In the Light of Logic

In the Light of Logic

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Solomon Feferman is one of the leading figures in the philosophy of mathematics. This volume brings together a selection of his most important recent writings, covering the relation between logic and mathematics, proof theory, objectivity and intentionality in mathematics, and key issues in the work of Godel, Hilbert, and Turing. A number of the papers appeared originally in obscure places and are not well-known, and others are published here for the first time. All of the material has been revised and annotated to bring it up to more

Product details

  • Hardback | 352 pages
  • 160 x 230 x 30mm | 698.54g
  • Oxford University Press Inc
  • New York, United States
  • English
  • Annotated
  • New.
  • 0195080300
  • 9780195080308
  • 1,640,977

Review quote

Feferman's book shows that, far from being over, work on the foundations of mathematics is vibrant and continuing, perched deliciously but precariously between mathematics and philosophy. * The Mathematical Intelligencer * an outstanding collection, highly informative, sometimes provocative, often insightful, and throughout displaying the great clarity and command which are hallmarks of the author's writing. * Geoffrey Hellman, Philosophia Mathematica, Vol. 9, No. 2, 2001 *show more

Table of contents

I: FOUNDATIONAL PROBLEMS ; 1. Declining the undecidable: Wrestling with Hilbert's Problems ; 2. Infinity in Mathematics: Is Cantor necessary? ; 3. The logic of mathematical discovery vs. the logical structure of mathematics ; II: FOUNDATIONAL WAYS ; 4. Foundational Ways ; 5. Working Foundations ; III: GODEL ; 6. Godel's life and work ; 7. Kurt Godel: conviction and caution ; 8. Introductory note to Godel's 1993 lecture ; IV: PROOF THEORY ; 9. What does logic have to tell us about mathematical proofs? ; 10. What rests on what? The proof-theoretic analysis of mathematics ; 11. Godel's Dialectica interpretation and its two-way stretch ; V: COUNTABLY REDUCIBLE MATHEMATICS ; 12. Infinity in mathematics: Is Cantor necessary? (Conclusion) ; 13. Weyl vindicated: Das Kontinuum 70 years later ; 14. Why a little bit goes a long way: Logical Foundations of scientifically applicable mathematicsshow more