Dag Prawitz on Proofs and Meaning

469 Pages·2015·3.358 MB·English

by  Heinrich Wansing (eds.)

Outstanding Contributions to Logic
Volume 7
Editor-in-Chief
Sven Ove Hansson, Royal Institute of Technology, Stockholm, Sweden
Editorial Board
Marcus Kracht, Universität Bielefeld
Lawrence Moss, Indiana University
Sonja Smets, Universiteit van Amsterdam
Heinrich Wansing, Ruhr-Universität Bochum
More information about this series at http://www.springer.com/series/10033
Heinrich Wansing
Editor
Dag Prawitz on Proofs
and Meaning
123
Editor
Heinrich Wansing
Bochum
Germany
ISSN 2211-2758 ISSN 2211-2766 (electronic)
ISBN 978-3-319-11040-0 ISBN 978-3-319-11041-7 (eBook)
DOI 10.1007/978-3-319-11041-7
LibraryofCongressControlNumber:2014955373
SpringerChamHeidelbergNewYorkDordrechtLondon
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Preface
Theideaforthepresentvolumegoesback,asfarasIremember,toabrainstorming
amongRyszardWójcicki,JacekMalinowski,andmyselfattheTrendsinLogicVII
conferenceinFrankfurt/Main,September2009.Ontheoccasionofameetingwith
a representativefrom Springer, Ryszard Wójcicki, quite enthusiastically, presented
his thoughts on a new book series within the Studia Logica Library, an ambitious
seriesmeanttopresentOutstandingContributionstoLogicwithvolumesdedicated
to eminent living logicians. It certainly comes as no surprise at all that during the
brainstormingseveral important logicians immediately came toour minds and that
Dag Prawitz was one of them.
After this meeting some time elapsed before the first steps were taken to start
concrete book projects, and the division of labor had it that I should act as the
coordinator of the volume for Dag Prawitz. Eventually, I approached Dag Prawitz
inordertosuggesttheproject,toinvitehimtothinkaboutasuitabletopicandtitle,
andtoproposeapossiblevolumeeditor.Amostnaturalvolumeeditor,itseemedto
me, would have been Peter Schroeder-Heister, whose doctoral dissertation Dag
Prawitz had co-supervised, who is very familiar with Prawitz’s work, and who
would have been a natural choice anyway because of his great expertise in proof
theory and proof-theoretic semantics. However, since there is a long-standing plan
for a joint monograph by Prawitz and Schroeder-Heister, the idea came up that I
might edit the book, a plan I finally approved.
Soonafter,asuitabletitleforthevolumewasfound:DagPrawitzonProofsand
Meaning. Moreover, a list of prospective contributors was compiled, and the
response to the invitations for the volume was very positive and encouraging. In
September 2012, a book workshop was held at Ruhr-University Bochum. During
this highly productive event, Dag Prawitz not only presented a first version of his
own contribution to the envisaged book, but also carefully commented on most of
the other papers for his Outstanding Contributions to Logic volume. Various
contributors to the volume, including Dag Prawitz himself, met at the 2nd Con-
ference on Proof-Theoretic Semantics at the University of Tübingen, March 2013,
andattheworkshopMeaning:ModelsandProofsinMunich,October2013.Bythe
v
vi Preface
endof2013,thevolumewasalmostcomplete,awaitingsomefinalcorrectionsand
polishing.
Meanwhile, it took a long period of time for the first (other) volumes of the
new book series to appear, a period in which Ryszard Wójcicki resigned as the
Editor-in-ChiefoftheTrendsinLogicbookseries,inwhichIagreedtotakeover
responsibility for Trends in Logic, and in which Sven Ove Hansson agreed to
become the Editor-in-Chief of Outstanding Contributions to Logic.
Now that the volume Dag Prawitz on Proofs and Meaning is finally ready for
production, I have the privilege to thank, first of all, professor Dag Prawitz for his
kindandthoughtfulcooperation.Itwasagreatpleasuretoexchangethoughtswith
him in person and via e-mail, and like many other contributors to the volume, I
benefited form Dag’scareful andconstructive comments.It was a pleasure,too,to
see the volume developing, and I am grateful to all the other contributors for their
kindcooperationaswellastheirpatience.Inaddition,IwouldliketothankAndrea
Kruse, Caroline Willkommen, Roberto Ciuni, and Judith Hecker for their general
