Zdania kłamcy i prawdomówcy w klasycznych logikach prawdy oraz fałszu

Abstract

Liar and truth-teller sentence in the classical logics of truth and falsehood

Adding the content implication, a new intentional connective, to the language for the classical propositional logic has some far-reaching effects. Such extended language appears to be general, although it does not contain names for sentences. This fact has another consequence: no self-referential sentence is antinomial, particularly, the liar sentence does not lead to the antinomy. Thus, it appears that it is possible to define a truth on the language with the content implication. The approach is tested on two well-known paradoxical cases: the liar sentence on the logic of truth, and the truth-teller sentence on the logic of falsehood.