Negative sentences are avoidable. Saying something negative in a positive way, and maintaining the significance of what is said is more than difficult. This is the reason why grammarians and careful writers are averse to negative sentences. Yet, newspapers are teeming with such illogical sentences. Some text editors write an intro with negative pronouns, like nobody, none, no one, nothing, not less than etc.
Such text writers perhaps think a sentence beginning with a negative pronoun is more agreeable than a positive one. Such sentences are colourless, hesitating, tame and non-committal. William Strunk JR and EB White wrote: “Use the word not as a means of denial or in antithesis, never as a means of evasion.”
For example, nobody will visit this place. This sentence may be rewritten: few will visit this place. A sentence with an indefinite pronoun, like “nobody” at the beginning, leads a story to nothingness. It indicates the writer is not clear about what he wants to say. It is an irresolute sentence. Similarly, there is hardly any anathema towards the indefinite pronoun “nobody or none or no one.”
Beginning a story with such pronouns denotes the writer's lack of thought. It is a tame pronoun. But placing negative and positive in opposition makes a sentence stronger than usual one. An example from Julius Caesar makes it clear: Not that I loved Caesar less, but that I loved Rome more. Here, ‘not’ has been used as an antithesis.

Strunk and White further wrote: “If those who have studied the art of writing are in accord on any one point, it is this: the surest way to arouse and hold the reader’s attention is by being specific, definite, and concrete.” The writers, like Homer, Dante, Shakespeare and Milton are great and effective, because they deal in particulars and report the details that matter. Their words and expressions portray lively images.
A text writer should look for constructions phrased negatively, it is no easy to tell or it does not happen often. The sentences can always be rewritten: it is hard to tell or it happens rarely. Such sentences are shorter as well as more definite. It is also necessary to keep in mind that if negative sentences pile up, the writer may lose how many he has used and end up opposite of what he meant.
The sentences, like “That does not mean we don’t think there are not things that can be improved,” leave readers scratching their heads. And replacing two negatives with a positive saves space too. When the negative is a separate word, the result is the same, but such sentences are generally avoided, for they lack clarity.
William Thackeray’s “Not a clerk in that house did not tremble before her” is an obscure sentence. The better way of saying this is: “Every clerk or all the clerks in that house trembled before her.” Two negatives may, however, be placed in two separate clauses.
For example, there is no one present that did not weep. It means everybody wept. But there is a problem. Positive ‘may’ and negative ‘must not’ are often found together. John Ruskin wrote: "Your labour only may be sold; your soul must not.”
Two further points, concerning the verb auxiliary verb ‘may’ here present themselves: ‘May,’ with negative infinitive denotes possibility. ‘You may not know,’ signifies: it is possible that you do not know. Usually, the ‘not’ is attracted to the verb in accordance with the general tendency to what seems to be an idiomatic expression. A Hope wrote: "I may not be an Earl, but I have the perfect right to be useful.”