Truth, Proof and Infinity : A Theory of Constructive Reasoning

P. Fletcher

ISBN 10: 0792352629 / ISBN 13: 9780792352624

Published by Springer Okt 1998, 1998

About this Item

Neuware - 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-Löf 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.

Seller Inventory # 9780792352624

Bibliographic Details

• Title: Truth, Proof and Infinity : A Theory of Constructive Reasoning
• Publisher: Springer Okt 1998
• Publication Date: 1998
• Language: English
• ISBN 10: 0792352629
• ISBN 13: 9780792352624
• Binding: Buch
• Condition: Neu
• Dimensions: 234W x 156H x 27D millimeters 234 millimeters width by 156 millimeters height by 27 millimeters depth
• Weight: 835 grams

About this title

Synopsis

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-Löf 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.