This 2006 book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications.

Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.

Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

1. Introduction. 2. The Syntax of Modal Sentential Calculi. 4. Semantics for Logical Necessity. 5. Semantics for S5. 6. Relational World Systems. 7. Quantified Modal Logic. 8. The Semantics of Quantified Modal Logic. 9. Second-Order Modal Logic. 10. Semantics of Second-Order Modal Logic. Afterword. Bibliography. Index.

An introductory textbook on modal logic the logic of necessity and possibility.

Logic: The Basics is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as: · mathematical preliminaries · propositional logic · quantified logic (first monadic, then polyadic) · English and standard ‘symbolic translations’ · tableau procedures. Alongside comprehensive coverage of the standard topics, this thoroughly revised second edition also introduces several philosophically important nonclassical logics, free logics, and modal logics, and gives the reader an idea of how they can take their knowledge further. With its wealth of exercises (solutions available in the encyclopedic online supplement), Logic: The Basics is a useful textbook for courses ranging from the introductory level to the early graduate level, and also as a reference for students and researchers in philosophical logic.

The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, "Modal Logics and Philosophy" places its emphasis firmly on showing how useful modal logic can be as a tool for formal philosophical analysis. In part 1 of the book, the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, obligation and permission.

"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.

This book develops a novel generalization of possible world semantics, called ‘world line semantics’, which recognizes worlds and links between world-bound objects (world lines) as mutually independent aspects of modal semantics. Addressing a wide range of questions vital for contemporary debates in logic and philosophy of language and offering new tools for theoretical linguistics and knowledge representation, the book proposes a radically new paradigm in modal semantics. This framework is motivated philosophically, viewing a structure of world lines as a precondition of modal talk. The author provides a uniform analysis of quantification over individuals (physical objects) and objects of thought (intentional objects). The semantic account of what it means to speak of intentional objects throws new light on accounts of intentionality and singular thought in the philosophy of mind and offers novel insights into the semantics of intensional transitive verbs.

The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter