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In the histories formulation of quantum theory, sets of coarse-grainedhistories, that are called consistent, obey classical probability rules. It hasbeen argued that these sets can describe the semi-classical behaviour of closedquantum systems. Most physical scenarios admit multiple different consistentsets and one can view each consistent set as a separate context. Usingpropositions from different consistent sets to make inferences leads toparadoxes such as the contrary inferences first noted by Kent [Physical ReviewLetters, 78(15):2874, 1997]. Proponents of the consistent histories formulationargue that one should not mix propositions coming from different consistentsets in making logical arguments, and that paradoxes such as the aforementionedcontrary inferences are nothing else than the usual microscopic paradoxes ofquantum contextuality as first demonstrated by Kochen and Specker theorem.  In this contribution we use the consistent histories to describe amacroscopic (semi-classical) system to show that paradoxes involvingcontextuality (mixing different consistent sets) persist even in thesemi-classical limit. This is distinctively different from the contextuality ofstandard quantum theory, where the contextuality paradoxes do not persist inthe semi-classical limit. Specifically, we consider different consistent setsfor the arrival time of a semi-classical wave packet in an infinite squarewell. Surprisingly, we get consistent sets that disagree on whether the motionof the semi-classical system, that started within a subregion, ever left thatsubregion or not. Our results point to the need for constraints, additional tothe consistency condition, to recover the correct semi-classical limit in thisformalism and lead to the motto `all consistent sets are equal', but `someconsistent sets are more equal than others'.

Contrary Inferences for Classical Histories within the Consistent Histories Formulation of Quantum Theory