  In [11], 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 [1, 2, 3] 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 [17] 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
meanings 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.
