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BROUWER’S WEAK COUNTEREXAMPLES AND TESTABILITY: FURTHER REMARKS

Published online by Cambridge University Press:  13 March 2013

CHARLES MCCARTY
CHARLES MCCARTY*
Affiliation:
1408 E, LONGVIEW AVENUE, BLOOMINGTON, IN 47403, USA
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Abstract

Straightforwardly and strictly intuitionistic inferences show that the Brouwer– Heyting–Kolmogorov (BHK) interpretation, in the presence of a formulation of the recognition principle, entails the validity of the Law of Testability: that the form ¬ f V ¬¬ f is valid. Therefore, the BHK and recognition, as described here, are inconsistent with the axioms both of intuitionistic mathematics and of Markovian constructivism. This finding also implies that, if the BHK and recognition are suitably formulated, then Brouwer’s original weak counterexample reasoning was fallacious. The results of the present article extend and refine those of McCarty, C. (2012). Antirealism and Constructivism: Brouwer’s Weak Counterexamples. The Review of Symbolic Logic. First View. Cambridge University Press.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 3 , September 2013 , pp. 513 - 523
Copyright
Copyright © Association for Symbolic Logic 2013 

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