Ordering description and many-valued logics. J. N. Martin’s attempt at interpretation of Lukasiewicz’s system

Abstract

The article presents two attempts at applying J. Lukas iewicz's three-valued logic to analysis of the so-called gradable properties: T. Czeżowski's so-called ordering logics and J. Martin's attempt to connect Lukas iewicz's logic and the neo-Platonian hierarchy of entities. Unfortunately, those attempts were not successful. It can be noticed that in his approach Czeżowski mixed up gradability of truth with gradability of other properties. Martin found that Lukasiewicz's enriching of the division between truth and falsity with a third value suggests some neo-Platonian ontology in which truth - interchangeable with entity - is subject to gradation. However, he does not give an intuitively convincing way of reducing Lukas iewicz's threevalued logic to the corresponding Boole's algebra of compound properties (hence, to a structure belonging to the classical logic).