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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Truth, Proof and Infinity: A Theory of Constructive Reasoning

Truth, Proof and Infinity: A Theory of Constructive Reasoning

Fletcher, P.

Paperback

Series: Synthese Library, Book 276

General ComputersHistory & Philosophy of ScienceLogic

ISBN10: 9048151058
ISBN13: 9789048151059
Publisher: Springer Nature
Published: Dec 7 2010
Pages: 470
Weight: 1.47
Height: 0.97 Width: 6.14 Depth: 9.21
Language: English
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.

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