Intuitionistic mathematics does not needex falso quodlibet

Topoi 13 (2):127-133 (1994)

Neil Tennant
Ohio State University
We define a system IR of first-order intuitionistic relevant logic. We show that intuitionistic mathematics (on the assumption that it is consistent) can be relevantized, by virtue of the following metatheorem: any intuitionistic proof of A from a setX of premisses can be converted into a proof in IR of eitherA or absurdity from some subset ofX. Thus IR establishes the same inconsistencies and theorems as intuitionistic logic, and allows one to prove every intuitionistic consequence of any consistent set of premisses.
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DOI 10.1007/BF00763511
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References found in this work BETA

Natural Logic.H. A. Lewis & Neil Tennant - 1981 - Philosophical Quarterly 31 (125):376.
Perfect Validity, Entailment and Paraconsistency.Neil Tennant - 1984 - Studia Logica 43 (1-2):181 - 200.

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Cut for Core Logic.Neil Tennant - 2012 - Review of Symbolic Logic 5 (3):450-479.
Carnap, Gödel, and the Analyticity of Arithmetic.Neil Tennant - 2008 - Philosophia Mathematica 16 (1):100-112.

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