When to use double negatives in written English?

Question

I have always been a little confused as to when to use double negatives when writing (I am unsure if this is what they are termed in English, it is the term used in Mathematics).

E.g. when to use:

"I am not staying!"

Thus using two negatives - not & staying

...as opposed to:

"I am going!"

Here using a single positive - going.

Both sentences begin with "I am..." which infers that the person is going to do something, but then this can either be followed by two negatives, so to speak; "...not staying" which cancel each other out and mean going, or it can simply be followed by the word "...going."

In Mathematics a double negative is equal to a positive, and this also seems to be the case in the English language (and perhaps others). However when to use either one seems up for debate.

There are plenty of other examples, e.g. "I am not unregistered." or "I am registered."

Answer 1

A common use of a double negative is when someone is countering a negative. Imagine the following exchange:

A: You are the most insensitive person I know!
B: That's not true. I am not insensitive. That's just nonsense!
A: It's not nonsense. It's the honest truth.

Such use of double negatives is quite common, regardless of their propriety.

• Toll Booths Not Unlikely Places for Arrests and DWI Charges law offices website
• ...and it is not unlikely that the same species might attack both plants... (hawaii.edu/)
• Various phrases were thought to encompass the requisite degree of probability— 'not unlikely', 'substantial probability', 'likely', 'liable to result', 'serious ... (lawbook: The Law of Contract)
• To blame Russia's G8 suspension solely on the annexation of Crimea is not only incorrect, but suggests the KNS is purposely portraying the G8... (Knox News)
• Getting people off welfare is NOT uncaring - it's a moral duty and the only way to save us from fiscal suicide (Daily mail)
• I am not unsympathetic to your views on the state of the world in general. (book)
• ...courage is not inconsistent with caution. (Tufts.edu)

This could go on all day. These are blatant examples. There are many more using words that carry a negative meaning without the prefix un- or in-.