  It is known that "quantum non locality", leading to the violation of Bell's
inequality and more generally of classical local realism, can be attributed to
the conjunction of two properties, that we call here elementary locality and
predictive completeness. Taking this point of view, we show again that quantum
mechanics violates predictive completeness, allowing to make contextual
inferences, which can in turn explain why quantum non locality does not
contradict relativistic causality. But if the usual quantum state $\psi$ is
predictively incomplete, how to complete it ? We give here a set of new
arguments to show that $\psi$ should be completed indeed, not by looking for
any "hidden variables", but rather by specifying the measurement context, which
is required to define actual probabilities over a set of mutually exclusive
physical events.
