| Truth, Proof and Infinity: A Theory of Constructive Reasoning Contributor(s): Fletcher, P. (Author) |
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ISBN: 9048151058 ISBN-13: 9789048151059 Publisher: Springer OUR PRICE: $189.99 Product Type: Paperback - Other Formats Published: December 2010 |
| Additional Information |
| BISAC Categories: - Philosophy | Logic - Science | Philosophy & Social Aspects - Computers | Computer Science |
| Dewey: 510.1 |
| Series: Synthese Library (Paperback) |
| Physical Information: 0.97" H x 6.14" W x 9.21" (1.47 lbs) 470 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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-L f 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. |
