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Why do people tend to use negation of negative statement?
Let us see an example statement,

he is not unhealthy, ...

The above statement can have beginning like

he is healthy, ...

Why exactly do we use this and exactly when (where)?

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    If I am "not rich" that does not mean I am poor. If someone is "not unhealthy" that does not mean they are healthy. It would be wrong to assume a polarisation - there are 50 shades of grey. – Weather Vane Jun 27 '19 at 19:02
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    It is a matter of emphasis. Double negatives are tricky for those whose native language uses them differently. – GEdgar Jun 27 '19 at 19:54
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    It may be used for emphasis, or it may be used for the exact opposite. It's just a litotes. An exceptionally common figure of speech in absolutely every language. It doesn't matter whether that language has double negatives or how it uses them. Frankly, I'm struggling to see how this is a question about English. Saying "John is smart" is not the same as saying "John is not stupid". Everywhere in every language. Everyone knows what the difference is and when to pick one over the other. Which depends on the cultural context and social customs more heavily than the language spoken. – RegDwigнt Jun 27 '19 at 21:37
  • Because they can't get no satisfaction from a positive statement. – Hot Licks Jun 27 '19 at 22:28
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    "Not unhealthy" doesn't mean "healthy." In fact, a reason for someone to say that could be to point out the fact that while not unhealthy, he's also not healthy, meaning he's not sick enough to be sick but not well enough to be well--a middle ground. Of course, another reason would be to negate someone saying that he was unhealthy, like if someone says, "John's unhealthy," to contradict that, I would more likely say, "He's not unhealthy," rather than, "He's healthy." – Benjamin Harman Aug 26 '19 at 22:09
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To expand on what Weather Vane said in their comment, there's a variety of shading of meaning that could be going on.

"He is not unhealthy" doesn't mean "he is healthy." In this case, there's a bit of a fine line with the meaning of "healthy", but that's for medical people to define, not English. A person can be healthy and still feel physically bad.

In Weather Vane's example of wealth, there's a much broader range to work with. Let me explain.

"I'm not poor" can be used by different people and mean different things in different contexts. A businessperson can joking say "I'm not poor" when asked about their earnings to mean that they are reasonably well off, possibly actually rich, and are declining to answer the question specifically.

A poor person saying "I'm not poor" might be said defensively, if you point out their meager paying job, low cost vehicle that's in disrepair, shabby clothing, poor grooming habits, etc. In this context, they could be defending their honor and ignoring the potential fact that they actually are poor.

An "average" person with a reasonably decent job, a family, car(s), debt, home/apartment, etc. might say "I'm not poor" to say that they are living comfortably, but not really gaining ground financially. They might also end that same sentence with "but I'm not rich either" to accentuate that they aren't really making grounds or to put off the idea they have expensive tastes.

A couple phrases I hate are "you're not wrong" and "I don't disagree". What the person is often really saying is that they can't admit that someone else is correct or that they agree with a potential competitor. Both of these can be used as a way to end a conversation.

It's perfectly OK to say "you're not wrong, but you're not totally correct, either". This is not only a complete sentence, but also a complete thought. This allows someone to be partially correct. Also, saying "I somewhat/partially agree" is less ambiguous and more conducive to continuing a conversation.

Saying that someone is "not not guilty" involves legal definitions. In law, there's not really such thing as "innocent". Laws are set up so that someone is guilty or not guilty, so if someone is "not not guilty", it means they are guilty.

As you can see, the context of the statements are entirely necessary to define what a negative, double negative, and other negations can mean. It goes to show that English is about as clear as mud and why even native speakers have problems with it's use.

I hope I helped, but I wouldn't be surprised if I didn't.

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It's an example of litotes, an understatement, although the precise interpretation may depend on content. See the definition of litotes.

a figure of speech and form of verbal irony in which understatement is used to emphasize a point by stating a negative to further affirm a positive, often incorporating double negatives for effect

[Wikipedia]

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Because talking about the negation of something is not the same as talking positively about the opposite. Even if the "something" itself was expressed as a negation of something to begin with.

In the first instance you are emphasizing the negation. In your example, the phrase "He is not unhealthy, ..." may continue to talk about avoiding unhealthy habits or supporting a healthy lifestyle, all for the sake of not falling ill. Whether he is healthy then, or "just fine" is left open and deemed not important.

