Truth in Mathematics

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

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 Gödel'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-Löfand 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.

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