  By analyzing the concept of contextuality (Bell-Kochen-Specker) in terms of
pre-and-post-selection (PPS), it is possible to assign definite values to
observables in a new and surprising way. Physical reasons are presented for
restrictions on these assignments. When measurements are performed which do not
disturb the pre- and post-selection (i.e. weak measurements), then novel
experimental aspects of contextuality can be demonstrated including a proof
that every PPS-paradox with definite predictions implies contextuality. Certain
results of these measurements (eccentric weak values with e.g. negative values
outside the spectrum), however, cannot be explained by a "classical-like"
hidden variable theory.
