I agree. It is definitely not an issue of phrasing. I have had so many discussions where people fail to comprehend the concrete differences between converse, inverse, contrapositive, especially in relation to causality/mechanism. To me this seems to be especially bad in political discussions on facebook, but also, is even a critical issue among some PhD level synthetic organic chemistry students - where "mechanism" is a very important concept.

I am certain that these people would miss this problem on a first pass, second pass, and maybe even third or fourth pass.

> Then there's the issue of negation. "if P then Q" negated is "if not Q then not P".

No, "if P then Q" negated is "P and not-Q"

"If not-P then not-Q" is the inverse of "if P then Q".

"If not-Q then not-P" is the contrapositive of "if P then Q".

  S is true -> the negation of S is false
            -> the contrapositive of S is true
            -> (nothing at all about the inverse of S)