Ebook: Alternative Logics. Do Sciences Need Them?

Initially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected in this volume address and explore the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In Part II the authors offer several logics that deviate in different ways from classical logics. The twelve papers in Part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. Most of the contributions are revised and partially extended versions of papers presented at a conference of the same title of the Académie Internationale de Philosophie des Sciences held at the Internationales Forschungszentrum Salzburg in May 1999. Others have been added to complete the picture of recent research in alternative logics as they have been developed for applications in the sciences.

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Initially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected in this volume address and explore the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In Part II the authors offer several logics that deviate in different ways from classical logics. The twelve papers in Part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. Most of the contributions are revised and partially extended versions of papers presented at a conference of the same title of the Acad?mie Internationale de Philosophie des Sciences held at the Internationales Forschungszentrum Salzburg in May 1999. Others have been added to complete the picture of recent research in alternative logics as they have been developed for applications in the sciences.

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Initially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected in this volume address and explore the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In Part II the authors offer several logics that deviate in different ways from classical logics. The twelve papers in Part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. Most of the contributions are revised and partially extended versions of papers presented at a conference of the same title of the Acad?mie Internationale de Philosophie des Sciences held at the Internationales Forschungszentrum Salzburg in May 1999. Others have been added to complete the picture of recent research in alternative logics as they have been developed for applications in the sciences.

Content:
Front Matter....Pages I-XVII
Front Matter....Pages 1-1
Why Is It Logical to Admit Several Logics?....Pages 3-26
Does Metaphysics Need a Non-Classical Logic?....Pages 27-39
Logic and the Philosophical Interpretation of Science....Pages 41-54
How Set Theory Impinges on Logic....Pages 55-63
Geometries and Arithmetics....Pages 65-78
Remarks on Criteria of Truth and Models in Science....Pages 79-86
Significant? Not Significant? The Dilemma of Statistical Induction in Scientific Research....Pages 87-92
Front Matter....Pages 93-93
Outline of a Paraconsistent Category Theory....Pages 95-114
Combinatory Logic, Language, and Cognitive Representations....Pages 115-148
Extending the Realm of Logic: The Adaptive-Logic Programme....Pages 149-164
Comments on Jaakko Hintikka’s Post-Tarskian Truth....Pages 165-173
Front Matter....Pages 175-175
Applied Logics for Computer Science....Pages 177-203
Stochastic versus Deterministic Features in Learning Models....Pages 205-213
Praxic Logics....Pages 215-231
Reasons from Science for Limiting Classical Logic....Pages 233-248
The Language of Interpretation in Quantum Physics and Its Logic....Pages 249-256
Why Objectivist Programs in Quantum Theory Do Not Need an Alternative Logic....Pages 257-268
Does Quantum Physics Require a New Logic?....Pages 269-284
Experimental Approach to Quantum-Logical Connectives....Pages 285-298
From Semantics to Syntax: Quantum Logic of Observables....Pages 299-321
Front Matter....Pages 175-175
An Unsharp Quantum Logic from Quantum Computation....Pages 323-338
Quantum Logic and Quantum Probability....Pages 339-347
Operator Algebras and Quantum Logic....Pages 349-360
Back Matter....Pages 361-367

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Initially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected in this volume address and explore the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In Part II the authors offer several logics that deviate in different ways from classical logics. The twelve papers in Part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. Most of the contributions are revised and partially extended versions of papers presented at a conference of the same title of the Acad?mie Internationale de Philosophie des Sciences held at the Internationales Forschungszentrum Salzburg in May 1999. Others have been added to complete the picture of recent research in alternative logics as they have been developed for applications in the sciences.

Content:
Front Matter....Pages I-XVII
Front Matter....Pages 1-1
Why Is It Logical to Admit Several Logics?....Pages 3-26
Does Metaphysics Need a Non-Classical Logic?....Pages 27-39
Logic and the Philosophical Interpretation of Science....Pages 41-54
How Set Theory Impinges on Logic....Pages 55-63
Geometries and Arithmetics....Pages 65-78
Remarks on Criteria of Truth and Models in Science....Pages 79-86
Significant? Not Significant? The Dilemma of Statistical Induction in Scientific Research....Pages 87-92
Front Matter....Pages 93-93
Outline of a Paraconsistent Category Theory....Pages 95-114
Combinatory Logic, Language, and Cognitive Representations....Pages 115-148
Extending the Realm of Logic: The Adaptive-Logic Programme....Pages 149-164
Comments on Jaakko Hintikka’s Post-Tarskian Truth....Pages 165-173
Front Matter....Pages 175-175
Applied Logics for Computer Science....Pages 177-203
Stochastic versus Deterministic Features in Learning Models....Pages 205-213
Praxic Logics....Pages 215-231
Reasons from Science for Limiting Classical Logic....Pages 233-248
The Language of Interpretation in Quantum Physics and Its Logic....Pages 249-256
Why Objectivist Programs in Quantum Theory Do Not Need an Alternative Logic....Pages 257-268
Does Quantum Physics Require a New Logic?....Pages 269-284
Experimental Approach to Quantum-Logical Connectives....Pages 285-298
From Semantics to Syntax: Quantum Logic of Observables....Pages 299-321
Front Matter....Pages 175-175
An Unsharp Quantum Logic from Quantum Computation....Pages 323-338
Quantum Logic and Quantum Probability....Pages 339-347
Operator Algebras and Quantum Logic....Pages 349-360
Back Matter....Pages 361-367
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