Truth, proof, and infinity
Subtitle: a theory of constructions and contructive reasoning
By: Peter Fletcher, Department of Mathematics, Keele University, United Kingdom
Series: Synthese library -- volume 276; Synthese library -- v. 276.
Published: 1998
Language: eng
Number of pages: 469
ISBN-13: 9789401736169; 9789048151059
Subjects: Mathematics; Philosophy; Arithmetic; Mathematical analysis
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-Lf 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.
Notes: Includes bibliographical references and index.

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