Modal Logic for Philosophers

This book on modal logic is especially designed for philosophy students. It provides an accessible yet technically sound treatment of modal logic and its philosophical applications. Every effort is made to simplify the presentation by using diagrams instead of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dicto distinction. Discussion of philosophical issues concerning the development of modal logic is woven into the text. The book uses natural deduction systems, which are widely regarded as the easiest to teach and use. It also includes a diagram technique that extends the method of truth trees to modal logic. This provides a foundation for a novel method for showing completeness that is easy to extend to quantifiers. This second edition contains a new chapter on logics of conditionals, an updated and expanded bibliography, and is updated throughout. A number of technical results have also been clarified and streamlined.Preface to the second edition; Introduction; 1. The System K: a foundation for modal logic; 2. Extensions of K; 3. Basic concepts of intensional semantics; 4. Trees for K; 5. The accessibility of relation; 6. Trees for extensions of K; 7. Converting trees to proofs; 8. Adequacy of propositional modal logics; 9. Completeness of using canonical models; 10. Axioms and their corresponding conditions on R; 11. Relations between the modal logics; 12. Systems of quantified modal logic; 13. Semantics for quantified modal logics; 14. Trees for quantified modal logics; 15. The adequacy of quantified modal logics; 16. Completeness of quantified modal logics using trees; 17. Completeness using canonical models; 18. Descriptions; 19. Lambda Abstraction; 20. Conditionals.