The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come.
Contributors
Paul Benacerraf, George Boolos, John P. Burgess, Charles S. Chihara, Michael Detlefsen, Michael Dummett, Hartry Field, Kit Fine, Bob Hale, Richard G. Heck, Jnr. , Geoffrey Hellman, Penelope Maddy, Karl-Georg Niebergall, Charles D. Parsons, Michael D. Resnik, Matthias Schirn, Stewart Shapiro, Peter Simons, W. W. Tait, Crispin Wright.
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.
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
