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 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...
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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.
1Truth and the foundations of mathematics. An introduction12Truth and objectivity from a verificationist point of view413Constructive truth in practice534On founding the theory of algorithms715Truth and knowability: on the principles C and K of Michael Dummett1056Logical completeness, truth, and proofs1177Mathematics as language1318Truth, rigour, and common sense1479How to be a naturalist about mathematics16110The mathematician as a formalist18111A credo of sorts20312Mathematical evidence21513Mathematical definability23314True to the pattern25315Foundations of set theory27316Which undecidable mathematical sentences have determinate truth values?29117Two conceptions of natural number31118The tower of Hanoi329Complete bibliography353Index371
