The papers collected in this volume were written over a period of some eight or nine years, with some still earlier material incorporated in one of them. Publishing them under the same cover does not make a con tinuous book of them. The papers are thematically connected with each other, however, in a way which has led me to think that they can naturally be grouped together. In any list of philosophically important concepts, those falling within the range of application of modal logic will rank high in interest. They include necessity, possibility, obligation, permission, knowledge, belief, perception, memory, hoping, and striving, to mention just a few of the more obvious ones. When a satisfactory semantics (in the sense of Tarski and Carnap) was first developed for modal logic, a fascinating new set of methods and ideas was thus made available for philosophical studies. The pioneers of this model theory of modality include prominently Stig Kanger and Saul Kripke. Several others were working in the same area independently and more or less concurrently. Some of the older papers in this collection, especially 'Quantification and Modality' and 'Modes of Modality', serve to clarify some of the main possibilities in the semantics of modal logics in general.

John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across philosophy of mathematics, logic, and philosophy of language.

In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would ?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? no one could have foreseen that in a short time modal logic would become a lively source of ideas and methods for analytical philosophers,historians of philosophy,linguists, epistemologists and computer scientists. The aim which oriented the composition of this book was not to write a new manual of modal logic (there are a lot of excellent textbooks on the market, and the expert reader will realize how much we bene?ted from manyofthem)buttoo?ertoeveryreader,evenwithnospeci?cbackground in logic, a conceptually linear path in the labyrinth of the current panorama of modal logic. The notion which in our opinion looked suitable to work as a compass in this enterprise was the notion of multimodality, or, more speci?cally, the basic idea of grounding systems on languages admitting more than one primitive modal operator.

Ideal for exercise science, athletic training, and physical therapy students, this updated edition of Knight and Draper’sTherapeutic Modalities: The Art and Science covers the knowledge and skills needed to select the best therapeutic modality for each client injury. This edition helps students hone their clinical decision-making skills by teaching both the how and the why of each therapeutic modality, offering the application that today’s student craves. Retaining the accessible student-friendly writing style and focus on kinesthetic learning that made the book so successful, the third edition is enhanced by new chapters, new photos, and significant updates throughout that reflect the latest research and advances in the field.

This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic (the so-called non-normal modal logics). In addition, the book discusses a broad range of topics, including standard modal logic results (i.e., completeness, decidability and definability); bisimulations for neighborhood models and other model-theoretic constructions; comparisons with other semantics for modal logic (e.g., relational models, topological models, plausibility models); neighborhood semantics for first-order modal logic, applications in game theory (coalitional logic and game logic); applications in epistemic logic (logics of evidence and belief); and non-normal modal logics with dynamic modalities. The book can be used as the primary text for seminars on philosophical logic focused on non-normal modal logics; as a supplemental text for courses on modal logic, logic in AI, or philosophical logic (either at the undergraduate or graduate level); or as the primary source for researchers interested in learning about the uses of neighborhood semantics in philosophical logic and game theory.

The leisure to do the thinking whose results are gathered here has largely been provided by the Academy of Finland, whose support has also made possible the help and co-operation of a group of younger logicians and philosophers. Less tangible support and help is unfortunately harder to record and to thank for. Once again, in working on the many themes I have tried to weave together in this book I have incurred more intellectual and moral debts I can in so many words acknowledge here. Let me only say that the closer to home I get the greater they become. I have especially in mind my colleagues and students at Stanford; my colleagues in Helsinki; the past and present members of my research group in Helsinki; and incom parably more than anybody else my wife Soili. Helsinki, April 1975 JAAKKO HINTIKKA INTRODUCTION A literal-minded reader might easily object to the (sub)title of this volume. What is to be found here, he might allege, are neither models, nor modalities stricto sensu, nor yet any completely new applications of modal logic. Even though the purpose of the title is only to signal the con tinuity between the present volume and its predecessor, Models for Modalities (D. Reidel Publishing Co., Dordrecht, 1969), the objection is sufficiently well taken to serve as an excuse for an attempt to put my enterprise in a wider perspective.