Since the 17th century, English grammarians have spoken out against constructions with double negatives. Before the 17th century, double negatives were considered perfectly acceptable in English, like in present-day Spanish, French and many other languages of the world. Even today we're often taught to avoid a double negative.
The idea is that we should try to avoid saying something like:
- He didn't not get the prize.
This is because in logic, two nots cancel each other out. So the statement above would logically mean: