In the Light of Logic (Logic and Computation in Philosophy Series)

Feferman, Solomon

Oxford University Press Inc（1999/01発売）

• 製本 Hardcover:ハードカバー版／ページ数 352 p.
• 言語 ENG
• 商品コード 9780195080308
• DDC分類 511.3

基本説明

It brings together a selection of Solomon Feferman's most important recent writings, covering the ralation between logic and mathematics, proof theory, objectivity and intensionality in mathematics.

Full Description

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 Gödel, 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 date.

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 mathematics