Potentiality and Contradiction in Quantum Mechanics

TL;DR

This paper explores the logical and metaphysical nature of superposition states in quantum mechanics, arguing they are better understood as contraries rather than contradictions, based on an analysis of their philosophical assumptions.

Contribution

It applies the square of opposition to quantum states, clarifying their logical relations and advocating for a contrary interpretation over contradictory in superposition.

Findings

Superposition states are better modeled as contraries.

Metaphysical assumptions influence interpretations of quantum states.

Contrary interpretation aligns more plausibly with quantum logic.

Abstract

Following J.-Y.B\'eziau in his pioneer work on non-standard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in \cite{are14}. Our conclusion was that such states are \ita{contraries} (\ita{i.e.} both can be false, but both cannot be true), contradicting previous analyzes that have led to different results, such as those claiming that those states represent \ita{contradictory} properties (\ita{i. e.} they must have opposite truth values). In this chapter we bring the issue once again into the center of the stage, but now discussing the metaphysical presuppositions which underlie each kind of analysis and which lead to each kind of result, discussing in particular the idea that superpositions represent potential contradictions. We shall argue that the analysis according to which states in superposition are contrary rather than contradictory is still more plausible.