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In (da Costa and de Ronde, 2014), Newton da Costa together with the author ofthis paper argued in favor of the possibility to consider quantumsuperpositions in terms of a paraconsistent approach. We claimed that, eventhough most interpretations of quantum mechanics attempt to escapecontradictions, there are many hints that indicate it could be worth while toengage in a research of this kind. Recently, Arenhart and Krause (2014) haveraised several arguments against this approach. In the present paper we attemptto answer the main questions presented by Arenhart and Krause. We will argue,firstly, that the obstacles presented by them are based on a specificmetaphysical stance, which we will characterize in terms of what we call theOrthodox Line of Research (OLR). Secondly, that this is not necessarily theonly possible line, and that a different one, namely, a ConstructiveMetaphysical Line of Research (CMLR) provides a different perspective in whichthe Paraconsistent Approach to Quantum Superpositions (PAQS) can be regarded asa valuable prospect that could be used by different interpretations of quantummechanics. Finally, we provide a set of specific answers to the main problemsraised by Arenhart and Krause in order to clarify our line of research as wellas the original perspective introduced by the PAQS.

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