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

Abstract

In [16], Newton da Costa together with the author of this paper argued in favor of the possibility of considering quantum superpositions in terms of a paraconsistent approach. There we argued that, even though most interpretations of Quantum Mechanics (QM) 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 [1] have raised several arguments against this approach. In the present paper we attempt to answer the main questions and obstacles presented by them. We will argue, firstly, that the obstacles presented by Arenhart and Krause are based on a specific metaphysical stance, which we will characterize in terms of what we call the Orthodox Line of Research (OLR). Secondly, that this is not necessarily the only possible line, and that a different one, namely, a Constructive Metaphysical Line of Research (CMLR) provides a different perspective in which the Paraconsistent Approach to Quantum Superpositions (PAQS) can be regarded as a valuable prospect that could be used by different interpretations of quantum mechanics. Finally, we provide a set of specific answers to the main problems raised by Arenhart and Krause in order to clarify our line of research as well as the original perspective introduced by the PAQS.