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The Philosophy of Mathematics Today

The Philosophy of Mathematics Today


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About the Book

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.

Table of Contents:
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

Review :
`Review from previous edition essential reading for all those interested in the area.' Graham Priest, Studia Logica `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 philosophical enquiry engaged in to date ... a formidable collection.' Fraser MacBride, Mind


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Product Details
  • ISBN-13: 9780199262625
  • Publisher: Oxford University Press
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 983 gr
  • ISBN-10: 0199262624
  • Publisher Date: 22 May 2003
  • Height: 235 mm
  • No of Pages: 650
  • Spine Width: 35 mm
  • Width: 156 mm


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