Contrapositives are one of my favorite things in simple logic to demonstrate the difference between rigorous logic and our human heuristic logic. Mathematically

Contrapositives are one of my favorite things in simple logic to demonstrate the difference between rigorous logic and our human heuristic logic. Mathematically, contrapositives are identical to the original statement, but extremely frequently, if not almost always, they sound different to us humans. If more people understood them, there's a number of dumb internet debates that could finally die, where X -> Y isn't immediately obviously wrong to our human brains and may even sound correct but !Y -> !X is immediately obviously wrong.