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Singapore Math

Thursday, March 25, 2010

Bad Algebra and the Double Negative

In algebra, two negatives make a positive; in English, two negatives cancel each other – or are equivalent to an affirmative.

Expressions like 'The middle class didn’t get nothing from the government' or 'Nobody told me nothing' are regarded as illiterate in current English, and they’d be avoided. Yet, arguably, using two negatives (like not or no or never) helps make the negation stronger:
Math editors cannot not write.
Math writers cannot not plagiarize.

In 18th century England, to standardize the English language, language experts believed that multiple negatives were illogical. Using algebra as an analogy, they claimed that two negatives make a positive, and disallowed speaking styles like 'She don’t know nothing' or 'He don’t never look at me.' The argument was neither good logic nor good algebra; in algebra, -x plus -x equals -2x, not 2x. The two negatives equal two negatives. So, double negatives are no-no's.

Logical or not, the rule has been a success, and double negatives like 'I don’t know nothing about it' tend to label a speaker as unrefined. People with a little knowledge pounce on a double negative as self-righteously as they decry a split infinitive. As a result, one seldom sees expressions involving not and clear negatives like nothing or nobody in writing.
“You ain’t seen nothin’ yet!” Ronald Reagan US President
Basically, double negatives aren’t wrong, and some languages use repeated negatives to strengthen the effect. The logic had since changed, and a sequence of negatives came to be regarded as self-canceling instead of reinforcing each other.

Just like there’s almost an exception to every rule, a double negative can be a positive statement – it can be useful as a way of emphasizing a point, as in this sentence:

The managing editor was not unaware of the plagiarism.

At the least, a double negative is acceptable when it’s used as a kind of figure of speech with intentional canceling effect, as in It has not gone unnoticed (= It most certainly has been noticed). In fact, a double negative is an effective way to make a mildly positive statement. For example, instead of undermining the creativity of an editor, a critic may write that she 'is not untalented.'

Here are some double negatives which are actually positive statements:

Double negative: He doesn’t dislike her.
Positive meaning: He likes her (Well, sort of …).

Double negative: We cannot pretend and do nothing.
Positive meaning: We must do something.


The double negative, neither-nor, defies the so-called logic that two negatives cancel each other. We don’t say: 'Neither substitution or elimination can solve the simultaneous linear equations,' avoiding a double negative. In standard English we use two negatives, with no idea that they cancel each other: 'Neither substitution nor elimination can solve the simultaneous linear equations.'

Beware of words like barely, hardly and scarcely
which have negative meaning.

We’re also less consistent with negatives like hardly or scarcely. It’s uncommon to hear

I can’t hardly recall the formula.
I don’t hardly think I should.

Standard usage requires cutting one of the negatives:

I can hardly recall the formula.
I hardly think I should or I don’t think I should.

When but has a negative meaning, there is still more confusion, even though standard usage dictates a single negative:

 I can’t help but imagine the worst. 
I can’t help imagining the worst. 

I don’t doubt but that she means well. 
I don’t doubt that she means well.

That double negative is still popular today although language gurus urge us not to use it. If we say that 'Saddam is not entirely dictatorial,' we leave very little for the positive, only whatever small amount of non-dictatorship between entirely and not entirely. If we say that Hitler is 'not half bad,' we may be allowing at least 50 percent on the positive side. If I say that Mao’s views on democracy are 'hardly without prejudice,' I am certainly accusing him of some prejudice, but the negative approach seems to make feel safer from libel suits.

Although the double negative is considered ungrammatical in good writing, however, as we saw earlier, it can serve as an effective way to make a positive statement. At the worst, we may be judged as being uncivilized if we misuse the double negative – we may not impress positively on the reader or listener.

Let me end by saying that it’s not unthinkable that in a not uneducated move in a not too distant future, no small number of editors will be revealing their not unhidden talents to the not unchallenging task of freeing non-uneditable manuscripts of double negatives.

Non-negatively yours


Which of the following are incorrect?
(a) I wouldn’t be surprised if she didn’t show up unannounced.
(b) The men unloosened their ties.
(c) We will go irregardless of the weather.
(d) Not for nothing was Mathematics called 'the Queen of Sciences.'
(e) I am a friend of him who is an enemy of my enemy.
(f) Don’t give me no wrong answers.
(g) She doesn’t need no tuitions.
(h) We didn’t write nothing.
(i) I didn’t know hardly anybody who didn’t want me to edit.


Allen, Robert (2005). How to Write Better English. Penguin Books.

Dolainski, Stephen (2004). Grammar Traps: A Handbook of the 20 Most Common Grammar Mistakes And How o Avoid Them. Toluca Lake, CA: Paragraph Publishers.

Gorrell, Robert (1994). Watch Your Language!: Mother Tongue and Her Wayward Children. Reno, Nevada: University of Nevada Press.

© Yan Kow Cheong, March 24 2010.

1 comment:

Anonymous said...

I'd love your feedback on a math manipulative that I invented called the ZeroSum Ruler that allows students to use absolute value to solve integer addition and subtraction problems. http://zerosumruler.wordpress.com/

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