A Defense of the Paraconsistent Approach to Quantum Superpositions (Reply to Arenhart and Krause)

In da Costa and de Ronde (2013) we discussed the possibility of considering quantum superpositions in terms of a paraconsistent approach. We argued that, even though most interpretations of quantum mechanics attempt to escape contradictions, there are many reasons that indicate it could be worthwhile to engage in a research of this kind. Recently, Arenhart and Krause (2016) have raised several arguments against this Paraconsistent Approach to Quantum Superpositions (PAQS). In this paper I attempt to answer the main questions and obstacles presented by them. I will argue, firstly, that the obstacles addressed by Arenhart and Krause are based on a specific stance grounded on an actualist metaphysics—which implicitly presupposes classical logic. Secondly, that there are many interpretations that investigate the possibility of developing a different mode of existence to that of actuality for which the PAQS might be regarded as a valuable prospect. Finally, we provide a set of specific answers to the main problems raised by Arenhart and Krause in order to clarify the original perspective introduced by the PAQS.