Must what precedes the colon be a complete sentence?

Question

I learned from English that the words preceding the colon should form a complete sentence:

Between independent clauses when the second explains or illustrates the first

The colon is used to separate two independent clauses when the second explains or illustrates the first. In such usage, the colon functions in much the same way as the semicolon. As with the semicolon, do not capitalize the first word after the colon unless the word is ordinarily capitalized.

And I don't know if it also applies in German.

Let me quote this paragraph from the Neujahrsansprache der Bundeskanzlerin der Bundesrepublik Deutschland.

Liebe Mitbürgerinnen und Mitbürger,

heute Abend stehen wir nicht nur am Beginn eines neuen Jahres, sondern auch eines neuen Jahrzehnts. Ich bin überzeugt: Wir haben gute Gründe, zuversichtlich zu sein, dass die in wenigen Stunden beginnenden 20er Jahre des 21. Jahrhunderts gute Jahre werden können - wenn wir unsere Stärken nutzen, wenn wir auf das setzen, was uns verbindet, wenn wir uns daran erinnern, was wir in den letzten Jahrzehnten gemeinsam erreicht haben.

We can see that Merkel used Ich bin überzeugt: which is incomplete, then I wonder if it is correct or not?

Answer 1

Principally:

Please note that the rules for the use of interpunction in German are often very different from those in English. Unfortunately, they are also pretty difficult - or say complicated becaue there are so many different situations.

For example, you would not put a comma after Zum Beispiel in German like here after for example. Generally speaking, English tends to set commas where a speaking break would be desirable. That's not how German uses commas.

There is a very good book Duden Handbuch Zeichensetzung that you could use for diving into the topic. It has a lot of examples for all kinds of cases. Of the 200 pages of the book, about 130 are on the correct use of commas. (The use of the colon is less complicated.)

As for your narrower question:

Ich bin überzeugt.

is indeed not a totally satisfyingly complete sentence. Native speakers would feel an urge to add something, e.g.

Ich bin überzeugt, dass... xyz.

Ich bin überzeugt von der Wahrhaftigkeit seiner Aussage.

But in your example, the somewhat "deficient" use of the required additions to the verb is justified through the direct enumeration of all these things that folow (things the speaker says she is convinced of). So,

Ich bin überzeugt: Der Mond besteht aus Käse.

is indeed a well-formed sentence.

Note that in German, the sentence after the colon will start with a capital letter as long as what follows the colon is a complete sentence. That's different from English where you start the sentence after the colon with a lower case letter even if the sentence is a complete one.

There is one case where "Ich bin überzeugt" could stand alone:

A: Na, was der Paul da wieder erzählt hat... das kommt mir doch reichlich übertrieben vor.
B: Hm... ja, es klingt überzogen... aber ehrlich gesagt, ich glaube ihm.
A: Bist du überzeugt?
B: Ich bin überzeugt.

Here the "Ich bin überzeugt" can stand alone because the missing part is implicitely clear to the participants of the conversation; it has been mentioned already and can now be left out.