Truth in Mathematics

Hardcover | September 1, 1998

EditorH. G. Dales, G. Oliveri

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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 Godel's theorem and the development of the notion ofindependence 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-Lofand their discussions of this problem. It provides anoverview of the forefront of current thinking, and is a valuable introduction and reference for researchers in the area.

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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 Godel's theorem and the development of the notion ofindependence in mathematicshave led to new vi...

Garth Dales is at University of Leeds. Gianluigi Oliveri is at Wolfson College, Oxford.

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Format:HardcoverPublished:September 1, 1998Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:019851476X

ISBN - 13:9780198514763

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Table of Contents

1. Truth and the foundations of mathematics. An introduction2. Truth and obvjectivity from a verificationist point of view3. Constructive truth in practice4. On founding the theory of algorithms5. Truth and knowability: on the principles of C and K of Michael Dummett6. Logical completeness, truth, and proofs7. Mathematics as a language8. Truth, rigour, and common sense9. How to be a naturalist about mathematics10. The mathematician as a formalist11. A credo of sorts12. Mathematical evidence13. Mathematical definability14. True to the pattern15. Foundations of set theory16. Which undecidable mathematical sentences have determinate truth values?17. Two conceptions of natural number18. The tower of Hanoi