Hi Akalsi!
Thank you for your question, which goes not just to Cannot Be True questions, but to conditional reasoning overall. Let's consider a simple example:
"If A then B."
We would diagram this relationship as
A
B
and the contrapositive is
B A.
Remember that it is only the sufficient condition that shows us anything. In the case of this original relationship and the contrapositive, our two sufficient conditions are A and
B. The two necessary conditions, B and
A, don't show us anything.
So, in a Mistaken Reversal, the error is in saying that because we have B, then we
must have A. That's treating the necessary condition, B, as if it were a sufficient condition. B can't show us
anything definitive about A, which means it can't show us that A must be present. It also can't show us that A must be
absent. Since B can't show us anything definitive about A, then the presence or absence of A is up in the air. It's a Could Be True. The only reason a Mistaken Reversal is a "mistake" is that it treats a Could Be True ("If B then A might be present, but we don't actually know") as if it were a Must Be True ("If B then A must be present").
And the same thing goes for a Mistaken Negation. Remember that
A is only properly a necessary condition, found in the contrapositive
B A. Since
A is a necessary condition, it can't show us anything, just like B could not show us anything.
So, in a Cannot Be True question, a Mistaken Reversal or a Mistaken Negation is incorrect because it is a Could Be True.
Please let me know if I can be of further assistance.
Thanks,
Ron
