Why modal interpretations of quantum mechanics must abandon classical reasoning about physical properties

Modal interpretations of quantum mechanics propose to solve the measurement problem by rejecting the orthodox view that in entangled states of a system which are nontrivial superpositions of an observable's eigenstates, it is meaningless to speak of that observable as having a value or corresponding to a property of the system. Though denying this is reminiscent of how hidden-variable interpreters have challenged orthodox views about superposition, modal interpreters also argue that their proposals avoid any of the objectionable features of physical properties that beset hidden-variable interpretations, like contextualism and nonlocality. Even so, I shall prove that modal interpreters of quantum mechanics are still committed to giving up at least one of the following three conditions characteristic of classical reasoning about physical properties: (1) Properties certain to be found on measuring a system should be counted as intrinsic properties of the system. (2) If two propositions stating the possession of two intrinsic properties by the system are regarded as meaningful, then their conjunction should also correspond to a meaningful proposition about the system possessing a certain intrinsic property; and similarly for disjunction and negation. (3) The intrinsic properties of a composite system should at least include (though need not be exhausted by) the intrinsic properties of its parts. Conditions 1–3 are by no means undeniable. But the onus seems to be on modal interpreters to tell us why rejecting one of these is preferable to an ontology of properties incorporating contextualism and nonlocality.