Well, I am not sure about this. I am Norwegian - not Danish. But If you reverse the expression, wouldn't you still use the definite form in the first word: "Enkelhedens modsætning er sandhed"?
"Enkelheds modsætning er sandhed" is certainly wrong from a Norwegian point of view, while "Modsætningen af enkelhed er sandhed" works, Is it the same in Danish - maybe a native Danish speaker could comment on this?
Or.... you could say that this use of the definite marker has got to do with more general patterns in Germanic and Romance (in which compound readings of this sort are not available). It is a use of the definite marker that has generic reference and you find a lot of them. The expressions would simply be ungrammatical without it.That is actually true of Danish come to think of it. I think it has to do with the verbal expression of it. If you said "enkelheds modsætning er sandhed" it would sound like "enkelhedsmodsætning" is a big compound word. In order to prevent confusion, the bestemt form is added to make enkelheden/sandheden
In the quote from Niels Bohr "Sandhedens modsætning er enkelhed." the "Sandhedens" has an affix -en on it, while "enkelhed" not. Is the "sandheden" here some specific thing, or the concept of reality generally?
Going back to the original question,
and adding to the post above by myšlenka, I would say that the Danish s-genitive as in sandhedens modsætning, generally requires the use of the definite or the indefinite article in the singular to be grammatical.
Please consider these more simplistic examples,
Pigens cykel (definite form) vs. en piges cykel (indefinite form).
Fuglens rede (def.) vs. en fugls rede (indef.)
Moderens kærlighed vs. en moders kærlighed
We generally don´t use a bare noun in the genitive form in the singular, likely because they are morphed into compound nouns, as in these examples
piges cykel => pigecykel
fugls rede=> fuglerede
moders kærlighed => moderkærlighed
Off the top of my head I can only think of a few situations where the bare noun may be used in the genitive in an occasional fixed expression and in literary/lyrical contexts, mands minde, fugls føde, and Mands kvinde ( Novel by Moberg)
The use of the indefinite article in the OP example and in myslenka´s examples would also be grammatical, although some sentences might seem slightly forced or unnatural simply because we more commonly use the definite article to imply a general or conceptual idea of usage. But in the right context they could work.
Sandhedens modsætninger vs. en sandheds modsætninger
Demokratiets udvikling vs. et demokratis udvikling
Havets hemmeligheder vs. et havs hemmeligheder
Kongerigets fald vs et kongeriges fald
Menneskets anatomi vs. et menneskes anatomi
In the original quote by Bohr, the definite form sandheden conceptualizes the truth in an all-encompassing way as opposed to en sandhed, a truth, one truth, even any truth.
In the quote, enkelthed is the predicate nominative and modifiers are optional depending on the context and intent. The use of the definite article would have been grammatical here, creating a parallel construction with sandheden, i.e. sandhedens modsætning er enkeltheden, The use of the bare noun, however, adds an element of linguistic definition,- simplicity defined as in, "enkelthed er sandhedens modsætning."