Probing Contextuality with Pre- and Post-selection

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 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 {\it 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. Surprising theoretical implications are discussed.