  In the histories formulation of quantum theory, sets of coarse-grained
histories, that are called consistent, obey classical probability rules. It has
been argued that these sets can describe the semi-classical behaviour of closed
quantum systems. Most physical scenarios admit multiple different consistent
sets and one can view each consistent set as a separate context. Using
propositions from different consistent sets to make inferences leads to
paradoxes such as the contrary inferences first noted by Kent [Physical Review
Letters, 78(15):2874, 1997]. Proponents of the consistent histories formulation
argue that one should not mix propositions coming from different consistent
sets in making logical arguments, and that paradoxes such as the aforementioned
contrary inferences are nothing else than the usual microscopic paradoxes of
quantum contextuality as first demonstrated by Kochen and Specker theorem.
  In this contribution we use the consistent histories to describe a
macroscopic (semi-classical) system to show that paradoxes involving
contextuality (mixing different consistent sets) persist even in the
semi-classical limit. This is distinctively different from the contextuality of
standard quantum theory, where the contextuality paradoxes do not persist in
the semi-classical limit. Specifically, we consider different consistent sets
for the arrival time of a semi-classical wave packet in an infinite square
well. Surprisingly, we get consistent sets that disagree on whether the motion
of the semi-classical system, that started within a subregion, ever left that
subregion or not. Our results point to the need for constraints, additional to
the consistency condition, to recover the correct semi-classical limit in this
formalism and lead to the motto `all consistent sets are equal', but `some
consistent sets are more equal than others'.
