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 every model of full conventional set theory can be extended conservatively to a model of intuitionistic set plus class theory, a model in which...

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Main Author:	McCarty Charles
Format:	Article
Language:	English
Published:	Sciendo 2018-06-01
Series:	Studies in Logic, Grammar and Rhetoric
Subjects:	negation truth value intuitionistic set theory use theory of meaning
Online Access:	https://doi.org/10.2478/slgr-2018-0018

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spelling	doaj-74d4de612015449b858703784fc150932021-09-05T14:02:01ZengSciendoStudies in Logic, Grammar and Rhetoric0860-150X2199-60592018-06-01541899810.2478/slgr-2018-0018slgr-2018-0018Logical rules and the determinacy of meaningMcCarty Charles0Department of Philosophy, Indiana University,Indiana, USAThe 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.https://doi.org/10.2478/slgr-2018-0018negationtruth valueintuitionistic set theoryuse theory of meaning
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	McCarty Charles
spellingShingle	McCarty Charles Logical rules and the determinacy of meaning Studies in Logic, Grammar and Rhetoric negation truth value intuitionistic set theory use theory of meaning
author_facet	McCarty Charles
author_sort	McCarty Charles
title	Logical rules and the determinacy of meaning
title_short	Logical rules and the determinacy of meaning
title_full	Logical rules and the determinacy of meaning
title_fullStr	Logical rules and the determinacy of meaning
title_full_unstemmed	Logical rules and the determinacy of meaning
title_sort	logical rules and the determinacy of meaning
publisher	Sciendo
series	Studies in Logic, Grammar and Rhetoric
issn	0860-150X 2199-6059
publishDate	2018-06-01
description	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.
topic	negation truth value intuitionistic set theory use theory of meaning
url	https://doi.org/10.2478/slgr-2018-0018
work_keys_str_mv	AT mccartycharles logicalrulesandthedeterminacyofmeaning
_version_	1717809213618520064

Logical rules and the determinacy of meaning

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