What's so logical about the ''logical'' axioms?
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.
meaning of the logical connectives and quantifiers
scientific article; zbMATH DE number 3902613