Truth in Mathematics

by H. G. Dales, G. Oliveri

Overview

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 Gödel 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-Löf, this volume provides an overview of the forefront of current thinking and a valuable introduction for researchers in the area.

Product Details

ISBN-13:	9780198514763
Publisher:	Oxford University Press
Publication date:	12/10/1998
Series:	Oxford Science Publications
Pages:	392
Product dimensions:	6.40(w) x 9.30(h) x 1.00(d)

About the Author

University of Leeds

Wolfson College, Oxford

Table of Contents

1. Truth and the foundations of mathematics. An introduction, H.G. Dales and G. OliveriI. Knowability, constructivity, and truth2. Truth and objectivity from a verificationist point of view, Dag Prawitz3. Constructive truth in practice, Douglas S. Bridges4. On founding the theory of algorithms, Yiannis N. Moschovakis5. Truth and knowability: on the principles of C and K of Michael Dummett, Per Martin-löfII. Formalism and naturalism6. Logical completeness, truth, and proofs, Gabriele Lolli7. Mathematics as a language, Edward G. Effros8. Truth, rigour, and common sense, Yu I. Manin9. How to be a naturalist about mathematics, Penelope Maddy10. The mathematician as a formalist, H.G. DalesIII. Realism in mathematics11. A credo of sorts, V.F.R. Jones12. Mathematical evidence, Donald A. Martin13. Mathematical definability, Theodore A. Slaman14. True to the pattern, Gianluigi OliveriIV. Sets, undecidability, and the natural numbers15. Foundations of set theory, W.W. Tait16. Which undecidable mathematical sentences have determinate truth values?, Hartry Field17. Two conceptions of natural number, Alexander George and Daniel J. Velleman18. The tower of Hanoi, W. Hugh Woodin