| Quantum logic,as construed by most authors,generally refers to logic systems with non-Boolean algebraic semantics.The birth of quantum logic is marked by Birkhoff and von Neumann's 1936 paper,with the title “The Logic of Quantum Mechanics”.Now it is commonly considered that the most relevant non-Boolean structure of quantum logic is presented by the set of all closed subspaces of a certain Hilbert space,which forms an orthomodular lattice.Since all Boolean algebras are orthomodular lattices but the converse is not true,the algebraic structure of this kind of quantum logic has a much broader range than classical proposition logic.Different from common definition,we interpret quantum logic as “the logics about the nature of quantum mechanics”.As a result,certain non-classical logics,including three-valued logic,paraconsistent logic and non-reflexive logic,are all quantum logic systems.Such a broader view greatly facilitates a pluralist recognition of these systems.We believe that quantum logical systems offer a perfect support for logical pluralism based on Carnap's principle of tolerance.Every such system reasonably interprets quantum mechanics from a particular point of view.We cannot,based on either empirical facts or the mathematical foundation of quantum mechanics,establish any system as the absolutely correct quantum logic,nor should we deny other systems just because of the merits of one particular system.To prove this,we will follow the following line of arguments.Chapter 1 is the introduction,in which the current literature on quantum logic,the significance and methodology of this research will be analyzed.Since quantum logical systems are always discussed along with interpretation theories of quantum mechanics,in Chapter 2 we have to present several such theories after a concise history of quantum mechanics.Note that our presentation will be a very limited one,involving only those interpretations that will be used in the following chapters,for such topics are peripheral to our main theme.Chapter 3 is concerned with Reichenbach's philosophical thoughts on quantum mechanics and his three-valued quantum logic.The former insights remind us that phenomena from classical mechanics are as much in need of interpretations as quantum mechanical ones,and that the differences between different interpretations are not essential.Although specific interpretations of classical phenomena are free from “causal anomalies”,for most interpretations this is not true.Therefore,factors like “causal anomalies” cannot be absolute criteria to pick out the best interpretation.On the other side,although the three-valued quantum logic are facing difficulties,as a “restricted interpretation” of quantum mechanics it does offer reasonable explanations to certain quantum mechanical phenomena.Hence,the pluralism of quantum interpretations solves the “correctness” issue of the three-valued quantum logic.Chapter 4 includes an introduction to da Costa's paraconsistent logic and nonreflexive logic and his concrete methods to answer philosophical questions of quantum mechanics.If we use the ability to interpret quantum mechanics to assess these quantum logical systems,we will find the solutions to quantum superposition and quantum identity are quite satisfying.Besides,through analysis of the semantical problems of these systems,we will find it unintelligible to refute non-classical logics with the seemingly classical characters of their meta-languages.Chapter 5 introduces “quantum logic” in the sense for which the term usually stands,that is,quantum logics in algebraic approaches.Our presentation will start from the usual conception of “quantum logic”,passing by what von Neumann had intended for this subject,and end with an analysis of the methodology of the operationalists.Quantum logic in the usual sense is certainly the closest to the mathematical structure of quantum mechanics,but the frequency interpretation of probability does not make sense in it.What von Neumann was trying to do is change the underlying algebra so that the resulting logic would be compatible with the frequency interpretation,but his result does not perfectly resolve the problem either.On the other side,the operationalists have also been trying out different algebras to get reasonable quantum logics.We will argue in this chapter that the principle of operationalism could serve to avoid the problem of “criticize pluralism with the pluralist principle”.The full solution to this problem would be offered by Carnap's “principle of tolerance”,which will appear in the next chapter.In Chapter 6 we will deal with philosophical issues of quantum logic,including the relation of logic and experience,the problem of universality of logic and logical pluralism by which these problems can be circumvented.Putnam and other scholars once argued that new quantum phenomena force us to revise our logic,to replace the old classical logic with the so-called “quantum logic”.Such a proposal is advisable in a restricted sense.But he has also suggested that classical logic is actually “quantum logic” in disguise,and thus logic is as revisable as geometry with the development of our experience.Such an idea,however,cannot stay true unconditionally,but hinges on specific interpretations of quantum mechanics.We will argue that Putnam's monist view on quantum logic is unsuccessful,and we must take on a pluralist view instead.Furthermore,the fact that Carnap's principle of tolerance and Susan Haack's logical plurism can be reconciled could prevent logical plurism from being absolutized.Finally,we propose a methodological principle called “generalized principle of correspondence”,which stems from philosophical ideas of quantum mechanics,and serves to facilitate the innovation of nonclassical logics.Chapter 7 contains the conclusions of this essay.Summing up the main ideas of the previous chapters,we will reach an understanding and sympathy of the plurist view of quantum logics. |
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