In this paper we intend to discuss the importance of providing a physicalrepresentation of quantum superpositions which goes beyond the mere referenceto mathematical structures and measurement outcomes. This proposal goes in theopposite direction to the project present in orthodox contemporary philosophyof physics which attempts to "bridge the gap" between the quantum formalism andcommon sense "classical reality" --precluding, right from the start, thepossibility of interpreting quantum superpositions through non-classicalnotions. We will argue that in order to restate the problem of interpretationof quantum mechanics in truly ontological terms we require a radical revisionof the problems and definitions addressed within the orthodox literature. Onthe one hand, we will discuss the need of providing a formal redefinition ofsuperpositions which captures explicitly their contextual character. On theother 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 focusesinstead on the conceptual representation of superpositions themselves. In thisrespect, after presenting three necessary conditions for objective physicalrepresentation, we will provide arguments which show why the classical(actualist) representation of physics faces severe difficulties to solve thesuperposition problem. Finally, we will also argue that, if we are willing toabandon the (metaphysical) presupposition according to which 'Actuality =Reality', then there is plenty of room to construct a conceptual representationfor quantum superpositions.
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