/28/2003
Edition description:	New Edition
Pages:	650
Product dimensions:	9.20(w) x 6.10(h) x 1.40(d)

Table of Contents

Introduction.
PART I: ONTOLOGY, MODELS, AND INDETERMINACY.
1: What Mathematical Truth Could Not Be—1 (Paul Benacerraf). 2: Is Platonism Epistemologically Bankrupt? (Bob Hale). 3: Do We Have a Determinate Conception of Finiteness and Natural Number? (Hartry Field). 4: Logical Consequence: Models and Modality (Stewart Shapiro). 5: Tarski's Thesis and the Ontology of Mathematics (Charles Chihara).
PART II: MATHEMATICS, SCIENCE, AND METHOD.
6: Naturalizing Mathematical Methodology (Penelope Maddy). 7: Occam's Razor and Scientific Method (John P. Burgess). 8: Beyond Definitionism—But Not Too Far Beyond (Geoffrey Hellman). 9: Holistic Mathematics (Michael D. Resnik).
PART III: FINITISM AND INTUITIONISM.
10: Finitism and Intuitive Knowledge (Charles Parsons). 11: Hilbert's Finitism and the Notion of Infinity (Karl-Georg Niebergall and Matthias Schirn). 12: Constructive Existence Claims (Michael Detlefsen).
PART IV: FREGE AND THE FOUNDATIONS OF ARITHMETIC.
13: On the Harmless Impredicativity of N= ('Hume's Principle') (Crispin Wright). 14: Neo-Fregeans: In Bad Company? (Michael Dummett). 15: Response to Dummett (Crispin Wright). 16: Die Grundlagen der Arithmetik, 82-3 (George Boolos and Richard G. Heck). 17: The Finite and the Infinite in Frege's Grundgesetze der Arithmetik (Richard G. Heck).
PART V: SETS, STRUCTURE, AND ABSTRACTION.
18: Zermelo's Conception of Set Theory and Reflection Principles (W. W. Tait). 19: Structure and Abstraction (Peter Simons). 20: The Limits of Abstraction (Kit Fine).
Index