Truth in mathematics
著者
書誌事項
Truth in mathematics
Clarendon, 1998
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注記
Based on lectures given at the conference "Truth in mathematics"(Mussomeli,Sicily,Italy,13-20 Sept.,1995)
Includes complete bibliography (p. 353-370) and index
内容説明・目次
内容説明
The nature of truth in mathematics is a problem which has exercised the minds of thinkers from at least the time of the ancient Greeks. The great advances in mathematics and philosophy in the twentieth centuryand in particular the proof of Goedel's theorem and the development of the notion of independence in mathematicshave led to new viewpoints on this question in our era. This book is the result of the interaction of a number of outstanding mathematicians and
philosophersincluding Yurii Manin, Vaughan Jones, and Per Martin-Loefand their discussions of this problem. It provides an overview of the forefront of current thinking, and is a valuable introduction and reference for researchers in the area.
目次
- 1. Truth and the foundations of mathematics. An introduction
- 2. Truth and obvjectivity from a verificationist point of view
- 3. Constructive truth in practice
- 4. On founding the theory of algorithms
- 5. Truth and knowability: on the principles of C and K of Michael Dummett
- 6. Logical completeness, truth, and proofs
- 7. Mathematics as a language
- 8. Truth, rigour, and common sense
- 9. How to be a naturalist about mathematics
- 10. The mathematician as a formalist
- 11. A credo of sorts
- 12. Mathematical evidence
- 13. Mathematical definability
- 14. True to the pattern
- 15. Foundations of set theory
- 16. Which undecidable mathematical sentences have determinate truth values?
- 17. Two conceptions of natural number
- 18. The tower of Hanoi
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