When and why to use a double negative by negating an adjective with ‘un-’

Question

I’m wondering when and why a double negative in a sentences should/would be used.

I came across the following:

[…] was mit weiteren, nicht unerheblichen Kosten verbunden ist.

Why not just write:

[…] was mit weiteren, erheblichen Kosten verbunden ist.

In my head, both sentences mean the same.

Further actions will result in high costs.

Is there a purpose of using a double negative or is it just personal preferences?

Answer 1

This is not exactly the ‘double negative’ one mainly refers to when using that word. Grammatically, it is a single negative that merely applies to an adjective whose meaning was reversed by a prefix.

There is a considerable difference between these two statements:

Die Kosten sind erheblich.

Die Kosten sind nicht unerheblich.

The first clearly says that the costs are significant (implying high) while the second merely says that the costs are not neglegible (implying moderate to high). In fact, the second can be rephrased to the following sentence with a similar meaning:

Die Kosten sind nicht vernachlässigbar.

The difference between the first and the second sentence presented in this answer can be understood logically (i.e. mathematically). If costs are erheblich, that leaves little room for discussion; they must be very high. If costs are not erheblich, then they just don’t quite fit into that top-tier category. Conversely, if costs are unerheblich, they are pretty much the opposite of erheblich namely pretty low. If they are not unerheblich, the just don’t fit into that bottom-tier definition.

Note that this means that a sentence such as the following is not necessarily a contradiction:

Die Kosten sind nicht erheblich aber auch nicht unerheblich.

It merely means that the costs are somewhere in the middle grounds.

Negation used in this way is a figure of speech called litotes. (Thanks to chirlu!)

Answer 2

You are right, but the tendency of the doubly negated sentence is to soften the final claim. Often this happens out of modesty or false modesty. Much like these English phrase:

Not unfamiliar, not unrelated, not unheard of

If I had to give a rule for this complicated and situational phenomenon, I would advise to replace the double negated claim A by a statement slightly more moderate than A. In some cases though, the statement is absolute and can't be softened. These cases, however, account but for a tiny fraction of double negatives:

Frau Lu hier ist noch unverheiratet!
Nein, ich bin nicht unverheiratet!

here, the phrasing was prompted by previous sentence. Furthermore, consider this list:

Nicht unverheiratet = verheiratet
Nicht unmöglich ~ möglich, tendenziell unwahrscheinlich
Nicht unerheblich ~ erheblich oder nicht zu vernachlässigen
Nicht unerfahren ~ erfahren, meist bescheiden gemeint
Nicht unansehnlich ~ ansehnlich, meist ein Versuch unbeeindruckt zu wirken

Let's say, Miss Zuo finds Mister Lu attractive. Miss Pumbelchuke is aware of it and wants to embarrass her. Miss Zuo might state:

Er ist nicht unansehnlich.

This allows her to retain some aloofness. Generally, the connotation is quite different from:

Er ist ansehnlich.

and comes close to

Er ist ganz ansehnlich. ,

where ganz considerably softens the claim. Unfortunately, with nicht unerheblich you picked a much harder and more situational case. Fundamentally, I would interpret nicht unerheblich as a softening as well. It could well appear in the context of wanting to soften an accusation:

Herr Pervatender, Sie haben durch Ihre nicht gerade ungefährlichen Spekulationen unserer Firma nicht unerheblichen Schaden zugefügt.

To me, it's much easier (less brave) to voice these, than the direct counterparts. On the other hand, such softening is reminiscent of elaborate or formal speech. So it might intimidate some people even more. That's how I interpret the comment by npe. Yet, I would be much, much more intimidated by the direct accusation.