We articulate a collection of desiderata for an account of the dynamical quantities of a physical theory, and we present a theory that meets these desiderata in the case of quantum mechanics. Our theory retains a distinction between the values of dynamical quantities and the truth values of sentences asserting that a system has a particular value of a particular quantity. This allows our theory to incorporate the phenomenon of quantum indeterminacy as a pattern in the properties instantiated by a system in a particular quantum state, while also retaining the semantics of classical logic. We contrast our theory with quantum logic, which flattens the distinction between quantity values and truth values, and we address a series of objections that have been raised to previous attempts to reconcile quantum indeterminacy with classical logic.
We articulate a collection of desiderata for an account of the dynamical quantities of a physical theory, and we present a theory that meets these desiderata in the case of quantum mechanics. Our theory retains a distinction between the values of dynamical quantities and the truth values of sentences asserting that a system has a particular value of a particular quantity. This allows our theory to incorporate the phenomenon of quantum indeterminacy as a pattern in the properties instantiated by a system in a particular quantum state, while also retaining the semantics of classical logic. We contrast our theory with quantum logic, which flattens the distinction between quantity values and truth values, and we address a series of objections that have been raised to previous attempts to reconcile quantum indeterminacy with classical logic.
Abstract Uses a historical approach to explore the extent to which quantum theory mandates indeterminism. Drawing on important examples in the history of physics, it discusses explicitly the crucial distinction – often overlooked in the philosophical literature – between indeterminacy of physical quantities and causal indeterminism. It pursues at a more sophisticated level, issues raised in Ch. 2 concerning determinism and indeterminism in modern science. It concludes that quantum indeterminacy is an objective feature of the world, but that the jury is still out regarding quantum indeterminism.
The term proposition usually denotes in quantum mechanics (QM) an element of (standard) quantum logic (QL). Within the orthodox interpretation of QM the propositions of QL cannot be associated with sentences of a language stating properties of individual samples of a physical system, since properties are nonobjective in QM. This makes the interpretation of propositions problematical. The difficulty can be removed by adopting the objective interpretation of QM proposed by one of the authors (semantic realism, or SR, interpretation). In this case, a unified perspective can be adopted for QM and classical mechanics (CM), and a simple first order predicate calculus L(x) with Tarskian semantics can be constructed such that one can associate a physical proposition (i.e., a set of physical states) with every sentence of L(x). The set Pf of all physical propositions is partially ordered and contains a subset PTf of testable physical propositions whose order structure depends on the criteria of testability established by the physical theory. In particular, PTf turns out to be a Boolean lattice in CM, while it can be identified with QL in QM. Hence the propositions of QL can be associated with sentences of L(x), or also with the sentences of a suitable quantum language LTQ(x), and the structure of QL characterizes the notion of testability in QM. One can then show that the notion of quantum truth does not conflict with the classical notion of truth within this perspective. Furthermore, the interpretation of QL propounded here proves to be equivalent to a previous pragmatic interpretation worked out by one of the authors, and can be embodied within a more general perspective which considers states as first order predicates of a broader language with a Kripkean semantics.
Abstract It is often claimed that quantum mechanics entails that there is indeterminacy in the world, in the sense that physical systems can lack a precise value for a property. Indeed, a radical form of indeterminacy, in which systems have almost none of the properties we normally attribute to them, can be shown to follow from a particular interpretation of quantum mechanics—the bare theory. However, the bare theory is shown to be incoherent. Still, a more limited form of indeterminacy can be located in spontaneous collapse, hidden variables, and many-worlds theories. This indeterminacy is unlike that which arises classically, having nothing to do with ordinary forms of vagueness or the composition of large objects out of smaller parts. Indeterminacy in quantum mechanics can perhaps be avoided, but there seems little reason to do so.
Mature theories of physical science associate states with systems, for instance with particles or waves in classical physics. The quantities whose values comprise states in classical mechanics, namely position and momentum, are chosen, first of all, for predictive purposes. Everything that one would want to say about classical systems can, it seems, be said in terms of properties: specification of the properties of a system gives a complete specification of its state, and conversely. Quantum mechanics associates states with physical systems; whatever else these might be, systems are the particulars which bear physical properties. The former is non-reduced state, the quantum state proper, while the latter is the reduced state, the class of quantitative properties possessed by the system. The state therefore determines which quantities and which properties are instantiated. The non-reductive account of states was initially appealing because it seemed to promise some additional explanatory scope.
Scholars have wondered for a long time whether quantum mechanics (QM) subtends a quantum concept of truth which originates quantum logic (QL) and is radically different from the classical (Tarskian) concept of truth. We show in this paper that QL can be interpreted as a pragmatic language of pragmatically decidable assertive formulas, which formalize statements about physical systems that are empirically justified or unjustified in the framework of QM. According to this interpretation, QL formalizes properties of the metalinguistic concept of empirical justification within QM rather than properties of a quantum concept of truth. This conclusion agrees with a general integrationist perspective, according to which nonstandard logics can be interpreted as theories of metalinguistic concepts different from truth, avoiding competition with classical notions and preserving the globality of logic. By the way, some elucidations of the standard concept of quantum truth are also obtained.
Abstract The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either ‘true ’ or ‘false’, describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of ‘no go ’ theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton ‘uniqueness theorem ’ is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The conceptual implications of the resulting account are traced down and analyzed at length. In this light, the traditional conception of correspondence truth may be viewed as a species or as a limit case of the more generic proposed scheme of contextual correspondence when the non-explicit specification of a context of discourse poses no further consequences.