Why Modal Interpretations Must Abandon Classical Reasoning About Possible Properties

In several papers Rob Clifton studied the limitations of modal interpretations (MI) to account for physical properties. From these works he derived a lesson to be learned by modal interpretations, namely, that MI must abandon classical reasoning about (actual) properties. In this paper we extend this investigation to a generalized modal scheme in which also possible properties are taken into account. Following previous papers in which we have derived a modal Kochen-Specker theorem [Domenech, Freytes and de Ronde 2006, 2008a], we investigate its relation to the discourse involved with modal properties in the specific scheme of MI. We present a formal discussion regarding the meaning of the notion of possibility in the orthodox formalism of quantum mechanics and conclude that, contrary to the presupposed ideas, is not classical. More specifically, in relation to modal interpretations the consequences are twofold: i) Modal interpretations with semantic probabilities (MISP) must abandon ---not only classical reasoning about actual properties but also--- classical reasoning about possible properties. ii) Modal interpretations with hidden variables (MIHV) are forced to leave aside the orthodox formulation of quantum mechanics and look for an alternative formal scheme which can provide a classical notion of possibility.