Dag Prawitz on Proofs and Meaning

1. Front Matter

   Pages i-xiii

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2. Prawitz, Proofs, and Meaning

   • Heinrich Wansing

   Pages 1-32

3. A Short Scientific Autobiography

   • Dag Prawitz

   Pages 33-64

4. Explaining Deductive Inference

   • Dag Prawitz

   Pages 65-100

5. Necessity of Thought

   • Cesare Cozzo

   Pages 101-120

6. On the Motives for Proof Theory

   • Michael Detlefsen

   Pages 121-145

7. Inferential Semantics

   • Kosta Došen

   Pages 147-162

8. Cut Elimination, Substitution and Normalisation

   • Roy Dyckhoff

   Pages 163-187

9. Inversion Principles and Introduction Rules

   • Peter Milne

   Pages 189-224

10. Intuitionistic Existential Instantiation and Epsilon Symbol

    • Grigori Mints

    Pages 225-238

11. Meaning in Use

    • Sara Negri, Jan von Plato

    Pages 239-257

12. Fusing Quantifiers and Connectives: Is Intuitionistic Logic Different?

    • Peter Pagin

    Pages 259-280

13. On Constructive Fragments of Classical Logic

    • Luiz Carlos Pereira, Edward Hermann Haeusler

    Pages 281-292

14. General-Elimination Harmony and Higher-Level Rules

    • Stephen Read

    Pages 293-312

15. Hypothesis-Discharging Rules in Atomic Bases

    • Tor Sandqvist

    Pages 313-328

16. Harmony in Proof-Theoretic Semantics: A Reductive Analysis

    • Peter Schroeder-Heister

    Pages 329-358

17. First-Order Logic Without Bound Variables: Compositional Semantics

    • William W. Tait

    Pages 359-384

18. On Gentzen’s Structural Completeness Proof

    • Neil Tennant

    Pages 385-414

19. A Notion of C-Justification for Empirical Statements

    • Gabriele Usberti

    Pages 415-450

20. Dag Prawitz’s Published Books and Papers, by Year (Selected)

    • D. Prawitz

    Pages 451-458

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934.

The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics.

In addition, there are chapters about inversion principles, normalization of p

roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.

• C-Justification for empirical statements
• Cut-elimination, substitution and normalization
• Explaining deductive inference
• Fusing quantifiers and connectives
• General-elimination harmony and higher-level rules
• Gerhard Gentzen
• Hypothesis-discharging rules in atomic bases
• Inferential semantics
• Intuitionistic existential instantiation and epsilon symbol
• Inversion principles and introduction rules
• Necessity of thought
• Prawitz, proofs and meaning
• cut-elimination
• motives for proof theory
• natural deduction
• proof-theoretic semantics
• sequent calculus
• structural proof theory

“Swedish logician and philosopher Dag Prawitz and his distinguished contributions to philosophical and mathematical logic are the focus of this book. … This is an excellent book, celebrating not only Prawitz’s career, but also a movement in the contrary direction of W. V. O Quine’s views against the so-called (somehow prejudicially) ‘deviant’ logics, and I cannot forbear from congratulating the editor for the distinctive choice of topics and for the general tone of the book.” (Walter Carnielli, Computing Reviews, May, 2015)

• Bochum, Germany

  Heinrich Wansing

Heinrich Wansing is a professor of logic and epistemology at the Ruhr University Bochum (Germany). He is known for his work in philosophical logic, including the semantics and proof theory of modal, constructive, paraconsistent, many-valued and other non-classical logics. Moreover, he is the editor-in-chief of the book series Trends in Logic (Springer)

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