The Oxford Dictionary of English says a double negative “is a negative statement containing two negative elements (for example he didn’t say nothing)” and “a positive statement in which two negative elements are used to produce the positive force, usually for some rhetorical effect, for example there is not nothing to worry about!” It is rather like in mathematics where multiplying two negative values together make a positive one. Two negative elements can be used to produce a positive one.
To sum up, the above-said dictionary states “According to standard English grammar a double negative used to express a single negative such as I don’t know nothing rather than I don’t know anything is incorrect. The rules dictate that the two negative elements cancel each other out to give an affirmative statement, so that I don’t know nothing would be interpreted as I know something.”
Double negatives have often been frowned upon by serious linguists, but should they be? Are there any circumstances where they are acceptable? Well, yes there are.
So, carry on with those double negatives if they seem to serve a purpose, or if they do not serve no purpose! It is quite easy to tie oneself in knots with these. As Bart Simpson once wrote on a blackboard in The Simpsons “I won’t not use no double negatives”.