Faces of Inconsistency

Abstract

The concept of inconsistency has become recently the subject of many studies focused on the principle ex contradictione sequitur quodlibet which is a hallmark of the classical inconsistency. Stanisław Jaśkowski was the first who took a non-classical standpoint toward this principle building a system of propositional logic which rejects this classical principle. Rejecting it implies important consequences for the concept of classical negation, and poses the question in which properties the op-eration of negation should be endowed. The intention of this article is to define the concept of inconsistency as well as the concept of negation in a way satisfying the main intuitions natural language users connect with the two notions occurring in propositions containing vague concepts. The vagueness of natural language dis-course leads to the phenomenon of the seeming contradiction characteristic of natural language. A non-standard consequence relation for such a language has been defined in terms of preferential semantics making use of the concept of most classical model. This non-standard consequence relation is applied to the ethical discourse. The concepts introduced in this article have been used to an interpretation of the contradictories of Plato's Parmenides, as well as to the rejection of dialetheism.