Dialetheic truth theory: inconsistency, non-triviality, soundness, incompleteness

The best-known application of dialetheism is to semantic paradoxes such as the Liar. In particular, Graham Priest has advocated the adoption of an axiomatic truth theory in which contradictions arising from the Liar paradox can be accepted as theorems, while the Liar sentence itself is evaluated as being both true and false. Such eccentricities might be tolerated, in exchange for great rewards. But in this note I show that it is not possible in Priest’s truth theory to express certain semantic facts about that very theory, and thus that it enjoys no definite advantage over more orthodox approaches to semantic paradox. Key words: Paraconsistent logic, dialetheism, truth theory. 1 Naive axiomatic truth theory Let L be a first-order language with equality containing semantic and arithmetic vocabulary. I will say that an axiomatic truth theory T for L is naive if it has the following characteristics: (i) T is expressed in L (ii) T contains a significant subset of the standard axioms of P...

• Type: Conference
• Year: 2007
• Where: LANMR
• Authors: Federico Marulanda Rey
• Keywords: Axiomatic Truth Theory, LANMR 2007, Logical Reasoning, Semantic, Truth Theory