  Modal interpretations have the ambition to construe quantum mechanics as an
objective, man-independent description of physical reality. Their second
leading idea is probabilism: quantum mechanics does not completely fix physical
reality but yields probabilities. In working out these ideas an important motif
is to stay close to the standard formalism of quantum mechanics and to refrain
from introducing new structure by hand. In this paper we explain how this
programme can be made concrete. In particular, we show that the Born
probability rule, and sets of definite-valued observables to which the Born
probabilities pertain, can be uniquely defined from the quantum state and
Hilbert space structure. We discuss the status of probability in modal
interpretations, and to this end we make a comparison with many-worlds
alternatives. An overall point that we stress is that the modal ideas define a
general framework and research programme rather than one definite and finished
interpretation.
