<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The use of conventional logical connectives either in logic, in mathematics, or in both cannot determine the meanings of those connectives. This is because every model of full conventional set theory can be extended conservatively to a model of intuitionistic set plus class theory, a model in which the meanings of the connectives are decidedly intuitionistic and nonconventional. The reasoning for this conclusion is acceptable to both intuitionistic and classical mathematicians. En route, I take a detour to prove that, given strictly intuitionistic principles, classical negation cannot exist.</p></abstract>

The use of conventional logical connectives either in logic, in mathematics, or in both cannot determine the meanings of those connectives. This is because every model of full conventional set theory can be extended conservatively to a model of intuitionistic set plus class theory, a model in which the meanings of the connectives are decidedly intuitionistic and nonconventional. The reasoning for this conclusion is acceptable to both intuitionistic and classical mathematicians. En route, I take a detour to prove that, given strictly intuitionistic principles, classical negation cannot exist.

Logical rules and the determinacy of meaning

Studies in Logic, Grammar and Rhetoric

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Logical rules and the determinacy of meaning"}

The use of conventional logical connectives either in logic, in mathematics, or in both cannot determine the meanings of those connectives. This is because...

Logical rules and the determinacy of meaning

Publié en ligne: 16 nov. 2018

Pages: 89 - 98

DOI: https://doi.org/10.2478/slgr-2018-0018

Mots clés
negation, truth value, intuitionistic set theory, use theory of meaning

© 2018 Charles McCarty, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Logical rules and the determinacy of meaning

Publié en ligne: 16 nov. 2018

Pages: 89 - 98

DOI: https://doi.org/10.2478/slgr-2018-0018

Mots clésnegation, truth value, intuitionistic set theory, use theory of meaning

© 2018 Charles McCarty, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
negation, truth value, intuitionistic set theory, use theory of meaning