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The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today

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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.

Author(s): Johan van Benthem, Gerhard Heinzmann, Manuel Rebuschi, Henk Visser (eds.)
Series: Logic, Epistemology, and the Unity of Science, 3
Publisher: Springer
Year: 2006

Language: English
Pages: 348
Tags: Logic; Philosophy; Mathematical Logic and Foundations

Front Matter....Pages 10-10
Introduction: Alternative Logics and Classical Concerns....Pages 1-7
Epistemic Models, Logical Monotony and Substructural Logics....Pages 11-23
Semantics as Based on Inference....Pages 25-36
Effectiveness....Pages 37-49
Does Gödel's Incompleteness Theorem Prove that Truth Transcends Proof?....Pages 51-73
Transpositions....Pages 75-86
Front Matter....Pages 88-88
Many-Valued and Kripke Semantics....Pages 89-101
The Logic of Complementarity....Pages 103-120
Semantics for Naive Set Theory in Many-Valued Logics....Pages 121-136
Front Matter....Pages 138-138
Continuity and Logical Completeness: An Application of Sheaf Theory and Topoi....Pages 139-149
What is Categorical Structuralism?....Pages 151-161
Category Theory as a Framework for an in re Interpretation of Mathematical Structuralism....Pages 163-179
Categories, Sets and the Nature of Mathematical Entities....Pages 181-192
Front Matter....Pages 194-194
Truth, Negation and Other Basic Notions of Logic....Pages 195-219
Signalling in IF Games: A Tricky Business....Pages 221-241
Independence-Friendly Logic and Games of Incomplete Information....Pages 243-259
IF and Epistemic Action Logic....Pages 261-281
Front Matter....Pages 284-284
Naturalizing Dialogic Pragmatics....Pages 285-297
Logic as a Tool of Science Versus Logic as a Scientific Subject....Pages 299-310
Non-Normal Dialogics for a Wonderful World and More....Pages 311-334
Front Matter....Pages 336-336
Louis Joly as a Platonist Painter?....Pages 337-341