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

## TL;DR

This paper introduces a new logical framework based on partitions to interpret quantum mechanics as describing an objectively indefinite reality, challenging traditional wave-particle duality views.

## Contribution

It develops a mathematical theory linking partitions to quantum indefiniteness, providing a literal interpretation of quantum states as objectively indefinite.

## Key findings

- Mathematics of QM as the math of indefiniteness
- Wave propagation as evolution of indefinite states
- Reinterpretation of wave-particle duality

## Abstract

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).