Logic, foundations of mathematics, and computability theory
著者
書誌事項
Logic, foundations of mathematics, and computability theory
（Proceedings of the Fifth International Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada, 1975, pt. 1）（The University of Western Ontario series in philosophy of science, v. 9）
D. Reidel, c1977
- : pbk
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注記
Includes bibliographies and index
内容説明・目次
- 巻冊次
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ISBN 9789027707086
内容説明
The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division over the years know well, the work undertaken by its members varies greatly and spans a number of fields not always obviously related. In addition, the volume of work done by first rate scholars and scientists in the various fields of the Division has risen enormously. For these and related reasons it seemed to the editors chosen by the Divisional officers that the usual format of publishing the proceedings of the Congress be abandoned in favour of a somewhat more flexible, and hopefully acceptable, method of pre sentation. Accordingly, the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of Science. The volumes are entitled, Logic, Foundations of Mathematics and Computability Theory, Foun dational Problems in the Special Sciences, Basic Problems in Methodol ogy and Linguistics, and Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science."
- 巻冊次
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: pbk ISBN 9789027707093
内容説明
The twentieth century has witnessed a striking transformation in the understanding of the theories of mathematical physics. There has emerged clearly the idea that physical theories are significantly characterized by their abstract mathematical structure. This is in opposition to the tradi tional opinion that one should look to the specific applications of a theory in orrter to understand it. One might with reason now espouse the view that to understand the deeper character of a theory one must know its abstract structure and understand the significance of that structure, while to understand how a theory might be modified in light of its experimental inadequacies one must be intimately acquainted with how it is applied. Quantum theory itself has gone through a development this century which illustrates strikingly the shifting perspective. From a collection of intuitive physical manoeuvers under Bohr, through a formative stage in which the mathematical framework was bifurcated (between Schrodinger and Heisenberg) to an elegant culmination in von Neumann's Hilbert space formulation, the elementary theory moved, flanked even at this later stage by the ill-understood formalisms for the relativistic version and for the field-theoretic alternative; after that we have a gradual, but constant, elaboration of all these quantal theories as abstract mathematical structures (their point of departure being von Neumann's formalism) until at the present time theoretical work is heavily preoccupied with the manipulation of purely abstract structures.
目次
I. Formal Development of the Theory of Quantum Logic.- Spectral Theory in Quantum Logics.- Semantics of the Minimal Logic of Quantum Mechanics.- Representations of Groups as Automorphisms on Orthomodular Lattices and Posets.- The Conditional in Abstract and Concrete Quantum Logic.- On the Logical Structure of Quantum Mechanics.- II. Philosophy of Quantum Mechanics and Philosophy of Logic.- Matter, Space and Logic.- The Physics of Logic.- Complementarity, Context Dependence, and Quantum Logic.- Is Logic Empirical?.- III. Probability Theory and Quantum Logic.- Conditional Probabilities in Non-Boolean Possibility Structures.- Foundations of a Quantum Probability Theory.- Two Concepts of Probability in Physics.- IV. *-Algebras and Quantum Logic.- Foundations for Quantum Mechanics.- A Survey of Axiomatic Quantum Mechanics.- V. Quaternions, Quantification and Quantum Logic.- Notes On Quaternion Quantum Mechanics.- The Leibniz Project.
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