Introduction: The Many Branches of Belnap’s Logic

Abstract

In this introduction to the Outstanding contributions to logic volume devoted to Nuel Belnap's work on indeterminism and free action, we provide a brief overview of some of the formal frameworks and methods involved in Belnap's work on these topics: theories of branching histories, specifically "branching time" and "branching space-times", the stit ("seeing to it that") logic of agency, and case-intensional first order logic. We also draw some connections to the contributions included in this volume. Abstracts of these contributions are included as an appendix.Nuel Belnap's work in logic and in philosophy spans a period of over half a century. During this time, he has followed a number of different research lines, most of them over a period of many years or decades, and often in close collaboration with other researchers: 1 relevance logic, a long term project starting from a collaboration with Alan Anderson dating back to the late 1950s and continued with Robert Meyer and Michael Dunn into the 1990s; the logic of questions, developed with Thomas Steel in the 1960s and 1970s; display logic in the 1980s and 1990s; the revision theory of truth, with Anil Gupta, in the 1990s; and a long-term, continuing interest in indeterminism and free action. This book is devoted to Belnap's work on the latter two topics. In this introduction, we provide a brief overview of some of the formal frameworks and methods involved in that work, and we draw some connections to the contributions included in this volume. Abstracts of these contributions are presented in Appendix A. 1 The biographical interview with Nuel Belnap provides some additional information on these research lines and on some of the collaborations. About this BookThis book contains essays devoted to Nuel Belnap's work on indeterminism and free action. Philosophically, these topics can seem far apart; they belong to different sub-disciplines, viz., metaphysics and action theory. This separation is visible in philosophical logic as well: The philosophical topic of indeterminism, or of the open future, has triggered research in modal, temporal and many-valued logic; the philosophical topic of agency, on the other hand, has led to research on logics of causation and action. In Belnap's logical work, however, indeterminism and free agency are intimately linked, testifying to their philosophical interconnectedness.Starting in the 1980s, Belnap developed theories of indeterminism in terms of branching histories, most notably "branching time" and his own "branching spacetimes". At the same time, he pursued the project of a logic of (multi-)agency, under the heading of stit, or "seeing to it that". These two developments are linked both formally and genetically. The stit logic of agency is built upon a theory of branching histories-initially, on the Prior-Thomason theory of so-called branching time. The spatio-temporal refinement of that theory, branching space-times, in turn incorporates insights from the formal modeling of agency. Both research lines arise in one...