On quantum logic and quantum metaphysics

Jonas R. Becker Arenhart, Raoni Wohnrath Arroyo

We provide a brief introduction to the special issue dedicated to logical and metaphysical aspects of contemporary issues concerning identity and individuality in quantum mechanics. After a discussion of the main theme, we present the contributed papers and the historical motivations for the special issue.

C. Piron

Tim Maudlin

Translated here into Polish is Tim Maudlin’s “Distilling Metaphysics from Quantum Physics,” which is a chapter of The Oxford Handbook of Metaphysics. The author discusses six important metaphysical issues on which quantum physics sheds new light. He shows how differently each of the three main intepretations of quantum theory (von Neumann’s and GRW collapse theory, Bohm’s hidden variable theory, and Everett’s many-worlds theory) views each of them. The issues discussed are determinism, determinateness, the role of the observer, uncertainty and complementarity, quantum logic, and entanglement and non-locality.

George Svetlichny

Steven French, Décio Krause

Abstract Traditionally by ‘quantum logic’, one understands the study of the lattice of the subspace of Hilbert space. Here, ‘quantum logic’ is taken to be the underlying logic of quantum physics. Following Schrödinger’s idea that the standard concept of identity cannot be applied to quantum objects, a kind of ‘non-reflexive’ logic called Schrödinger logic is presented, in which the reflexive law of identity is taken not to apply. First order Schrödinger logics are presented, and extended to higher order logics and also to an intensional logic. Classical semantics is presented, and a weak completeness theorem is sketched. The last part of the chapter covers a logic of sortal predicates for which a quasi-set semantics is delineated. This completes the formal framework capable of accommodating quantum non-individuality and thus the initial understanding of Born, Heisenberg, and Schrödinger, as well as the second horn of the above metaphysical underdetermination, can be formally represented.

Thomas A. Brody