Truth And Provability

Existence, Truth, and Probability

This book includes some of the most original and influential contributions to logic and the philosophy of logic during the past twenty years. It contains thirty-five essays, many of which started new trends in logic. For example, some of the essays in Part One gave birth to what is now known as free logic, and some of the essays in Part Two were among the earliest contributions to what is now known as truth-value semantics. The essays in Part Three are contributions to and improvements of already extant logics, such as intuitionistic logic, natural deduction, and the logic of sequents. Introductions to the parts of the book cover the history of the contributions and their importance. The essays have been thoroughly revised since their publication in learned journals.

Intuitionistic Proof Versus Classical Truth

This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers – both new and previously published – it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism. The author explores Brouwer’s idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwer’s work. These figures include Michael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting. This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics.

Provability and Truth