I used to teach the idea that English has characteristics just like mathematics, but I do not any longer because, as you might suspect, every English rule, unlike mathematics, has exceptions. While 1 + 1 always did, always does, and always will = 2, honest writing teachers must admit to their students that language is far more subjective, all too often laden with uneducated opinion and fraught with majority- or authority-rule tastes.
Take the rule claiming two negatives make a positive, just like math. Saying "I am not unaware" means I am aware, saying "I cannot make a mistake" asserts I want to do something correctly, and saying "I will not hurt you" implies you will be safe with me.
But you can't count on two negatives making a positive. For example, you can imagine an astronomy professor facetiously saying, "Galileo did not err when he distanced himself from heliocentrism during the Inquisition." In fact, you can't even depend on two positives making a positive. If you asked whether I was willing to freefall from the roof of a 14-story building, you can picture me ironically replying, "Sure I would do that."
Too much depends on context for insisting on right-wrong rulings for English usage. Ain't that right?
