Truth, Proof and Infinity - A Theory of Constructive Reasoning (Paperback, Softcover reprint of hardcover 1st ed. 1998)

Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it. However, the meaning of the terms `construction' and `proof' has never been adequately explained (although Kriesel, Goodman and Martin-Loef have attempted axiomatisations). This monograph develops precise (though not wholly formal) definitions of construction and proof, and describes the algorithmic substructure underlying intuitionistic logic. Interpretations of Heyting arithmetic and constructive analysis are given. The philosophical basis of constructivism is explored thoroughly in Part I. The author seeks to answer objections from platonists and to reconcile his position with the central insights of Hilbert's formalism and logic. Audience: Philosophers of mathematics and logicians, both academic and graduate students, particularly those interested in Brouwer and Hilbert; theoretical computer scientists interested in the foundations of functional programming languages and program correctness calculi.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Synthese Library, 276
Release date:	December 2010
First published:	1998
Authors:	P. Fletcher
Dimensions:	240 x 160 x 24mm (L x W x T)
Format:	Paperback
Pages:	470
Edition:	Softcover reprint of hardcover 1st ed. 1998
ISBN-13:	978-90-481-5105-9
Categories:	Books > Science & Mathematics > Science: general issues > Philosophy of science Books > Computing & IT > General theory of computing > General Books > Computing & IT > Applications of computing > General Books > Humanities > Philosophy > Topics in philosophy > Logic Books > Science & Mathematics > Mathematics > Mathematical foundations > General Books > Philosophy > Topics in philosophy > Logic
LSN:	90-481-5105-8
Barcode:	9789048151059

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