Oğuz Akçelik

Human beings are endowed with finite cognitive capacities so that there are forever unknown truths. This fact is stated by non-omniscience thesis (NO). On the other hand many philosophers, especially semantic antirealists, hold that all truths (even the unknown ones) are knowable, and this is stated by the knowability principle (KP). The so-called Knowability Paradox consists in the derivation of a contradiction from the conjunction of (NO) and (KP). We shall show that the derivation of such a contradiction can be blocked by interpreting (NO) as the thesis that there are truths forever unknown to actual agents. We further provide a solution to the so-called Paradox of Idealization which consists in the derivation of a contradiction from the following, initially plausible, premises. First, thesis (FU) stating that there are feasibly unknowable truths in the sense of truths knowable only by idealized agents, second, thesis (NI) stating that there are no idealized agents, and third, above mentioned thesis (KP). We show that by interpreting (NI) as stating that no actual agent is idealized, the derivation of contradiction from the conjunction of (FU), (NI), and (KP) is blocked.

This thesis is about the structure and unity of atomic Fregean Thoughts as abstract structured entities which are the meanings and the primary truth-bearers of sentences as well as the objects of attitudes. We explicate Frege’s theory of Thoughts to argue that it is the most adequate semantic theory for explaining the meaning and truth of natural language expressions. However, there are certain problems concerning the structure and unity of Fregean Thoughts. Our initial conjecture is that Frege’s theory is incomplete in the sense of being vulnerable to certain puzzles and paradoxes, hence the problems concerning the structure and unity of atomic Thoughts demonstrate the apparent need of certain interpretations and supplementations to Frege’s semantic framework. For the problems concerning the structure, we focus on the apparent tension between the Context Principle and the Compositionality Principles, and Frege’s conflicting theses regarding the structural analysis and decomposition of Thoughts. For the problems concerning the unity, we deal with a unique problem, namely the concept horse paradox. In this thesis, we present our emendatory framework to interpret the sense and denotation functions as lambda-abstracts and provide our solution to the paradox. We claim that a grammatical subject, i.e., the concept horse, can denote a concept occurring in a context in which it is mentioned. Hence, the occurrence of the concept horse denotes an unsaturated concept. To conclude, we provide a satisfactory semantic theory of Thoughts and preserve the nature of Fregean intuitions about the philosophy of language.

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.