Modality, Potentiality and Contradiction in Quantum Mechanics

TLDR: The Paraconsistent Approach to Quantum Superpositions (PAQS) as mentioned in this paper was proposed by Newton da Costa and de Ronde in 2013, and it has been used to analyze the meaning of modality, potentiality, and contradiction in QM.

Abstract: In da Costa and de Ronde (Found Phys 43:845–858, 2013), 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 (New dimensions of the square of opposition, Philosophia Verlag, Munich, 2014; Logique et Analyse, 2014; The Road to Universal Logic (volume II), Springer, 2014) 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 de Ronde ( Los Alamos 2014) 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 meaning 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.