Say you have a conclusion, and you have drawn the parameters of your argument such that it bounds a certain set of hypotheticals. From the simple Bayesian perspective, it's basically just $A|B$. You've proven $A|B$, you've established $B$, and therefore you've proven $A$.
But then Bob comes along and makes an objection comes up that doesn't contest $B$, but instead some larger context $K$. He's talking about $(A|B)|K$, and that K is false (or not always true).
Is there a set of terms for their two perspectives? I'm not talking about just uncovering unwarranted assumptions or finding problems in proofs. I'm talking about the relative concept of being inside or outside of an argument. It doesn't matter whether Bob has a good point - he might be right or wrong, or he might be completely obliterating a proof for resting on a bad implicit premise, or he might be an annoying distraction for legitimately being out of bounds. But I am wondering if there is a set of terms for these two inside-versus-outside perspectives, kind of like "intensional/extensional" for semantics.