Truth in Mathematics [Hardcover]

The nature of truth in mathematics 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 century and in particular the work by G?del and the development of the notion of independence in mathematics have led to new and complex views on this question. Collecting the work of a number of outstanding mathematicians and philosophers, including Yurii Manin, Vaughan Jones, and Per Martin-L?f, this volume provides an overview of the forefront of current thinking and a valuable introduction for researchers in the area.

1. Truth and the foundations of mathematics. An introduction,H.G. Dales and G. Oliveri
I. Knowability, constructivity, and truth
2. Truth and objectivity from a verificationist point of view,Dag Prawitz
3. Constructive truth in practice,Douglas S. Bridges
4. On founding the theory of algorithms,Yiannis N. Moschovakis
5. Truth and knowability: on the principles ofCandKof Michael Dummett,Per Martin-l?f
II. Formalism and naturalism
6. Logical completeness, truth, and proofs,Gabriele Lolli
7. Mathematics as a language,Edward G. Effros
8. Truth, rigour, and common sense,Yu I. Manin
9. How to be a naturalist about mathematics,Penelope Maddy
10. The mathematician as a formalist,H.G. Dales
III. Realism in mathematics
11. A credo of sorts,V.F.R. Jones
12. Mathematical evidence,Donald A. Martin
13. Mathematical definability,Theodore A. Slaman
14. True to the pattern,Gianluigi Oliveri
IV. Sets, undecidability, and the natural numbers
15. Foundations of set theory,W.W. Tait
16. Which undecidable mathematical sentences have determinate truth values?,Hartry Field
17. Two conceptions of naturl³#