Address and explore the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic.
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 here address 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. 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. The monograph provides a succinct picture of recent research in alternative logics as they have been developed for applications in the sciences.
I General Topics.- Why Is It Logical to Admit Several Logics?.- Does Metaphysics Need a Non-Classical Logic?.- Logic and the Philosophical Interpretation of Science.- How Set Theory Impinges on Logic.- Geometries and Arithmetics.- Remarks on Criteria of Truth and Models in Science.- Significant? Not Significant? The Dilemma of Statistical Induction in Scientific Research.- II Alternative Proposals.- Outline of a Paraconsistent Category Theory.- Combinatory Logic, Language, and Cognitive Representations.- Extending the Realm of Logic: The Adaptive-Logic Programme.- Comments on Jaakko Hintikka's Post-Tarskian Truth.- III Alternative Logics Motivated by Problems of Application to Science.- Applied Logics for Computer Science.- Stochastic versus Deterministic Features in Learning Models.- Praxic Logics.- Reasons from Science for Limiting Classical Logic.- The Language of Interpretation in Quantum Physics and Its Logic.- Why Objectivist Programs in Quantum Theory Do Not Need an Alternative Logic.- Does Quantum Physics Require a New Logic?.- Experimental Approach to Quantum-Logical Connectives.- From Semantics to Syntax: Quantum Logic of Observables.- An Unsharp Quantum Logic from Quantum Computation.- Quantum Logic and Quantum Probability.- Operator Algebras and Quantum Logic.