  The best mathematical arguments against a realistic interpretation of quantum
mechanics - that gives definite but partially unknown values to all observables
- are analysed and shown to be based on reasoning that is not compelling.
  This opens the door for an interpretation that, while respecting the
indeterministic nature of quantum mechanics, allows to speak of definite values
for all observables at any time that are, however, only partially measurable.
  The analysis also suggests new ways to test the foundations of quantum
theory.
