Higher-order metaphysics : An introduction

This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics used in metaphysics, and indicate a number of questions which can be raised in such systems using logical vocabulary alone. Using a further example, we return to applications of higher-order logics in metaphysics. We also mention key developments in the history of higher-order logic as it pertains to metaphysics. Finally, we mention certain arguments which have been raised against the use of higher-order logic, and some ways of responding to them.