support (in particular also during the workshop in 2012) and Tobias Koch for his
LaTeX-nical assistance.
Bochum, March 2014 Heinrich Wansing
Contents
1 Prawitz, Proofs, and Meaning. . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Heinrich Wansing
2 A Short Scientific Autobiography . . . . . . . . . . . . . . . . . . . . . . . . 33
Dag Prawitz
3 Explaining Deductive Inference. . . . . . . . . . . . . . . . . . . . . . . . . . 65
Dag Prawitz
4 Necessity of Thought. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Cesare Cozzo
5 On the Motives for Proof Theory . . . . . . . . . . . . . . . . . . . . . . . . 121
Michael Detlefsen
6 Inferential Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Kosta Došen
7 Cut Elimination, Substitution and Normalisation . . . . . . . . . . . . . 163
Roy Dyckhoff
8 Inversion Principles and Introduction Rules. . . . . . . . . . . . . . . . . 189
Peter Milne
9 Intuitionistic Existential Instantiation and Epsilon Symbol . . . . . . 225
Grigori Mints
10 Meaning in Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
Sara Negri and Jan von Plato
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viii Contents
11 Fusing Quantifiers and Connectives: Is Intuitionistic
Logic Different? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Peter Pagin
12 On Constructive Fragments of Classical Logic. . . . . . . . . . . . . . . 281
Luiz Carlos Pereira and Edward Hermann Haeusler
13 General-Elimination Harmony and Higher-Level Rules . . . . . . . . 293
Stephen Read
14 Hypothesis-Discharging Rules in Atomic Bases. . . . . . . . . . . . . . . 313
Tor Sandqvist
15 Harmony in Proof-Theoretic Semantics: A Reductive Analysis . . . 329
Peter Schroeder-Heister
16 First-Order Logic Without Bound Variables: Compositional
Semantics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
William W. Tait
17 On Gentzen’s Structural Completeness Proof. . . . . . . . . . . . . . . . 385
Neil Tennant
18 A Notion of C-Justification for Empirical Statements . . . . . . . . . . 415
Gabriele Usberti
19 Dag Prawitz’s Published Books and Papers, by Year
(Selected) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
About the Contributors
Cesare Cozzo studied at Rome, Florence and Stockholm. He is an Associate
Professor of Logic at the Department of Philosophy of the University of Rome
“LaSapienza.”Hismainresearchhasbeenintheoryofmeaningandphilosophyof
logic. He is author of three books: Teoria del significato e filosofia della logica
(Clueb, Bologna 1994), Meaning and Argument (Almqvist & Wiksell, Stockholm
1994), Introduzione a Dummett (Laterza, Roma 2008), and of several articles.
A significant part of his work has been focused on the idea that the sense of a
linguistic expression is given by some rules for its use in arguments: he has
developed a fallibilist and nonholistic version of this idea.
Michael Detlefsen is the McMahon-Hank II Professor of Philosophy at the
UniversityofNotreDame,wherehehasalsoservedastheeditoroftheNotreDame
Journal of Formal Logic since 1984. The main area of his scholarly interest is the
philosophy of mathematics. His current focus is freedom as an ideal of mathe-
matical inquiry.
KostaDošenisaProfessorofLogicattheFacultyofPhilosophyoftheUniversity
ofBelgrade.HeworksalsoattheMathematicalInstituteoftheSerbianAcademyof
SciencesandArts,wherehechairstheSeminarforGeneralProofTheory.Heused
tobeaprofessorattheUniversityofToulouseIII.HestudiedinBelgrade,andthen
inOxford,underMichaelDummett’ssupervision.HeistheauthorofthebooksCut
Elimination in Categories (Kluwer 1999), Proof-Theoretical Coherence (College
Publications 2004) andProof-Net Categories (Polimetrica 2007), ofwhich the last
twoareco-authored byZoranPetrić.Hepublishedmany papersinlogicandsome
related areas of mathematics—a few are in philosophy. He worked in modal logic
and intuitionistic logic, and pioneered the unified investigation of substructural
logics(henamedthemso).Ingeneralprooftheory,followingJoachimLambekand
Saunders Mac Lane, he works in categorial proof theory, in particular, on identity
of deductions.
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