Kai F. Wehmeier - Böcker

The received view of identity takes it to be a binary relation between objects like many others: specifically, identity is thought to be the binary relation every object bears to itself and to no others. As such, it is supposed to play a fundamental role in our conceptual scheme. It is also widely held that Gottlob Frege (1848-1925), after a false start in his Begriffsschrift of 1879, where he proposed that identity is a relation between signs, eventually came round to the now mainstream view, the first paragraph of his celebrated 1892 essay "On Sense and Reference" marking the transition. In Frege: Identity Challenges Reflection, Ulrich Pardey and Kai F. Wehmeier show that common wisdom is mistaken on both counts. First, careful exegesis shows that Frege did not repudiate the earlier, sign-based conception of identity in his 1892 essay, but instead defended it; moreover, that conception is in no way refuted by the collection of formal and philosophical objections that have been raised against it in subsequent decades. In particular, the Begriffsschrift theory of identity, far from being incompatible with quantification over objects, in fact affords an elegant, ontologically conservative integration of identity into predicate logic. Second, Pardey and Wehmeier argue that our conceptual scheme is not at all committed to a binary relation that every object bears to itself and only itself. Moreover, the tension between the alleged binarity of the identity relation and the logical impossibility of its ever relating two things, famously pointed out by Wittgenstein in the Tractatus, forms the basis of an argument for the logical incoherence of such a relation.

This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. The chapters of which this book is composed discuss the subject from a rich variety of angles, including the history of logic, the proper interpretation of logical validity, natural deduction rules, the notions of harmony and of synonymy, the structure of proofs, the logical status of equality, intentional phenomena, and the proof theory of second-order arithmetic. All chapters relate directly to questions that have driven Schroeder-Heister's own research agendaand to which he has made seminal contributions. The extensive autobiographical chapter not only provides a fascinating overview of Schroeder-Heister's career and the evolution of his academic interests but also constitutes a contribution to the recent history of logic in its own right, painting an intriguing picture of the philosophical, logical, and mathematical institutional landscape in Germany and elsewhere since the early 1970s. The papers collected in this book are illuminatingly put into a unified perspective by Schroeder-Heister's comments at the end of the book. Both graduate students and established researchers in the field will find this book an excellent resource for future work in proof-theoretic semantics and related areas.