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ANTIREALISM AND CONSTRUCTIVISM: BROUWER’S WEAK COUNTEREXAMPLES

Published online by Cambridge University Press:  03 October 2012

CHARLES McCARTY
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Abstract

Strictly intuitionistic inferences are employed to demonstrate that three conditions—the existence of Brouwerian weak counterexamples to Test, the recognition condition, and the BHK interpretation of the logical signs—are together inconsistent. Therefore, if the logical signs in mathematical statements governed by the recognition condition are constructive in that they satisfy the clauses of the BHK, then every relevant instance of the classical principle Test is true intuitionistically, and the antirealistic critique of conventional logic, once thought to yield such weak counterexamples, is seen, in this instance, to fail.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 1 , March 2013 , pp. 147 - 159
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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