Overview
- First volume to give a comprehensive account of Dag Prawitz's seminal contributions to proof theory and proof-theoretic semantics
- Offers original, up-to-date contributions by world-wide leading experts in structural proof theory and proof-theoretic semantics
- Includes topic of proofs and meaning approached from various disciplines in which logic is at home: philosophy, mathematics, and computer science
- Includes supplementary material: sn.pub/extras
Part of the book series: Outstanding Contributions to Logic (OCTR, volume 7)
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Table of contents (19 chapters)
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Front Matter
Keywords
- 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
About this book
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.Reviews
“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)
Editors and Affiliations
About the editor
Bibliographic Information
Book Title: Dag Prawitz on Proofs and Meaning
Editors: Heinrich Wansing
Series Title: Outstanding Contributions to Logic
DOI: https://doi.org/10.1007/978-3-319-11041-7
Publisher: Springer Cham
eBook Packages: Humanities, Social Sciences and Law, Philosophy and Religion (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-11040-0Published: 08 December 2014
Softcover ISBN: 978-3-319-36031-7Published: 22 September 2016
eBook ISBN: 978-3-319-11041-7Published: 27 November 2014
Series ISSN: 2211-2758
Series E-ISSN: 2211-2766
Edition Number: 1
Number of Pages: XIII, 458
Number of Illustrations: 6 b/w illustrations
Topics: Logic, Mathematical Logic and Foundations, Logics and Meanings of Programs