At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would generate a non-distributive lattice of propositions, and from quantum superpositions, which would entail new rules for quantum disjunctions. While the quantum logic program is not as popular as it once was, a crucial question remains unsettled: what is the relationship between the logical structures (...) of classical and quantum mechanics? In this essay we answer this question by showing that the original arguments promoting quantum logic contain serious flaws, and that quantum theory does satisfy the classical distributivity law once the full meaning of quantum propositions is properly taken into account. Moreover, we show that quantum mechanics can generate a distributive lattice of propositions, which, unlike the one of quantum logic, includes statements about expectation values which are of undoubtable physical interest. Lastly, we show that the lattice of statistical propositions in classical mechanics follows the same structure, yielding an analogue non-commutative sublattice of classical propositions. This fact entails that the purported difference between classical and quantum logic stems from a misconstructed parallel between the two theories. (shrink)

The aim of this paper is to show that the argument put forth by Bell and Hallett against Putnam's thesis regarding the invariance of meaning for quantum logical connectives is insufficient to establish their conclusion. By using an example from the causal theory of time, the paper shows how the condition they specify as relevant in cases of meaning variance in fact fails. As a result, the conclusion that negation undergoes a change of meaning in the quantum logical case is (...) left in doubt. The paper proceeds in three stages. First, a summary of Putnam's argument for the invariance of meaning in the case of quantum logical connectives is provided; this is followed by a review of the criticisms advanced against it by Bell and Hallett. Finally, it is shown how the main claim upon which their major criticism rests is unfounded. (shrink)

To the memory of John D. TrimmerThis paper assesses the impact of disjunctive facts on the quantum logic read off procedure. The purpose of the procedure is to transfer a significant quantum structure to a set of propositions; its first step is an attempt to discover that structure. Here I propose that disjunctive facts as traditionally conceived have blocked the procedure at its first step and have therefore subverted the best-known attempts to read off quantum logic. Recently however Allen Stairs (...) has proposed a view of disjunctive facts which re-establishes the possibility of reading off quantum logic. Both the traditional conception and Stairs’ revision of disjunctive facts are interesting in their own right, independent of quantum propositional logic. Too many things are called ‘quantum logic’. The term is disentangled and notation is fixed in this preliminary step which relies on basic lattice theory. (shrink)

In much the same way that it is possible to construct a model of hyperbolic geometry in the Euclidean plane, it is possible to model quantum logic within the classical propositional calculus.

In this paper we construct the ortholattices arising in quantum logic starting from the phenomenologically plausible idea of a collection of ensembles subject to passing or failing various “tests.” A collection of ensembles forms a certain kind of preordered set with extra structure called anorthospace; we show that complete ortholattices arise as canonical completions of orthospaces in much the same way as arbitrary complete lattices arise as canonical completions of partially ordered sets. We also show that the canonical completion of (...) an orthospace of ensembles is naturally identifiable as the complete lattice of properties of the ensembles, thereby revealing exactlywhy ortholattices arise in the analysis of “tests” or experimental propositions. Finally, we axiomatize the hitherto implicit concept of “test” and show how they may be correlated with properties of ensembles. (shrink)

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 operationalrealistic 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. (shrink)

Some incompatibilists about free will or moral responsibility and determinism would abandon their incompatibilism were they to learn that determinism is true. But is it reasonable to flip-flop in this way? In this article, we contend that it is and show what follows. The result is both a defense of a particular incompatibilist strategy and a general framework for assessing other cases of flip-flopping.

This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at an intersection of the philosophy of physics and the philosophy of semantics, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence of rules. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of Bohr's (...) principle of correspondence, grounded in the principle of permanence, 3) a meaning-variance argument for quantum logic, which follows a line of critical reflections initiated by Weyl, and 4) an argument for semantic indeterminacy leveled against inferentialism about QM, inspired by Carnap's work in the philosophy of classical logic. (shrink)