  In (da Costa and de Ronde, 2014), 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 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 (2014) have
raised several arguments against this approach. In the present paper we attempt
to answer the main questions presented by Arenhart and Krause. We will argue,
firstly, that the obstacles presented by them 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.
