Revising logic

Abstract

In this thesis I explore the prospects for the revision of classical logic through an analysis of the philosophical arguments offered for and against such change. The body of the thesis is divided into two parts. In Part One I seek to establish a general picture of logical revision. The picture provides a defence of the conceptual possibility of logical revision and an account of the ways it can work. The first chapter is concerned with the comparison of different logical systems. I offer a classification of equivalence classes of logical systems in which a difference between 'rival' and 'non-rival' systems may be articulated. The second chapter is addressed to the 'kinematics' of logic: how logical systems change. Here my principal concern has been to explain the significance of the shared content that may endure through such change. The third chapter addresses the 'dynamics' of logic, exploring the forces that bring about theory change within logic. To this end I offer an account of the broader theoretical context of logical systems, and develop an application of a methodology adequate to describe and analyse logical theory change. Part Two consists of case studies of specific logical reform proposals, and is designed to illustrate the general picture defended in Part One. Four successive chapters address the claims made on behalf of intuitionistic logic, quantum logic, relevant logic and paraconsistent logic. Collectively, the case studies serve to examine the applicability of a general account of logical revision and to explore the finer detail of a variety of different debates within especially illustrative contexts.