According to philosophy of logic,quantum can be considered as a non-classical characterized by non-distributivity,and it takes scientific inference actually used by scientists of quantum mechanics as real prototypes or basis.Hillary Putnam concluded that logic can be revised globally due to reasons in terms of generation of quantum logic;while at same time he claimed that quantum logical connectives retained their classical meanings,which made him fall into a dilemma.After reexamining empirical reasons and the revision of argument on basis of several different interpretations of quantum mechanics,the authors of this paper found that metaphysical considerations are not negligible.And paper proposed that Correspondence Principle had methodological effect of resolving Putnam's Dilemma,and could explain reasonably continuity and innovation of quantum to classical logic.
According to philosophy of logic,quantum can be considered as a non-classical characterized by non-distributivity,and it takes scientific inference actually used by scientists of quantum mechanics as real prototypes or basis.Hillary Putnam concluded that logic can be revised globally due to reasons in terms of generation of quantum logic;while at same time he claimed that quantum logical connectives retained their classical meanings,which made him fall into a dilemma.After reexamining empirical reasons and the revision of argument on basis of several different interpretations of quantum mechanics,the authors of this paper found that metaphysical considerations are not negligible.And paper proposed that Correspondence Principle had methodological effect of resolving Putnam's Dilemma,and could explain reasonably continuity and innovation of quantum to classical logic.
This paper treats some of the issues raised by Putnam's discussion of, and claims for, quantum logic, specifically: that its proposal is a response to experimental difficulties; that it is a reasonable replacement for classical logic because its connectives retain their classical meanings, and because it can be derived as a logic of tests. We argue that the first claim is wrong(1), and that while conjunction and disjunction can be considered to retain their classical meanings, negation cruciallydoes not.The argument is conductedviaa thorough analysis of how the meet, join and complementation operations are defined in the relevant logical structures, respectively Boolean- and ortholattices(3). Since Putnam wishes to reinstate a realist interpretation of quantum mechanics, we ask how quantum logic can be a logic of realism. We show that it certainly cannot be a logic ofbivalencerealism (i.e., of truth and falsity), although itisconsistent with some form ofontologicalrealism(4). Finally, we show that while a reasonable explication of the idealized notion of test yields interesting mathematical structure, it by no means yields the rich ortholattice structure which Putnam (following Finkelstein) seeks.
We address the old question whether a logical understanding of Quantum Mechanics requires abandoning some of the principles of classical logic. Against Putnam and others (Among whom we may count or not E. W. Beth, depending on how we interpret some of his statements), our answer is a clear “no”. Philosophically, our argument is based on combining a formal semantic approach, in the spirit of E. W. Beth’s proposal of applying Tarski’s semantical methods to the analysis of physical theories, with an empirical–experimental approach to Logic, as advocated by both Beth and Putnam, but understood by us in the view of the operational- realistic tradition of Jauch and Piron, i.e. as an investigation of “the logic of yes–no experiments” (or “questions”). Technically, we use the recently-developed setting of Quantum Dynamic Logic (Baltag and Smets 2005, 2008) to make explicit the operational meaning of quantum-mechanical concepts in our formal semantics. Based on our recent results (Baltag and Smets 2005), we show that the correct interpretation of quantum-logical connectives is dynamical, rather than purely propositional. We conclude that there is no contradiction between classical logic and (our dynamic reinterpretation of) quantum logic. Moreover, we argue that the Dynamic-Logical perspective leads to a better and deeper understanding of the “non-classicality” of quantum behavior than any perspective based on static Propositional Logic.
The book investigates the ontology and logic of quantum physics. The first part discusses the relationship of theory and observation and different views on the ontological status of scientific theories. It introduces the fundamentals of quantum mechanics and some of its interpretations and their compatibility with various ontological positions. In the second part, implications of quantum mechanics on classical logic, especially on the distributive law and bivalence, as discussed by Garrett Birkhoff & John von Neumann (1936) and Hilary Putnam (1968), and their counterarguments are reconstructed and discussed. It is concluded that classical logic is sufficient for dealing with quantum mechanical propositions.
Putnam and Finkelstein have proposed the abandonment of distributivity in the logic of quantum theory. This change results from defining the connectives, not truth-functionally, but in terms of a certain empirical ordering of propositions. Putnam has argued that the use of this ordering (“implication”) to govern proofs resolves certain paradoxes. But his resolutions are faulty; and in any case, the paradoxes may be resolved with no changes in logic. There is therefore no reason to regard the partially ordered set of propositions as a logic—i.e. as embodying a criterion for soundness of proofs. Its role in quantum theory ought to be understood in an entirely different way.
Quantum mechanics predicts many surprising phenomena, including the two-slit interference of electrons. It has often been claimed that these phenomena cannot be understood in classical terms. But the meaning of “classical” is often not precisely specified. One might, for example, interpret it as “classical physics” or “classical logic” or “classical probability theory.” Quantum mechanics also suffers from a conceptual difficulty known as the measurement problem. Early in his career, Hilary Putnam believed that modifications of classical logic could both solve the measurement problem and account for the twoslit phenomena. Over 40 years later he had abandoned quantum logic in favor of the investigation of various theories - using classical logic and probability theory - that can accomplish these tasks. The trajectory from Putnam’s earlier views to his later views illustrates the difficulty trying to solve physical problems with alterations of logic or mathematics.
In this chapter, by ‘logic’ we mean Logica Magna (Great Logic), involving higher-order systems and set theories. We revise some of the main reasons provided by quantum theory to question the standard connectives, quantifiers, identity, and the notion of set ascribed by classical logic. In the end, we discuss the interesting fact that even if these argumentations are feasible, quantum theories (as done by the physicists) continue to be developed within standard frameworks, and we ask for the reasons. We presuppose that the reader is more acquainted with logic than with quantum mechanics, so we deserve more space for explanations in this field.