Truth, Proof and Infinity: A Theory of Constructive Reasoning

This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

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 not been adequately explained (although Kriesel, Goodman and Martin have attempted axiomatizations). 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. The text should be of interest to philosophers of mathematics and logicians, both academic and graduate student, particularly those interested in Brouwer and Hilbert. Also, theoretical computer scientists interested in the foundations of functional programming languages and program correctness calculi.