（よ）うではないか details
write + let's + let us
kakou de wa nai ka
let us; come, let's — a call addressed to a group
meaning: let us write
この問題については、もう一度みんなで考えようではないか。
kono mondai ni tsuite wa, mou ichido minna de kangaeyou de wa nai ka.
On this problem, let us think once more as a group. neutral
つまらないことで争うのはやめて、そろそろ仲直りしようじゃないか。
tsumaranai koto de arasou no wa yamete, sorosoro nakanaori shiyou ja nai ka.
Let's stop squabbling over nothing and make up. casual
- contraction
- polite
Examples
let us — a rallying call urging a group to act together
この問題については、もう一度みんなで考えようではないか。
kono mondai ni tsuite wa, mou ichido minna de kangaeyoudehanaika.
On this problem, let us think once more as a group. neutral
つまらないことで争うのはやめて、そろそろ仲直りしようじゃないか。
tsumaranai koto de arasou no wa yamete, sorosoro nakanaori shiyou ja nai ka.
Let's stop squabbling over nothing and make up. casual
皆様、力を合わせてこの困難を乗り越えようではありませんか。
minasama, chikara o awasete kono konnan o norikoeyou de wa arimasen ka.
Everyone, let us join forces and come through this difficulty. formal
Formation
{V-volitional}ではないかattaches to volitional
Variant notes
- （よ）うじゃないか — では→じゃ — the same call in blunt, back-slapping speech (やってみようじゃないか), where it can also read as a challenge rather than an invitation.
Notes
a moment of decision — a podium, an editorial, a locker room — never at one
person you are inviting along.
Related patterns
Similar
ましょう proposes a joint action between the people present (行きましょう); （よ）うではないか addresses a group as a body and belongs to speeches, editorials and pep talks — it is not what you say to one colleague about lunch.
ませんか genuinely asks and leaves the listener a clean refusal; the か here is rhetorical and expects assent, so the two are not one utterance at two politeness levels — declining a （よ）うではないか takes an argument, not a "すみません".
Lookalikes
ようではないか parses two ways, and only what precedes よう decides which — a verb stem makes it the volitional exhortation (考えようではないか), while a noun＋の, a na-adjective＋な or a plain clause makes it ようだ (まるで病気のようではないか, "doesn't it look like…?").