Truth and consistency

Jan Woleński

pp. 347-355

in: Essays on non-empiricist rigorous philosophy, Axiomathes 20, 2010.

Abstract

This paper investigates relations between truth and consistency. The basic intuition is that truth implies consistency, but the reverse dependence fails. However, this simple account leads to some troubles, due to some metalogical results, in particular the Gödel-Malcev completeness theorem. Thus, a more advanced analysis is required. This is done by employing the concept of ω-consistency and ω-inconsistency. Both concepts motivate that the concept of the standard truth should be introduced as well. The results are illustrated by an interpretation of the well-known logical square and its generalization.