The Age of Alternative Logics

by Van Benthem, Johan; Heinzmann, Gerhard; Rebuschi, Manuel; Visser, Henk

• ISBN13: 9781402050114
• ISBN10: 1402050119
• Format: Hardcover
• Copyright: 2006-12-30
• Publisher: Springer Verlag

Summary

In the last century developments in mathematics, philosophy, physics, computer science, economics and linguistics have proven important for the development of logic. There has been an influx of new ideas, concerns, and logical systems reflecting a great variety of reasoning tasks in the sciences. This volume reflects the multi-dimensional nature of the interplay between logic and science. It presents contributions from the world's leading scholars under the following headings: - Proof, Knowledge and Computation - Truth Values beyond Bivalence - Category-Theoretic Structures - Independence, Evaluation Games, and Imperfect Information - Dialogue and Pragmatics. The contents exemplify the liveliness of modern perspectives on the philosophy of logic and mathematics and demonstrate the growth of the discipline. It describes new trends, possible developments for research and new issues not normally raised in the standard agenda of the philosophy of logic and mathematics. It transforms rigid classical partitions into a more open field for improvisation.

Table of Contents

Acknowledgments	ix
1 Introduction: Alternative Logics and Classical Concerns	1	(10)
Johan van Benthem
Part I Proof, Knowledge and Computation
2 Epistemic Models, Logical Monotony and Substructural Logics	11	(14)
Mikaël Cozic
3 Semantics as Based on Inference	25	(12)
Jaroslav Peregrin
4 Effectiveness	37	(14)
Stewart Shapiro
5 Does Gödel's Incompleteness Theorem Prove that Truth Transcends Proof?	51	(24)
Joseph Vidal-Rosset
6 Transpositions	75	(14)
Henk Visser
Part II Truth Values Beyond Bivalence
7 Many-Valued and Kripke Semantics	89	(14)
Jean-Yves Béziau
8 The Logic of Complementarity	103	(18)
Newton C.A. da Costa, Décio Krause
9 Semantics for Naive Set Theory in Many-Valued Logics	121
Thierry Libert
Part III Category-Theoretic Structures
10 Continuity and Logical Completeness: An Application of Sheaf Theory and Topoi	139	(12)
Steve Awodey
11 What is Categorical Structuralism?	151	(12)
Geoffrey Hellman
12 Category Theory as a Framework for an in re Interpretation of Mathematical Structuralism	163	(18)
Elaine Landry
13 Categories, Sets and the Nature of Mathematical Entities	181	(14)
Jean-Pierre Marquis
Part IV Independence, Evaluation Games and Imperfect Information
14 Truth, Negation and Other Basic Notions of Logic	195	(26)
Jaakko Hintikka
15 Signalling in IF Games: A Tricky Business	221	(22)
Theo M.V. Janssen, Francien Dechesne
16 Independence-Friendly Logic and Games of Incomplete Information	243	(18)
Ahti-Veikko Pietarinen
17 IF and Epistemic Action Logic	261	(24)
Manuel Rebuschi
Part V Dialogue and Pragmatics
18 Naturalizing Dialogic Pragmatics	285	(14)
Gerhard Heinzmann
19 Logic as a Tool of Science Versus Logic as a Scientific Subject	299	(12)
Kuno Lorenz
20 Non-Normal Dialogics for a Wonderful World and More	311	(26)
Shahid Rahman
Part VI Appendix
Louis Joly as a Platonist Painter?	337	(6)
Roger Pouivet
INDEX	343