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In these pairs, are the ones containg である simply more formal? I think I've
seen both in writing.
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2015-08-07T22:28:25.473
26252
2015-08-08T00:22:27.070
9971
question
word-choice words written-language
であるので and であるのだ vs なので and なのだ
Basically, yes. To be a bit more strict about "formal", I'd rather say it
"objective" (vs "subjective"). That is, we hardly even use のだ when we have
informal speech.

Another point to notice is about であるのだ. The permissive range would be quite
narrow if you're going to end a sentence with it. Because, the overall mood of
a sentence is decided by the sentence-final particles, whereas であるのだ has だ in
its end right after である, which creates such a dissonance on how much formality
or subjectivity is intended, unless ～である is a part of some maxim, proverb or
solid fact. If you want the sentence to have an overall objective tone, try
なのである (であるのである is not ungrammatical, but a bit of a mouthful, you know...).
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2015-08-08T00:22:27.070
26253
2015-08-08T00:22:27.070
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answer