New Light on the Objective Indefiniteness or Literal Interpretation of Quantum Mechanics

17 Pages Posted: 7 Jan 2019

Date Written: December 21, 2018


The development of the new logic of partitions (= equivalence relations) dual to the usual Boolean logic of subsets, and its quantitative version as the new logical theory of information provide the basic mathematical concepts to describe distinctions/indistinctions, definiteness/indefiniteness, and distinguishability/indistinguishability. They throw some new light on the objective indefiniteness or literal interpretation of quantum mechanics (QM) advocated by Abner Shimony. This paper shows how the mathematics of QM is the math of indefiniteness and thus, literally and realistically interpreted, it describes an objectively indefinite reality at the quantum level. In particular, the mathematics of wave propagation is shown to also be the math of the evolution of indefinite states that do not change the degree of indistinctness between states. This corrects the historical wrong turn of seeing QM as "wave mechanics" rather than the mechanics of particles with indefinite/definite properties. For example, the so-called "wave-particle duality" for particles is the juxtaposition of the evolution of a particle having an indefinite position ("wave-like" behavior) with a particle having a definite position (particle-like behavior).

Keywords: objective indefiniteness in QM, wave-particle duality, Shimony, partition logic, logical information theory

Suggested Citation

Ellerman, David, New Light on the Objective Indefiniteness or Literal Interpretation of Quantum Mechanics (December 21, 2018). Available at SSRN: or

David Ellerman (Contact Author)

University of Ljubljana ( email )

School of Social Science
Ljubljana, CA


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