であるので and であるのだ vs なので and なのだ

Question

In these pairs, are the ones containg である simply more formal? I think I've seen both in writing.

Answer 1

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...).