Would you consider “I follow your reasoning, but I'm still not going to be swayed by it” to be a violation of evaluating first order statements? It's clearly p

Would you consider “I follow your reasoning, but I'm still not going to be swayed by it” to be a violation of evaluating first order statements? It's clearly part of critical thinking to be _capable_ of suspicion of purely logical reasoning, which to me is a pretty plain demonstration of my point. Or would you argue that any computation that admits its own potential for error isn't really critical thinking? It seems to me that you can't have it both ways here, while salvaging “first order logic” as a suitable formalization of the argument that this is all about in the first place. Remember, the point was not that this is or isn't a convincing argument, it's that it's so air-tight that the argument is _logically_ _invalid_. That's a _really_ high bar, and I'm not inclined to forgive its use as a colloqialism in this context.