The second instance would focus on achieving the positive statement. The phrase may continue similarly than above, but assume that he really is (or feels) healthy as a consequence. In that sense it's a stronger statement about the outcome, removing the grey zone of whatever may be between being healthy and having avoided falling sick.

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"He is not unhealthy" contrasts to "He is healthy" from the context of the statement. In general, if I were to hear "He is not unhealthy", I would imagine the use of a "but" to contraindicate in a subtle way his healthiness. For example:

He is not unhealthy, BUT he is always in the hospital

or

He is not unhealthy, BUT he has a horrible diet.

You could do something similar using

He is healthy, but he has horrible diet

It means the same thing, but it doesn't emphasize as much the fact of his unhealthy habits. Using the negation of a negative emphasizes that though something is true, there are a lot of opposite factors involved.

In general, when one negates a negative statement, something more complex is generally being expressed than just a positive statement. Take a look at the information provided below from the link provided above:

  1. Double Negatives Can Convey Complicated Meanings In more recent times, though, many writers have decided this is a much too simplistic view of English. Our language isn’t as straightforward as math. Some double negatives can subtly change the meaning of a sentence. “Not ungrammatical” seems like fainter praise than “grammatical.” Another example would be when you say something like “I’m not unhappy that Norman got fired.” You can’t go so far as to say you’re happy about it, but you’re not unhappy about it either. In this case, the “not” doesn’t cancel out the “unhappy.” “Not unhappy” isn’t the same as “happy.” It’s something more complicated.

  2. Double Negatives Can Keep the Emphasis on the Negative Occasionally, double negatives are useful when you want to place emphasis on something bad. For example, I once saw a sentence in the “New Scientist” that referred to “less unhealthy cigarettes.” "Less unhealthy" is a double negative—"healthier" would be the positive way to say it—but "less unhealthy" keeps the emphasis on cigarettes' dangers.

  3. Double Negatives Can Leave a Way Out In a 2016 paper, Merima Osmankadić from the University of Sarajevo did a deep dive on how people use double negatives in politics and found many of these uses and more. For example, double negatives can also leave the speaker a way out. It’s easier to back away from a statement in which you say it is “not unlikely” that someone is guilty than a statement in which you say it is “likely” that someone is guilty. It can also be perceived as being polite or being less threatening to make the statement in this slightly softer way. I also sometimes interpret such statements as concessions: Although you’d like to believe it’s not true, it could be. For example, if evidence was mounting that Squiggly committed a crime even though I didn’t want to believe it, I might say something like “Well, it’s not inconceivable that Squiggly stole the chocolate and lied about it.”

  4. Double Negatives Can Arise When There’s No Positive Equivalent Double negatives also pop up when there isn’t a direct positive phrase you can use. In fact, just today I noticed I used a double negative when my husband misread a candy bar that said it was a dark chocolate baton, thinking it said it was dark chocolate bacon. To which I replied, “Well, that wouldn’t be unheard of.” I could have reworded the sentence completely, but saying, “Well, that’s heard of” isn’t an option. It’s not something we say in English. Similar phrases Osmankadić highlighted include saying you are “not indifferent” to something (you can’t say you “are different” to something), and saying something “can’t continue indefinitely" (again, “definitely” isn’t the opposite of “indefinitely,” so you can’t say something will “continue definitely”). If you want to restate those sentences positively, you need to do a bigger rewrite than just getting rid of the double negatives.

  5. Double Negatives Can Create Parallelism Further, Osmankadić highlighted instances in which speakers used double negatives to embrace parallelism, for example in the line “It was unexpected but not unwelcome.” That has a nicer rhythm than “It was unexpected but welcome.”

Take some time to read the entire page.

If I were to sum up the usage of "negating a negative statement" in general terms, I would say as the article states, the usage is not as direct and simple as its literal meaning

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When the speaker wants to softening or downvoting the effect of adjective or an adverb, double negation is used.

Though double negation makes the sentence affirmative, the double negation talks about the caughtiousness of the speaker.Double negation is commonly used in a formal way of writing.

He is healthy ( less formal)

He is not unhealthy( very formal used especially in writing)

Here is a real example in the context used in the dictionary.. I think we need a context to explain the difference

A: The repair costs 5 pounds

B: Well, That is not unreasonable

Here B can say well, that is reasonable

But he wants to be cautious and tactful and used the double negation

Here is the link which helps us to know when double negation is used.

https://dictionary.cambridge.org/grammar/british-grammar/double-negatives-and-usage

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