162:, wherein 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 to the problem was a logic of properties with a three-valued semantics; each property could have one of three possible truth-values: true, false, or indeterminate. The formal properties of such a
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133:(the chapter titled "Deviant Logics"), Quine rejects the idea that classical logic should be revised in response to the paradoxes, being concerned with "a serious loss of simplicity", and "the handicap of having to think within a deviant logic". Quine, though, stood by his claim that logic is in principle not immune to revision.
282:. There are, however, few philosophers today who regard this logic as a replacement for classical logic; Putnam himself may not have held that view any longer at the end of his life. Quantum logic is still used as a foundational formalism for quantum mechanics: but in a way in which primitive events are not interpreted as
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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 a
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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.
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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 to entail the existence of the properties of momentum and position for quanta. Since the
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disputation about the objective existence of such entities is also a matter of dispute. Consequently intuitionistic logic is privileged over classical logic, when it comes to disputation concerning phenomena whose objective existence is a matter of controversy.
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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 is that of having a precisely observed position or
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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, which he believes is not inconsistent.
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propositions and that these quantum mechanical propositions can be combined in a similar way as propositions in classical logic. However, the algebraic properties of this structure are somewhat different from those of
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respects the classical truth tables, but not the laws of classical logic, because intuitionistic logic allows propositions to be other than true or false. Secondly, to be able to apply truth tables to describe a
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is. To grasp why, consider why truth tables work for classical logic: first, it must be the case that the variable parts of the proposition are either true or false: if they could be other values, or fail to have
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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
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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.
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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:
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Dummett, M. (1976), "Is Logic
Empirical?", in H. D. Lewis (ed.), Contemporary British Philosophy, 4th series (London: Allen and Unwin), pp. 45–68. Reprinted in M. Dummett,
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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.
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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
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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
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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.
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in the same way
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proposed that there was more to this correspondence than a loose analogy: that in fact there was a logical system whose semantics was given by a
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383:(Dordrecht: D. Reidel, 1968), pp. 216-241. Repr. as "The Logic of Quantum Mechanics" in Mathematics, Matter and Method (1975), pp. 174-197.
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status of the laws of logic? What sort of arguments are appropriate for criticising purported principles of logic? In his seminal paper "
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terms as possible outcomes of observations. As such, quantum logic provides a unified and consistent mathematical theory of physical
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at all, then the truth table analysis of logical connectives would not exhaust the possible ways these could be applied. For example
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is essential for the realist's understanding of how propositions are true of the world, in just the same way as he argues the
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