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W.V. QUINE What is the epistemological status of the laws of logic? What sort of arguments are appropriate for criticising purported principles of logic? In his seminal paper " Two Dogmas Of Empiricism ," the logician and philosopher W.V. Quine argued that all beliefs are in principle subject to revision in the face of empirical data, including the so-called Analytic Proposition s. Thus the laws of logic, being paradigmatic cases of analytic propositions, are not immune to revision. To justify this claim he cited the so-called ''paradoxes of Quantum Mechanics ''. Birkhoff and von Neumann proposed to resolve those paradoxes by abandoning the principle of distributivity, thus substituting their quantum logic for classical logic. Quine did not at first seriously pursue this argument, providing no sustained argument for the claim in that paper. In a later paper, "Variant logics," he explicitly repudiates the idea that classical logic is subject to revision. HANS REICHENBACH Reichenbach considered one of the anomalies associated with quantum mechanics, the problem of complementary properties. A pair of properties of a system is said to be complementary if each one of them can be assigned a truth value in some experimental setup, but there is no setup which assigns a truth value to both properties. The classic example of complementarity is illustrated by the Double-slit Experiment in which a photon can be made to exhibit particle-like properties or wave-like properties, depending on the experimental setup used to detect its presence. Another example of complementary properties are those of having a precisely observed position or momentum. Reichenbach approached the problem within the philosophical program of the logical positivists. As such the choice of an appropriate language was not a matter of the truth or falsity of a given language, in this case the language used to describe quantum mechanics, but a matter of "technical advantages of language systems". His solution was a logic of properties with a three-valued semantics; that is each property could have three possible truth-values: true, false or indeterminate. The formal properties of such a logical system can be given by a set of fairly simple rules, certainly far simpler than the "projection algebra" that Birkhoff and von Neumann had introduced a few years earlier. However, because of this simplicity, the intended semantics of Reichenbach's three-valued logic is unsuited to provide a foundation for quantum mechanics that can account for Observable s. FIRST ARTICLE: HILARY PUTNAM In his paper "Is logic empirical?" Putnam, H. “Is Logic Empirical?” Boston Studies in the Philosophy of Science, vol. 5, eds. Robert S. Cohen and Marx W. Wartofsky (Dordrecht: D. Reidel, 1968), pp. 216-241. Repr. as “The Logic of Quantum Mechanics” in Mathematics, Matter and Method (1975), pp. 174-197. were once believed to be truths about the physical space in which we live, now rather we believe we live in a Non-Euclidean world, with a different and fundamentally incompatible notion of Straight Line . In particular, he claimed that what physicists have learned about quantum mechanics provides a compelling case for abandoning certain familiar principles of classical logic for this reason: Realism about the physical world, which Putnam generally maintains, demands that we square up to the anomalies associated with quantum phenomena. Putnam understands realism about physical objects as involving that the properties of momentum and position exist for quanta. Since the Uncertainty Principle says that either of them can be determined, but both cannot be determined at the same time, he faces a paradox. He sees the only possible resolution of the paradox as lying in the embrace of quantum logic, in which he believes this is not inconsistent. QUANTUM LOGIC See Also: Quantum logic The formal laws of a physical theory are justified by a process of repeated controlled observations. This from a physicist's point of view is the meaning of the empirical nature of these laws. The idea of a propositional logic with rules radically different from of Projection Operator s on a Hilbert Space . This, actually, was the correct logic for reasoning about the microscopic world. In this view, classical logic was merely a limiting case of this new logic. If this were the case, then our "preconceived" Boolean logic would have to be rejected by empirical evidence in the same way Euclidean geometry (taken as the correct geometry of physical space) was rejected on the basis of (the facts supporting the theory of) General Relativity . This argument is in favour of the view that the rules of logic are empirical. That logic came to be known as s but rather in Operational terms as possible outcomes of observations. As such, quantum logic provides a unified and consistent mathematical theory of physical Observable s and Quantum Measurement . SECOND ARTICLE: MICHAEL DUMMETT In an article also titled "Is logic empirical?," depends upon distributivity: a truth table is a disjunction of conjunctive possibilities, and the validity of the exercise depends upon the truth of the whole being a consequence of the bivalence of the propositions, which is true only if the principle of distributivity applies. Hence Putnam cannot embrace realism without embracing classical logic, and hence his argument to endorse quantum logic because of realism about quanta is a hopeless case. Dummett's argument is all the more interesting because he is not a proponent of classical logic. His argument for the connection between realism and classical logic is part of a wider argument to suggest that, just as the existence of particular class of entities may be a matter of dispute, so disputation about the objective existence of such entities is Question Begging if use is made of classical logic. Consequently intuitionistic logic is privileged over classical logic, when it comes to disputation concerning phenomena whose objective existence is a matter of controversy. Thus the question, "Is logic empirical?," for Dummett, leads naturally into the dispute over Bivalence And Anti-realism , one of the deepest issues in modern Metaphysics . NOTES |
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