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Historically where did all of these different forms arise, and when are they used? I noticed that だ and である both have their place in different 文法形, what is the difference in their meaning? I know that in things like 論文 as well as, apparently, on Wikipedia である is used, but I really don't know why.

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Related: Where does です come from? – Darius Jahandarie Jul 20 '13 at 1:25
To add to the confusion, and to give some perspective, Japanese has accumulated even more copulas over its history, eg なり(=に+あり), たり(と+あり). Today, these sound archaic. – blutorange Aug 19 '13 at 4:30

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だ is a reduced form of である, which is itself a reduction of にてある (the particle で was originally にて). です is a reduced form of であります. As far as we can tell, the copular verb ('to be X') in Japonic has pretty much always been locative particle + ある. In Old Japanese it was なり (a reduction of にあり, back when あり was the 終止形), and in the Ryukyuan languages it tends to be something similar to ya- (probably にあり minus the n instead of the i). Pretty much all of Japanese has since replaced the に with で, but depending on where you are である can be reduced to any of だ, や or じゃ.

である tends to sound more formal and literary than だ/です. My guess is that its usefulness derives from the fact that sounds neither informal (like だ would be) nor deferential (like です would be), and is thus a useful alternative when 'talking to nobody', as it were - you'd use it when writing some sort of impersonal work (non-fiction or maybe third-person-narrator fiction), you'd never use it when speaking.

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cool - does this mean でござる/ございます was never involved in the history of the coupla except as a polite alternative? – jlptnone Jul 19 '13 at 18:52
Another difference between である and だ/です that the former retains more of its verbal properties and can be used as a 連体形 . For example, you can say 「ご本人であることの確認書類」, but not *「ご本人(だ・です)ことの確認書類」 – blutorange Jul 19 '13 at 21:52
Also, I've seen different theories about the history of です, would anybody have any credible sources (recent papers?) The 日本国語大辞典 considers it a contraction of でさうらふ(候)->でさう or でござります, kojien as well. Daijisen says 「で候」「でおはす」「でございます」「であります」など諸説ある Or I wonder, has it origin been lost in the mist of time, and perhaps all these words contributed to the contraction です? – blutorange Jul 19 '13 at 22:00
There are a number of theories for the origins of です, but we don't know for sure which is correct. – snailboat Jul 19 '13 at 22:00
"you'd never use (である) when speaking"?? People do use it in speaking if not in casual chitchat. – l'électeur Feb 12 '14 at 6:01

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