Here is a passage taken from a book:
Selbst die Muggel haben bemerkt, dass etwas los ist. [......] Nun, ganz dumm sind sie auch wieder nicht.
I don't quite get the meaning of this sequence of words. DeepL churns out the following translation for the second sentence:
Well they're not completely stupid either
Does "auch wieder" simply mean either in this context?
Yes. The "wieder" here has no good or word-for-word translation.
Let's look at it in detail:
ganz dumm sind sie nicht --> they are not completely stupid
ganz dumm sind sie auch nicht --> they are not completly stupid either
ganz dumm sind sie auch wieder nicht --> they are not completely stupid either. (thus basically the same as before)
The "wieder" here is a kind of particle which can be inserted in statements like above where a thing looks on the surface like it one way, but in detail, or closer consideration, that is not (always or entirely) the case. Thus here "all muggles are stupid" is commonly believed - but indeed, they are not completely stupid either when looking at them carefully.
Different example: "Da musst Du hin zum Ski-Fahren, da schneit es immer" - "Naja, ganz so stimmt das zum Glück auch (wieder) nicht. Aber es schneit genug und ist kalt genug, sodass von Dezember bis Februar immer Schnee liegt" (You have to go there for skiing, it's always snowing there" - "Well, luckily not quite. But it's cold enough and snows enough so that it's always snowy between December and February".
There is a direct English equivalent. The phrase translates
And then again, they are not completely stupid.
The meaning is the same. The construction is used when you have had a new thought that is different from or the opposite of what you have just said or of what might be implied.
The meaning is
(They are stupid, but) they are not completely stupid.
The word "wieder" in this case is either unnecessary or emphasis to "auch".
The usage of "auch" is also a little unusual here, because "auch" means something is the same or similar, in English "too". In this case it is used to contradict part of an earlier statement: "They are (completely) stupid. No, they are just mostly stupid."
"Auch wieder nicht", is a mix of "auch nicht" = "not either", and "wieder" is repetitive (="too/also") for an implied (but not actually mentioned) earlier statement. So in this context "selbst ... have recognized" is some kind of laurel on them, but the "selbst = even" is putting that positive statement into the negative, implying that they are actually quite dump. "Ganz dumm sind sie nicht = they are not entirely stupid", "ganz dumm sind sie auch nicht" = neither they are entirely stupid", and "ganz dumm sind sie auch wieder nicht" = "but again, they are not completely stupid either". I think DeepL is performing very well here.
The question is not find a "good" English translation of a German sentence. The question is why the translator chose to translate an English sentence into German in the way written down in your question.
I support vectory's and Tilman Schmidt's comments where they suggested to look at the original text. Quote from Harry Potter and the Philosopher's Stone (Chapter 1 - The Boy Who Lived):
"Oh yes, everyone's celebrating, all right," she said impatiently. "You'd think they'd be a bit more careful, but no - even the Muggles have noticed something's going on. It was on their news." She jerked her head back at the Dursleys' dark living-room window. "I heard it. Flocks of owls... shooting stars... Well, they're not completely stupid. They were bound to notice something. Shooting stars down in Kent - I'll bet that was Dedalus Diggle. He never had much sense."
This was said by Minerva McGonagall.
You see that DeepL reproduced exactly the original English sentence. The German translation is
Nun, sie sind nicht ganz dumm
or
Nun, ganz dumm sind sie nicht.
In your question one finds a somewhat more creative translation. The "auch wieder nicht" puts a bit more emphasis on the assertion that the muggles are actually stupid, but not as stupid to ignore something which is really obvious. Retranslating into English produces
Well, they are not completely stupid either.
I would argue that auch wieder nicht is a Low German turn of phrase, simply because a friend uses it often enough, whose idiolect I associate with this dialect continuum (Berlin/Brandenburg), and because “nun” as well as “ganz” in the quoted passage are diagnostic of this topolect, too. That's unreliable evidence, which only motivates my interest in the question. Note that “Low German” is an unspecific umbrella term.
From introspection of my own understanding, I cannot disagree with the previous answers. Wieder is intensifying ("unnecessary or emphasis", @RalfFriedl), redundant (@planetmaker's 2nd and 3rd example; "unnecessary” @RalfFriedl) and apparently a negative concord positive polarity item ("where a thing looks on the surface like it one way, but in detail, or closer consideration, that is not“ [sic!] @planetmaker). I'm slightly puzzled by @PaulFrost's evidence of different quotations, because I do not know the provinence of these texts in detail (actually, I'd see any official story as a parallel construction as part of the narrative).
On etymological grounds, I suggest two notable observations.
First, the etymology of nicht as univerbation of a negative polarity item ne and an enclitic wiht is remarkable in view of wieder. Second, a fricative anlaut in [auc]h-wieder from *xw > w may be informative for the origin of wiht, which is unknown. In conclusion, the translation using “either”, etymologically from Old English ǣghwæther, comes very close to being a cognate – close but no cigar. Compare German jeder, Old High German eogihwedar.
One could spin this further, *h-wi'a-ne', assuming reverse order of the elements underlying nicht, and reduplication from hypercorrection, *[*n]o(x)-wiht-ne-wiht, compare Greek ού, ουκ "not" (cf. Frisk, LSJ).
Alternatively, a relation to adv. gewiss "certainly”, Latin video “I see”, English wit, witness etc. is possible. See also hear as univerbation from PIE *h2eK- "sharp" + *h2ows- "ear", from *h2ew- "perceive".
Any relation between these items seems probable, though a solution has to remain ultimately uncertain.
In particular, auch "also" is an isolated development in German, compare Dutch ook, Old English eke "and" etc. Particle chains remain an intensive topic of research and professional translations (source?) are a valuable resource.
Etymology is of course subject to the etymological fallacy when responding to a meaning-in-context question.
Does "auch wieder" simply mean either in this context?
I'm afraid the extensive meaning of either is out of scope for a German language question. It's certainly not “simple”. Anyhow, turning to the evidence:
Selbst die Muggel haben bemerkt, dass etwas los ist. [......] Nun, ganz dumm sind sie auch wieder nicht.
I don't quite get the meaning of this sequence of words.
Note similar “auch nicht ganz blöd”, “auch wieder nicht verkehrt” and similar phrases using a common construction, all so “nicht von schlechten Eltern”. The auxillary verb, sein, is commonly omitted in interjection. Inverted subject position of the adjective as object, “Ganz dumm sind sie ...”, may be comparable to tmesis (e.g. jedenfalls, auf jeden Fall, auf jeden, Auf jeden sind Sie nicht ... falls ...).
The High German conjunction / adverb which best captures this meaning of wieder would be wiederum. NB: “in älterer sprache vertritt es oft einfaches wieder” (Grimm, Deutsches Wörterbuch, “wiederum”).
Compare wiederum “however" (dict.cc), Dutch hoe dan ook, "however", Ger. wie dem auch sei, wie auch immer "however, whatever" (en.Wiktionary), noting that ever has no certain etymology in Germanic, and that phonetic wi'a[*t] "wieder" matches quite closely. In conclusio,
Whatever. See also although / Ger. jedoch.
