The Mystifying 'Not' in the English Language
THE WORD ‘NOT’ enters the dictionaries as an adverb. It is considered a ‘negative adverb’ because it basically expresses the notion ‘no.’
In Modern Symbolic Logic, the word ‘not’ finds its place in the topic ‘negation’—a special kind of compound proposition. The word ‘not’ essentially appears in negative propositions because it is the one usually used to convey the negation (or denial, or refusal) of a particular proposition.
There are concepts or principles in the English language that refer to the multiple use of the word ‘not’ (and/or the words ‘no’ and ‘nothing’) in a sentence.
Standing for “negation of negation,” what is called ‘double negation’ uses two negatives in a sentence. Related to the compound statement ‘negation’, ‘double negation’ as a logical principle states that a statement and the negation of its negation mean one and the same thing. Simply expressed, it means that “two negatives make an affirmative.” So when your teacher confidently tells you, “It is not true that you are not cheating”, she is persistently stating, “You are (indeed) cheating.”
When correctly used in an appropriate context, ‘double negation’ can be a good ‘emphatic sentence’ and a powerful ‘counter statement’. In countering the charge that a person is ‘not innocent’ of a crime, his attorney may respond, “It is not true that the accused is not innocent.”
Like ‘double negation,’ what is called ‘double negative’ uses two negatives. But whereas ‘double negation’ necessarily forms a (complete) sentence, ‘double negative’ can be just a phrase which contains two negatives.
When carelessly put up, double negative can become ‘illiterate’ in current standard English. The Encarta dictionary for instance explains that the expression, “I don't know nothing” in which two negatives close to each other are meant to emphasize each other, is no longer up to standard. However, double negatives like, “That's not a good idea, I don't think”, in which the reinforcing negatives appear in distinct clauses, are deemed literate.
The double negative “It is not impossible” which is synonymous to “It is (positively) possible” can be acceptably used for emphasis or as a counter proposition. As an application, we can therefore say, “It is not impossible to learn useful things from Philosophy.” (Copyright 2013 by Jensen DG. Mañebog)