Which case is used in the first word, and why? What is the grammatical logic behind the use of this particular case?
Темным-темно
давным-давно
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Sign up to join this communityHistorically, it's instrumental case, or rather, one of the numerous usages of the instrumental in Russian: the emphatic instrumental (творительный усиления).
It can be used with adverbs (давным-давно, полным-полно), nouns (дурак дураком, змея змеёй), adjectives (белым-бела, черным-черна) and even verbs (есть поедом, слыхом не слыхивать etc.).
I failed to find a conclusive reasoning behind this, but I have a strong gut feeling that it's linked to the infinitive absolute, a Semitic construct which had been calqued into Greek and later to Church Slavonic when translating the Bible:
от дрéва же, éже разумѣ́ти дóброе и лукáвое, не снѣ́сте от негó: а въ óньже áще дéнь снѣ́сте от негó, смéртiю ýмрете (= "thou shalt surely die" in KJV, literally "you will die with a death").
áще же злóбою озлóбите я́, и возстенáвше возопiю́тъ ко мнѣ́, слýхомъ услы́шу глáсъ и́хъ (= "thou afflict them in any wise", "I will surely hear their cry"; literally "you will afflict them with an affliction", "I will hear them with my hearing")
Well, there's no case at all - those are just adverbs with reduplication. It's not that in words such as темным-темно
,светлым-светло
, давным-давно
, старым-старо
, пьяным-пьяно
we
Reduplication, whether with word repeated exactly or slightly changed it a very common thing for a lot of languages, and Russian is no exception for this. In fact, I can even claim that this is one of the most old and universal features that human languages share.
Using reduplication for intensification is also something very common. As of changing the root - it's not necessarily even has to be related to any grammatical category (such as cases) at all.
It's like asking what exactly from the grammatical standpoint is shm
in fancy-shmancy
. The other thing is that we actually can try to come up with some etymological explanation of how exactly we end up with this forms for exactly this particular adverbs, but not some other ones (why not "холодным-холодно" for example).
I'm not aware of a good overview of inflected reduplication in Russian but my guess would be that, anyways, this would be a better fit for Linguistics SE.