This Element looks at the problem of inter-translation between mathematical realism and anti-realism and argues that so far as realism is inter-translatable with anti-realism, there is a burden on the realist to show how her posited reality differs from that of the anti-realist. It also argues that an effective defence of just such a difference needs a commitment to the independence of mathematical reality, which in turn involves a commitment to the ontological access problem - the problem of how knowable mathematical truths are identifiable with a reality independent of us as knowers. Specifically, if the only access problem acknowledged is the epistemological problem - i.e. the problem of how we come to know mathematical truths - then nothing is gained by the realist notion of an independent reality and in effect, nothing distinguishes realism from anti-realism in mathematics.

Featuring fourteen new essays from an international team of renowned contributors, this volume explores the key issues, debates and questions in the metaphysics of logic. The book is structured in three parts, looking first at the main positions in the nature of logic, such as realism, pluralism, relativism, objectivity, nihilism, conceptualism, and conventionalism, then focusing on historical topics such as the medieval Aristotelian view of logic, the problem of universals, and Bolzano's logical realism. The final section tackles specific issues such as glutty theories, contradiction, the metaphysical conception of logical truth, and the possible revision of logic. The volume will provide readers with a rich and wide-ranging survey, a valuable digest of the many views in this area, and a long overdue investigation of logic's relationship to us and the world. It will be of interest to a wide range of scholars and students of philosophy, logic, and mathematics.

Featuring fourteen new essays from an international team of renowned contributors, this volume explores the key issues, debates and questions in the metaphysics of logic. The book is structured in three parts, looking first at the main positions in the nature of logic, such as realism, pluralism, relativism, objectivity, nihilism, conceptualism, and conventionalism, then focusing on historical topics such as the medieval Aristotelian view of logic, the problem of universals, and Bolzano's logical realism. The final section tackles specific issues such as Glutty theories, contradiction, the metaphysical conception of logical truth, and the possible revision of logic. The volume will provide readers with a rich and wide-ranging survey, a valuable digest of the many views in this area, and a long overdue investigation of logic's relationship to us and the world. It will be of interest to a wide range of scholars and students of philosophy, logic, and mathematics.