Used to make invitations or proposals. Used for major events, as opposed to every day stuff (not sure how to distinguish between the two.)
lucinda lohmanoota
so nowadays this whole grammar would usually be "しようか?” like 行きましょうか? (conv) 行こうではないか? (formal)
dc
行きましょうか is used as conv and is not formal, just polite. 行く is not a good ex becuase the formal form is 参りましょうか(謙譲語_けんじょうご).
Miki
Basically 'violitional form verb + dehanaika'. Vしようではないか。 Much the same meaning as 'violitional form verb' + 'ka' Vしようか。 Presumably the former is a little less 'pushy'?
Amatuka
My Japanese teacher (native Japanese) told me that this wasn't used much in conversation, but frequently in things like politician's speeches (hence the "peaceful society" example I suppose). Not 100% sure on this, can anyone else back this up?
quobobo
quobobo, you are right. We don't often use 〜ようではないか in conversation nowadays. Instead, as dc mentioned above, しようか、しましょう are used. Even a politician say 「平和で住みやすい社会を 作りましょう!」on street. 作ろう じゃありませんか is also used in speech.
Miki
quobobo - you are right about it not being used much in normal conversation. I also want to add that this is used to suggest or call for something that is relatively important (e.g world peace) and not trivial / everyday matters such as what food to eat etc.