Oğuz Akçelik

Our aim is to illuminate the interconnected notions of meaning and truth. For this purpose, we investigate the relationship between meaning theories based on commonsensical ‘means that’ and interpretive truth theories. The latter are Tarski–Davidson-style truth theories serving as meaning theories. We consider analytically true semantic principles containing ‘means’ and ‘means that’ side to side with ‘denotes’, ‘satisfies’, and ‘true’, which constitute the extensional semantic constants of interpretive truth theories. We show that these semantic constants are definable in terms of ‘means’ and ‘means that’ operators. The definitions themselves are semantic principles in the role of meaning postulates. We extend a meaning theory based on ‘means that’ by adjoining semantic principles to the axioms of the theory. Then, all axioms, hence all theorems, of a corresponding interpretive truth theory are provable in the extension of the meaning theory. Furthermore, every interpretive truth theory can be included in the extension of a corresponding meaning theory. Therefore, the extension of a meaning theory resulting from the adjunction of semantic principles constitutes a unified meaning-and-truth theory since it includes both a meaning theory and an interpretive truth theory.

In modern logic, each singular term must denote an object in the domain of quantification. This is due to the ontological assumptions of first order quantification logic with identity. However, this results in certain anomalies, i.e. expressibility and validity of inference problems. Free logic is a useful tool to analyze propositions and test the validity of arguments containing empty singular terms which have no referent in the domain of quantification. In this study, we will examine systematic definitions and extensional interpretations of free logics. One of the most promising future orientations of modern logic, free logic as a logic free of existential assumptions, does not take the concept of existence as a logical necessity. Instead, the fundamental assumption is that of ontological possibility, and hence it will be possible for propositions containing empty terms to have extensional interpretations.