If 'might p' expresses a proposition about what is compatible with a contextually-fixed body of knowledge, truth-value shifts across contexts reflect distinct propositions, not instability in a single proposition.

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Compatible with(as used in logic and philosophy generally): Able to exist or be true at the same time without contradicting each other. Two ideas are compatible if one doesn't rule out the other.
contextually-fixed body of knowledge(as used in epistemology and semantics): The set of facts and information that are assumed to be true in a particular situation or conversation.
distinct propositions(as used in logic and semantics): Different statements or claims; separate ideas that are not the same thing.
instability in a single proposition(as used in logic): The idea that one statement could be both true and false at the same time, which would make it unreliable or contradictory.
knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)

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