British witers seem to use them a lot, phrases like …" it is a not insonsierable poit of contention"…etc.
What’s the concenus on the use of DNs? Classy or pretentious? 
“Not inconsiderable” is not a double negative. It also doesn’t mean the same thing as “considerable”.
Yes, it is. ‘Not’ is a negative, and ‘in’ is in this case a negative. “Not inconsiderable” does not quite mean the same thing as “considerable”, since the litotes implies a lesser degree of existence (or simply understatement): it’s there, but it’s not huge.
No, it’s not. You can’t just disassemble a word into its component parts* and treat it as though it’s not a single unit.
*except contractions. “Can’t” is “can not”.
It is not uncommon for writers to use the literary trope called litotes (lie-tote-ease), which is technically a double negative functioning as understatement. While litotes is technically a double negative, it is not the ungrammatical sort like “…don’t got no…” and has both a long history and a special significance. As noted by begbert2, it carries a different flavor or connotation from the straight positive.
“Though she did not love him, she was not unwilling to go to the dance with him.” A different sense is arrived at from “…she was willing to go…”
According to Harbrace (Eleventh Edition), p. 49:
The example they give is the following sentence:
Moderator’s Note: I think it would not be inappropriate to move this thread to Cafe Society.
Ain’t no telling what the mods will do next.
Yes, this is a double negative construction, and yes, I think it’s overused. There are occasions where it’s appropriate, but those occasions do not IMO include smirking understatement; when folks use it in such a context, I generally find them pretentious.
Daniel
Yeah. Right.
Oh, wait. That’s a double positive.
Are double negatives in literature classy?
Ain’t no way, nohow.
I done ain’t got no nothing to not say in this thread.
No, wait…that’s still positive. I really don’t have anything else to add.
Characters use them in Jane Austen novels, sometimes.
That’s how you know Jane’s making fun of the character.
I don’t know about Austen but there are dialects in the British Isles that habitually used double negatives as intensifiers. Reproducing one of these in dialog would be accurate, although the speakers would normally be looked down upon by speakers of more standard dialects.
As for the OP: litotes can be used correctly or incorrectly, just as any other rhetorical device can be. There is no answer to the OP’s question. It depends on individual usage.
Ya can’t NOT think it’s classy.
Let’s get things correct.
A double negative is the use of two negative terms in order to emphasize negation. “You’ll not see nothing like the Mighty Quinn” uses two negative terms where either one would do. It does not imply a positive, and is even grammatically correct in some uses: “No, never!”
Litotes is using a negative and a word with a prefix of negation in order to imply something that, while not exactly positive, is the opposite of the prefixed word: “He was not unhappy that his boss was sent to jail.” This is different in connotation from the positive form: “He was happy that his boss was sent to jail.” If you’re “not unhappy,” you aren’t necessarily happy, but you aren’t unhappy either – it expresses an ambivalence. More commonly, it is used as an ironic understatment.
Both constructions have their uses and can be used badly or well.
Used in moderation, or in period literature, double negatives can make a point in an elegant/classy/quaint way. Conan Doyle used them from time to time, as when Holmes would tell Watson something like, “I think you will not find this case undiverting.”
This is not a double negative because the intended meaning of the sentence is positive.
Double negatives are part of natural language, not confusing at all, and recognized as such in most languages.
In English, the creation of that “rule”, as well as other rules, such as not splitting infinitives or not having a preposition at the end of a sentence, were designed by monks to create parallels to Latin structure when translating.
It is a litote, which, as has been explained over and over, is an understated positive even though it employs two negatives. Litotes are a rhetorical device of their own, not a double negative, not a positive, but somewhere in between.