  Physical superpositions exist both in classical and in quantum physics.
However, what is exactly meant by 'superposition' in each case is extremely
different. In this paper we discuss some of the multiple interpretations which
exist in the literature regarding superpositions in quantum mechanics. We argue
that all these interpretations have something in common: they all attempt to
avoid 'contradiction'. We argue in this paper, in favor of the importance of
developing a new interpretation of superpositions which takes into account
contradiction, as a key element of the formal structure of the theory, "right
from the start". In order to show the feasibility of our interpretational
project we present an outline of a paraconsistent approach to quantum
superpositions which attempts to account for the contradictory properties
present in general within quantum superpositions. This approach must not be
understood as a closed formal and conceptual scheme but rather as a first step
towards a different type of understanding regarding quantum superpositions.
