1. !=, ≠
In mathematical notation, we have for instance != or if someone wants to go to the trouble of finding the classical symbol ≠ (Unicode numer 2260) then they have a very elegant way of noting “is not equal to” in a mathematical or logical sense.
2. In-, im-, un-
Then we have the classic prefixes, which encapsulate the diglossia in English: un- prefixes grace Germanic roots in the main and in- or im- go with the Latin or French roots (the latter if the root begins with b, p, or m but for some reason not the other labials f and v) However, the cut-off is not strict, because in- can refer to something going into something also. So “information” does not mean a lack of formation – to get back to that idea you can non- or borrow un- from the Germanic stock for it, so for example you could comment that you found this whole article “uninformative”.
3. Dys-, dis-
Or there is disinformation. This dis- is an additional Latin based prefix showing that something has gone off in all directions, or in a wrong direction, with a more common version of that being dys- from Greek, which isn’t fussy about attaching to Latin roots either, so that you get dysfunctional people …
4. Mal-, mis-
and these people might be malformed also and be spreading misinformation, with mal- and mis- being two further prefixes that show that things are not really what the root says, they contradict the root. In Esperanto mal- is the universal negating prefix, in English or most natural West European languages it is not really good for neutral negation since the root in Latin “malus” (also, interestingly, “apple”) means “evil”.
5. Contra-, counter-
That brings us on to contra- or counter- which suggests not so much something not being something else, but rather coming from the opposite direction to something else. A counter-attack is still an attack. It’s just not the same one as the original attack. It’s coming from the opposite direction.
6. Non-
On top of all that there is also the classic non- as in “Non, non, non” (Margaret Thatcher). This is often attached to nouns from verbs, so you have non-smokers and non-drinkers, but you don’t tend to get unsmokers and undrinkers – that would almost suggest a reversal of the smoking or drinking process which may well be a non-pretty sight. On the other hand you get non-believers and unbelievers and people who disbelieve. Each of these terms gives its own shade of meaning but all around the idea of not being the thing the root is saying, or being the reverse of it.
7. A-, ana-
Greek roots also sometimes come into English with the “a-” or “ana-” prefixes that show that something is not something else or has not got it. You ‘ll find a lot of these in medical terms, for example, as well as in the scientific names of animals and plants, like Anableps.
Now, at this point you might be thinking that with all these mechanisms for saying that something is not something, English would not really need that many more, but modern language, in its weaselly way, has added a number of hidden ways of saying “not”.
8. Economical with, -challenged, zero-
One of these is to use the term “economic with”. Instead of saying that someone is “untruthful” or “a liar”, you can say that they are “economical with the truth”. You can get around saying someone does not dress well by calling that person “sartorially challenged” These circumlocutions often require a slight change in the root word and the humour is in getting people to think, although most examples are already by now in the realm of the cliche, and they tend to be used creatively challenged people. By which I mean zero-originality people, employing another “not”-related (as opposed to “unrelated” which is completely unrelated) neologism.
9. Quite, very, relatively, fairly, contextually (in combination with moral absolutes)
If someone claims to be “very honest”, “relatively faithful” or, to quote a certain Monty Python (see illustration) song, “fairly incorruptible”, it is just another way of saying “dishonest”, “unfaithful” and “corruptible”. Either a person is honest or they are not. Recently someone who tried in vain to rope me into a scheme countered my telling him that he was dishonest with the words “but I was honest with you”. Say no more.
10. Politically, etc
This is about the most weaselly of the lot of course, as people try to use this in denial of its meaning as a form of negation. Just as in the above case with “honest”, something is either correct or it isn’t. Therefore, saying something is “politically correct” means it isn’t really correct. In reality, it is incorrect. Saying that something is “diplomatically acceptable” means that it isn’t really acceptable. In reality, it is unacceptable. A person’s age also tends to be a question of fact, so if you want to tell me “I’m sixteen in May” it means in all probability “I’m not 16”. So get out of my cinema.