In this chapter I introduce the different versions of the modal interpretation, including the three on which I focus in this book. The property ascription of these versions is characterised by the map Wα ↦ {〈pj, Cαj〉}j which I call the core property ascription. In the next chapter I discuss how this core property ascription determines the full property ascription Wα ↦

The best modal interpretation

The best imaginable modal interpretation is, I guess, an interpretation which (A) ascribes at all times all the properties to a system which pertain to that system, and (B) ascribes these properties such that the classical logical relations between the negation, conjunction and disjunction of properties are satisfied.

The content of the first requirement (A) is clear: assuming that every projection onto a subspace of a Hilbert space ℋα represents one and only one property of α, it follows that all sets of definite-valued projections should contain all the projections in ℋα and that all the maps {.j}j should be maps from all the projections in ℋα to the values {0,1}.

The content of requirement (B) is, however, less clear because there is consensus neither about how to define the negation, conjunction and disjunction of properties in quantum mechanics nor about how to impose the logical relations. In Section 5.1 I present my choice for the definitions of the negation, conjunction and disjunction.