Modality, Potentiality and Contradiction in Quantum Mechanics

TL;DR

This paper advocates for a paraconsistent approach to quantum superpositions, arguing it better addresses quantum interpretational issues related to modality, potentiality, and contradiction than the contrariety approach.

Contribution

It defends the Paraconsistent Approach to Quantum Superpositions (PAQS) and analyzes the roles of modality and contradiction, supporting PAQS over the contrariety approach.

Findings

PAQS provides a more consistent interpretation of quantum superpositions.

Arguments favoring PAQS over CAQS in quantum interpretational debates.

Further development of paraconsistent logic in quantum mechanics.

Abstract

In [11], Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum mechanics (QM) attempt to escape contradictions, there are many hints that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause [1, 2, 3] have raised several arguments against this approach and claimed that, taking into account the square of opposition, quantum superpositions are better understood in terms of contrariety propositions rather than contradictory propositions. In [17] we defended the Paraconsistent Approach to Quantum Superpositions (PAQS) and provided arguments in favor of its development. In the present paper we attempt to analyze the meanings of modality, potentiality and contradiction in QM, and provide further arguments of why the PAQS is better suited, than the Contrariety Approach to Quantum Superpositions (CAQS) proposed by Arenhart and Krause, to face the interpretational questions that quantum technology is forcing us to consider.