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This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.

Logic --- Philosophy --- Philosophy & Religion --- Philosophy. --- Logic. --- Mathematical logic. --- Mathematical Logic and Foundations. --- Mathematical Logic and Formal Languages. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Psychology --- Science --- Reasoning --- Thought and thinking --- Mental philosophy --- Humanities --- Methodology --- Logic, Symbolic and mathematical. --- Computer science. --- Informatics --- Proof theory --- Semantics - Mathematical models --- Logic, symbolic and mathematical --- Semantics

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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 agenda andto 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.

Philosophy. --- Logic. --- Language and languages --- Mathematics --- Mathematical logic. --- Linguistics. --- Philosophy of Language. --- Philosophy of Mathematics. --- Mathematical Logic and Foundations.

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This open access book is the first ever collection of Karl Popper's writings on deductive logic. Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics. This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.

Logic --- Popper, Karl --- Lògica --- Argumentació --- Dialèctica (Lògica) --- Lògica deductiva --- Filosofia --- Intel·ligència --- Psicologia --- Abstracció --- Alteritat (Filosofia) --- Categories (Filosofia) --- Certesa --- Condicionals (Lògica) --- Definició (Lògica) --- Dilema --- Evidència --- Hipòtesi --- Inconsistència (Lògica) --- Inducció (Lògica) --- Intenció (Lògica) --- Judici lògic --- Lògica deòntica --- Metodologia --- Modalitat (Lògica) --- Nominalisme --- Positivisme lògic --- Probabilitats --- Raó suficient --- Sil·logisme --- Sofismes --- Teoria del coneixement --- Universals (Filosofia) --- Metodologia de la ciència --- Pensament --- Raonament --- Karl R. Popper --- Deductive Logic --- Logical Constants --- Proof-theoretic Semantics --- Classical Logic --- Non-classical Logic --- Inferential Definitions --- Mathematical Logic --- Negation --- Modalities --- History of Logic --- L.E.J. Brouwer --- Paul Bernays --- Rudolf Carnap --- Alonzo Church --- Kalman Joseph Cohen --- Henry George Forder --- Harold Jeffreys --- Stephen Cole Kleene

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