Alternative Logics. Do Sciences Need Them?

Front Cover
Paul A. Weingartner
Springer Science & Business Media, Mar 9, 2013 - Computers - 368 pages

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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Contents

Why Is It Logical to Admit Several Logics?
3
The Relevance of the Referents for Logic
21
Does Metaphysics Need a NonClassical Logic?
27
Noneism
33
Noneist Logic
37
Nature of and Contrasts Between the Two Programs
47
References
53
Inaccessible Cardinals
59
Some Examples Concerning Stochastic Learning Procedures
208
Praxic Logics
215
Variant Epistemologies
221
Variant SecondOrder Logics
227
Commensurability and Distributivity in Quantum Logic
236
References
247
The Language of Interpretation in Quantum Physics
249
Wider Issues
255

NonEuclidean Geometry
66
The General Structure of Models
72
Remarks on Criteria of Truth and Models in Science
79
Significant? Not Significant?
87
Outline of a Paraconsistent Category Theory
95
The Paraconsistent Theory OB1
104
References
113
Combinatory Logic as an Applicative Language
121
Operators in Combinatory Logic
130
Meaningless and Types
136
Conclusion
142
InconsistencyAdaptive Logics
156
In Conclusion
162
References
172
Using Logic for Program and Invariant Construction
184
Conclusion
201
The Search for an Empirical Logic
261
Conclusion
267
The Quantum Physical Reality
275
Conclusion
283
Experimental Approach to QuantumLogical Connectives
285
Conclusion
297
A Syntax
303
A Normed Quantum Logic of Observables
312
Final Remarks
319
QuantumLogical Gates
327
QuantumComputational Semantics
333
Quantum Logic and Quantum Probability
339
References
346
Von Neumann Lattices as Logics
354
Index
361
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