Say that Jim successfully argues that A implies B. He then establishes that A is true, and therefore B is true.
Then say that Bob comes along and says, "Well, what about K?" Meaning, that he believes "A implies B" is only true within some larger context K, and K might not always be true.
Bob may or may not have a good point - his point about K might demolish Jim's entire argument, or he may just be annoying by being "out of bounds", missing Jim's point entirely.
The question is, is there a set of terms that reflect Jim's and Bob's perspectives? Jim is only concerned with the boundaries of the argument, the boundaries defined by A. Jim is "inside" the argument. Bob is arguing "outside" the argument.
We often experience that when one person objects by saying that someone else is "technically" correct, but is objecting based off of some larger context. I am asking because I feel like I remember learning a set of terms (sort of like intensional/extensional) that make this distinction of being either inside or outside the argument, but I am not certain.
For a more concrete example, people may argue that behaving lawfully is the right thing to do, from an "inside the argument" perspective, while someone else may argue (hypothetically) that if the overall effects of behaving lawfully are unjust, that behaving lawfully is not the right thing to do, and that they must practice civil disobedience instead - they are "outside the argument".
So I am wondering if there are recognized terms for being inside or outside the world of an argument's established context.