Peter Schroeder-Heister on Proof-Theoretic Semantics

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.

Celebrates a seminal researcher's impact on our understanding of meaning Contributions by leading international experts on an influential research program in logic Offers a unique perspective on Peter Schroeder-Heister's contributions to proof-theoretic semantics This book is open access, which means that you have free and unlimited access

Auteur

Thomas Piecha is a philosopher, physicist, and computer scientist. His research interests include proof-theoretic and dialogical approaches in logic, the logical writings of Karl Popper, and the logical and physical foundations of computer science.

Kai Wehmeier is a professor of logic and philosophy of science at the University of California, Irvine. He has made contributions to mathematical and philosophical logic, formal semantics, the philosophy of language, and the history of analytic philosophy, with a special emphasis on Frege.

Contenu

Chapter 1. Proof-theoretic semantics: An autobiographical survey (Peter Schroeder-Heister).- Chapter 2. Grundlagen der Arithmetik, §17: Part 1. Frege's anticipation of the deduction theorem (Göran Sundholm).- Chapter 3. Frege's class theory and the logic of sets (Neil Tennant).- Chapter 4. The validity of inference and argument (Dag Prawitz).- Chapter 5. Kolmogorov and the general theory of problems (Wagner de Campos Sanz).- Chapter 6. Disjunctive syllogism without Ex falso (Luiz Carlos Pereira, Edward Hermann Haeusler and Victor Nascimento).- Chapter 7. The logicality of equality (Andrzej Indrzejczak).- Chapter 8. Eight rules for implication elimination (Michael Arndt).- Chapter 9. Focusing Gentzen's LK proof system (Chuck Liang and Dale Miller).- Chapter 10. Intensional harmony as Isomorphism (Paolo Pistone and Luca Tranchini).- Chapter 11. A note on synonymy in proof-theoretic semantics (Heinrich Wansing).- Chapter 12. Paradoxes, intuitionism, and proof-theoretic semantics(Reinhard Kahle and Paulo Guilherme Santos).- Chapter 13. On the structure of proofs (Lars Hallnäs).- Chapter 14. Truth-value constants in multi-valued logics (Nissim Francez and Michael Kaminski).- Chapter 15. Counterfactual assumptions and counterfactual implications (Bartosz Wickowski).- Chapter 16. Some set-theoretic reduction principles (Michael Bärtschi and Gerhard Jäger).- Chapter 17. Comments on the contributions (Peter Schroeder-Heister).