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Truth, Proof and Infinity: A Theory of Constructive Reasoning (Hardcover)

Author: Fletcher, Peter

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Product Overview

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-LC6f 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.

Specifications

Publisher Springer
Mfg Part# 9780792352624
SKU 202995046
Format Hardcover
ISBN10 0792352629
Release Date 4/10/2007
Product Attributes
Book Format Hardcover
Number of Pages 0470
Publisher Springer
Series Part 276
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