I can be nonplussed (in fact that is practically the ground state of my existence), but not plussed. I can also be indifferent; but if you are different, that doesn't mean you care, either. What do you call it when a word looks like the negation of another word but is not? The kind of words that Terry Pratchett takes delight in?
(possible 2nd question) I had started by looking up wittingly, seeing that I've never seen it used except in the phrase "wittingly or unwittingly", or ironically, as the opposite of unwittingly. There might even be another class of word like "wittingly", words that are only ever used with their opposite.