This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes (...) readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic. (shrink)

Despite the fact that Aristotle and Frege/Russell differ in how to understand the ambiguity in the meaning of the word “is”, their theories share a common feature: “is” does not have a normative meaning. This paper, however, (I) shows (a) that there is a normative meaning of “is” (and correspondingly a constative meaning of the word “ought”) and (b) that the ambiguity of “is” is itself ambiguous. Furthermore, it proposes (c) a performative criterion for making a distinction between constative and (...) normative “is”. Thereby, (II) a new interpretation of Kant’s critique of the ontological argument (CPR A 598/B626) makes sense: The difference between being as a real predicate and being as a position depends on the difference between “is” as a descriptive and “is” as a normative predicate. (III) The criterion also makes possible a new answer to Leibniz’s and Schelling’s question, “Why is there something rather than nothing?”: The “is” in “there is something” is normative and the question means “Why shall there be something rather than nothing?”. As “there shall be nothing” is self-refuting, the question evokes an ultimate foundation in a practical sense. (shrink)