The semantical framework for the positive view of this book is one in which entailment is understood primarily in terms of theory closure. This chapter outlines both the history of the notion, beginning with Alfred Tarski’s theory of closure operators, and the relationship between closure operators and the entailment connective. At the end of the chapter, it is shown how closure operators can be used to model a simple logic, Graham Priest’s logic N4.

A few years after his adoption of both a syntactical method and a principle of tolerance in the early thirties, Carnap turned to semantics when he learned about Tarski’s work on the definition of a truth predicate. How significant is this semantical turn? Carnap scholars have so much emphasized that The Logical Syntax anticipates Tarskian semantics that they tended to minimize the importance of Carnap’s adoption of a semantical approach. As a consequence, his semantical turn has not always been given the importance it deserves. Its meaning, scope and consequences have also often been misunderstood. This paper contributes to a re-evaluation of Tarski’s influence on Carnap in view of the fact that Carnap is far from having just followed Tarski’s way. We examine some specificities of Carnap’s approach of semantics. We also discuss what is left of the syntactic method after the adoption of semantics and what the relations between syntax and semantics become from the late thirties on. The following topics are given specific attention: languages, formal systems, and calculi; truth, L-truth, and L-validity; L-states, L-ranges, and state descriptions. We also analyze the impact of semantics on the principle of tolerance.

In current analytic philosophy, Carnapian explication has become a prominent method and theme again, also under the names of conceptual engineering and mathematical philosophy. But there are questions about the reach and limits of this method, and in particular, about the goals for which it is appropriate. In the present essay, this topic is approached by reconsidering the origins of Carnapian explication, in the sense of its original inspirations and guiding paradigms.This leads to the following questions: What were the underlying goals in those cases, thus the function or functions explication was supposed to serve, and how did it serve them? Also, were those functions sufficiently stable and uniform to provide helpful orientation for us, both with respect to Carnap and current appeals to explication? Insofar as answers to those questions are not as easy as one might think, already because the relevant aspects often remain implicit, an important dimension of explication should be subjected to further clarification and critique. What is at issue here, at bottom, is the dividing line, insofar as there is one, between philosophical and scientific goals, and with it, between the methodologies appropriate for each.