Dag Prawitz on Proofs and Meaning

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This volume honors Prof. Dag Prawitz for his significant contributions to philosophical and mathematical logic, particularly in structural proof theory and inference-based meaning theories. His work has greatly influenced modern proof theory and anti-realistic semantics. Prawitz is recognized as a key figure in natural deduction, alongside Gerhard Gentzen, who initially defined the concept in 1934. The book begins with an introductory paper that surveys Prawitz's extensive contributions, situating his work within a broader historical and systematic context. Subsequent chapters delve into specific aspects of Prawitz's research or explore open research problems related to core issues in structural proof theory. These range from philosophical essays to mathematical papers, addressing topics such as the necessity of thought, the theory of grounds, and computational justifications. The validity of inferences is examined through the lens of three "dogmas of proof-theoretic semantics." More formal discussions cover the constructive behavior of classical logic fragments and the modal logic S4, along with inversion principles, normalization of proofs, and proof-theoretic harmony. Prawitz also contributes a chapter outlining his views on the epistemic dimension of proofs, particularly why certain inferences effectively confer evidence on their conclusions when applied to premises already supported by evidence.