Vann McGee has recently argued that Belnap's criteria constrain the formal rules of classical natural deduction to uniquely determine the semantic values of the propositional logical connectives and quantifiers if the rules are taken to be open-ended, i.e., if they are truth-preserving within any mathematically possible extension of the original language. The main assumption of his argument is that for any class of models there is a mathematically possible language in which there is a sentence true in just those models. I show that this assumption does not hold for the class of models of classical propositional logic. In particular, I show that the existence of non-normal models for negation undermines McGee's argument.

Starting from certain metalogical results (the completeness theorem, the soundness theorem, and Lindenbaum-Scott theorem), I argue that first-order logical truths of classical logic are a priori and necessary. Afterwards, I formulate two arguments for the idea that first-order logical truths are also analytic, namely, I first argue that there is a conceptual connection between aprioricity, necessity, and analyticity, such that aprioricity together with necessity entails analyticity; then, I argue that the structure of natural deduction systems for FOL displays the analyticity of its truths. Consequently, each philosophical approach to these truths should account for this evidence, i.e., that first-order logical truths are a priori, necessary, and analytic, and it is my contention that the semantic account is a better candidate.

The concern of deductive logic is generally viewed as the systematic recognition of logical principles, i.e., of logical truths. This paper presents and analyzes different instantiations of the three main interpretations of logical principles, viz. as ontological principles, as empirical hypotheses, and as true propositions in virtue of meanings. I argue in this paper that logical principles are true propositions in virtue of the meanings of the logical terms within a certain linguistic framework. Since these principles also regulate and control the process of deduction in inquiry, i.e., they are prescriptive for the use of language and thought in inquiry, I argue that logic may, and should, be seen as an instrument or as a way of proceeding (modus procedendi) in inquiry.KEYWORDS: empirical interpretation of logical truths, ontological interpretation of logical truths, semantic interpretation of logical truths, the nature of logical truths 1 Ernest Nagel, "Logic without Ontology," in Naturalism and the Human Spirit, ed. Yervant H.

Karl R. Popper (1947a, b) took the central topic of logic to be the theory of deductive inference and the main problem he was concerned with in his early writings on deductive logic was to give a satisfactory definition for the notion of "deductive valid inference". Although his definition was supposed to be a generalization of Tarski's definition of logical consequence, Popper showed that the notion of "truth" can be avoided, even though its use is not objectionable. In addition, unlike Tarski's modeltheoretic (or, better, group-theoretic) criterion, he proposed an inferential criterion to draw a line between the formative (i.e., logical) and the non-formative signs (i.e., non-logical) and defined the validity of deductive inferences on the basis of inferential definitions. 1 Although the notion of truth can be avoided in this inferential foundational approach to deductive inferences, in some latter writings Popper acknowledged that the validity of deduction goes beyond the signs and the rules that govern their use, and emphasized the constitutive role that the notion of truth has for logical deduction: Deduction, I contend, is not valid because we choose or decide to adopt its rules as a standard, or decree that they shall be accepted; rather, it is valid because it adopts, and incorporates, the rules by which truth is transmitted from (logically stronger) premises to (logically weaker) conclusions, and by which falsity is re-transmitted from conclusions to premises. (This retransmission of falsity makes formal logic the Organon of rational criticism -that is, of refutation). (Popper 1962, 64) In addition, Popper et al. (1970, 18) took the notion of truth to be crucial for the applications of logic in the other areas of inquiry. With regard to these applications,

The book series Trends in Logic covers essentially the same areas as the journal Studia Logica, that is, contemporary formal logic and its applications and relations to other disciplines. The series aims at publishing monographs and thematically coherent volumes dealing with important developments in logic and presenting significant contributions to logical research.Volumes of Trends in Logic may range from highly focused studies to presentations that make a subject accessible to a broader scientific community or offer new perspectives for research. The series is open to contributions devoted to topics ranging from algebraic logic, model theory, proof theory, philosophical logic, non-classical logic, and logic in computer science to mathematical linguistics and formal epistemology. This thematic spectrum is also reflected in the editorial board of Trends in Logic. Volumes may be devoted to specific logical systems, particular methods and techniques, fundamental concepts, challenging open problems, different approaches to logical consequence, combinations of logics, classes of algebras or other structures, or interconnections between various logic-related domains.