  In this paper we intend to discuss the importance of providing a physical
representation of quantum superpositions which goes beyond the mere reference
to mathematical structures and measurement outcomes. This proposal goes in the
opposite direction to the project present in orthodox contemporary philosophy
of physics which attempts to "bridge the gap" between the quantum formalism and
common sense "classical reality" --precluding, right from the start, the
possibility of interpreting quantum superpositions through non-classical
notions. We will argue that in order to restate the problem of interpretation
of quantum mechanics in truly ontological terms we require a radical revision
of the problems and definitions addressed within the orthodox literature. On
the one hand, we will discuss the need of providing a formal redefinition of
superpositions which captures explicitly their contextual character. On the
other hand, we will attempt to replace the focus on the measurement problem,
which concentrates on the justification of measurement outcomes from "weird"
superposed states, and introduce the superposition problem which focuses
instead on the conceptual representation of superpositions themselves. In this
respect, after presenting three necessary conditions for objective physical
representation, we will provide arguments which show why the classical
(actualist) representation of physics faces severe difficulties to solve the
superposition problem. Finally, we will also argue that, if we are willing to
abandon the (metaphysical) presupposition according to which 'Actuality =
Reality', then there is plenty of room to construct a conceptual representation
for quantum superpositions.
