ua nt - p h / 99 02 04 2 v 1 1 0 Fe b 19 99 Quantum logic . A brief outline
نویسنده
چکیده
A more complete introduction of the author can be found in the book Quantum logic has been introduced by Garrett Birkhoff and John von Neumann in the thirties [BvN36]. They organized it top-down: The starting point is von Neumann's Hilbert space formalism of quantum mechanics. In a second step, certain entities of Hilbert spaces are identified with propositions, partial order relations and lattice operations — Birkhoff's field of expertise. These relations and operations can then be associated with the logical implication relation and operations such as and, or, and not. Thereby, a " nonclassical, " nonboolean logical structure is induced which originates in theoretical physics. If theoretical physics is taken as a faithful representation of our experience, such an " operational " [Bri27, Bri34, Bri52] logic derives its justification by the phenomena themselves. In this sense, one of the main ideas behind quantum logic is the quasi-inductive construction of the logical and algebraic order of events from empirical facts. This is very different from the " classical " logical approach, which is also top-down: There, the system of symbols, the axioms, as well as the rules of inference are mentally constructed, abstract objects of our thought. Insofar as our thoughts can pretend to exist independent from the physical Universe, such " classical " logical systems can be conceived as totally independent from the world of the phenomena.
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تاریخ انتشار 2005