What's so logical about the ''logical'' axioms?
type: Item
instance of: scholarly article
title: What's so logical about the ''logical'' axioms?
zbMATH Open document ID: 0566.03002
DOI: 10.1007/BF00370342
author: J. Blot
published in: Studia Logica
publication date: 1982-01-01T00:00:00Z
review text: Logical axioms are supposed to be valid independent of the way the world is. Hence, peculiarities of the world will be of little help for us in learning the meaning of the logical connectives and quantifiers. What is left then, the author argues with a reference to Wittgenstein, but to learn their meaning from the way they are used. Models of dialogues, carried out in a metalanguage shared between the participants, are set up for the purpose. It is argued, on the basis of a dialogue between an intuitionist and a classical logician, that the intuitionistic axioms do characterize the logical connectives and quantifiers, both for the intuitionist and the classical logician. The thesis is suggested that a set \(\Lambda\) of formulas and rules of inference in a language L form a logic for a set S of L-symbols if and only if the members of \(\Lambda\) characterize the possible use of the S-symbols in the opinion of any two users of L.
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 3902613
zbMATH Keywords: classical axioms
zbMATH Keywords: Logical axioms
zbMATH Keywords: meaning of the logical connectives and quantifiers
zbMATH Keywords: dialogues
zbMATH Keywords: intuitionistic axioms
Wikidata QID: Q114694676
MaRDI profile type: Publication
cites work: Q4052071
cites work: Q5536236
cites work: Q4414313
description: scientific article; zbMATH DE number 3902613