Interesting. It’s not clear that conspiracy theorists would disagree with scientists about the quality of an argument that touches on neither of their domains. It’s entirely possible that both are able to agree about good and bad arguments for (say) abortion rights, even if they have opposing positions. (E.g., they may well be able to agree that “X is a better argument than Y”, even when one disagrees with both, and the other agrees with both.)
We've been thinking about explanations in our research (see, e.g., https://arxiv.org/abs/2205.07938) and your example of explaining the wrong answer well is lovely.
I dislike these kinds of questions, because they're usually posed at a point well before the wave equations are presented. At this point, you are largely working with verbal explanations and, as you point out, verbal explanations are much harder to pin down.
Mathematically, if A implies B, and you are working to the best of your ability, you can't derive ~B (you may not be able to derive B,... (read more)