The Philosophy of Mathematics Today

Paperback | June 12, 2003

EditorMatthias Schirn

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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'sand Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come.

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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'sand Frege's foundational programmes. The co...

Matthias Schirn is at University of Munich.
Format:PaperbackDimensions:650 pages, 9.21 × 6.14 × 1.39 inPublished:June 12, 2003Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199262624

ISBN - 13:9780199262625

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Table of Contents

Introduction.PART I: ONTOLOGY, MODELS, AND INDETERMINACY1. Paul Benacerraf: What Mathematical Truth Could Not Be--12. 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 Modality5. Charles Chihara: Tarski's Thesis and the Ontology of MathematicsPART II: MATHEMATICS, SCIENCE, AND METHOD6. Penelope Maddy: Naturalizing Mathematical Methodology 7. John P. Burgess: Occam's Razor and Scientific Method8. Geoffrey Hellman: Beyond Definitionism - But Not Too Far Beyond9. Michael D. Resnik: Holistic MathematicsPART III: FINITISM AND INTUITIONISM10. Charles Parsons: Finitism and Intuitive Knowledge11. Karl-Georg Niebergall and Matthias Schirn: Hilbert's Finitism and the Notion of Infinity12. Michael Detlefsen: Constructive Existence ClaimsPART IV: FREGE AND THE FOUNDATIONS OF ARITHMETIC13. Crispin Wright: On the Harmless Impredicativity of N= (`Hume's Principle')14. Michael Dummett: Neo-Fregeans: In Bad Company?15. Crispin Wright: Response to Dummett16. George Boolos and Richard G. Heck: Die Grundlagen der Arithmetik, 82-317. Richard G. Heck: The Finite and the Infinite in Frege's Grundgesetze der ArithmetikPART V: SETS, STRUCTURE, AND ABSTRACTION18. W. W. Tait: Zermelo's Conception of Set Theory and Reflection Principles19. Peter Simons: Structure and Abstraction20. Kit Fine: The Limits of AbstractionIndex

Editorial Reviews

`Philosophy of Mathematics Today, a volume that collects together papers by many of the leading contemporary figures in the field, provides ample evidence that reflection upon mathematics and mathematical logic continues to provoke some of the most sophisticated and searching philosophicalenquiry engaged in to date ... a formidable collection.'Fraser MacBride, Mind