In 1944 Hans Reichenbach developed a three-valued propositional logic (RQML) in order to account for certain causal anomalies in quantum mechanics. In this logic, the truth-value _indeterminate_ is assigned to those statements describing physical phenomena that cannot be understood in causal terms. However, Reichenbach did not develop a deductive calculus for this logic. The aim of this paper is to develop such a calculus by means of First Degree Entailment logic (FDE) and to prove it sound and complete with respect (...) to RQML semantics. In Section 1 we explain the main physical and philosophical motivations of RQML. Next, in Sections 2 and 3, respectively, we present RQML and FDE syntax and semantics and explain the relation between both logics. Section 4 introduces \(\varvec{\mathcal {Q}}\) calculus, an FDE-based tableaux calculus for RQML. In Section 5 we prove that \(\varvec{\mathcal {Q}}\) calculus is sound and complete with respect to RQML three-valued semantics. Finally, in Section 6 we consider some of the main advantages of \(\varvec{\mathcal {Q}}\) calculus and we apply it to Reichenbach’s analysis of causal anomalies. (shrink)

Reichenbach's interpretation of quantum mechanics has been narrowly reduced to the advocacy of a three‐valued logic. His interpretation rests, though, on the same rich epistemological framework that shapes his influential analysis of space‐time theories. Different interpretations of the quantum formalism, with their conflicting ontologies and causes, emerge in this view as “equivalent descriptions”. One casualty of the conventionalist approach is the measurement problem. I give reasons for why Reichenbach's view on the nature of interpretations of quantum theory cannot be defended.

In the paper it is shown that every physically sound Birkhoff – von Neumann quantum logic, i.e., an orthomodular partially ordered set with an ordering set of probability measures can be treated as partial infinite-valued Łukasiewicz logic, which unifies two competing approaches: the many-valued, and the two-valued but non-distributive, which have co-existed in the quantum logic theory since its very beginning.

Peter Lewis ([1997]) has recently argued that the wavefunction collapse theory of GRW (Ghirardi, Rimini and Weber [1986]) can only solve the problem of wavefunction tails at the expense of predicting that arithmetic does not apply to ordinary macroscopic objects. More specifically, Lewis argues that the GRW theory must violate the enumeration principle: that 'if marble 1 is in the box and marble 2 is in the box and so on through marble n, then all n marbles are in the (...) box' ([1997], p. 321). Ghirardi and Bassi ([1999]) have replied that it is meaningless to say that the enumeration principle is violated because the wavefunction Lewis uses to exhibit the violation cannot persist, according to the GRW theory, for more than a split second ([1999], p. 709). On the contrary, we argue that Lewis's argument survives Ghirardi and Bassi' s criticism unscathed. We then go on to show that, while the enumeration principle can fail in the GRW theory, the theory itself guarantees that the principle can never be empirically falsified, leaving the applicability of arithmetical reasoning to both micro- and macroscopic objects intact. (shrink)

Following Lukasiewicz, we argue that future non-certain events should be described with the use of many-valued, not 2-valued logic. The Greenberger - Horne - Zeilinger 'paradox' is shown to be an artifact caused by unjustified use of 2-valued logic while considering results of future non-certain events. Description of properties of quantum objects before they are measured should be performed with the use of propositional functions that form a particular model of infinitely-valued Lukasiewicz logic. This model is distinguished by specific operations (...) of negation, conjunction and disjunction that are used in it. (shrink)