不无 / 不可不 / 无不: written double negatives
特殊句型 / special sentence patterns
Tone colorsā tone 1á tone 2ǎ tone 3à tone 4a neutral
Formal Chinese loves double negatives to nuance or strengthen:
• 不无 + N ("not without") = some: 不无道理 (not without reason), 不无遗憾 (not without regret). → softens.
• 不可不 + V ("cannot not") = must: 不可不防 (you must guard against it). → strengthens.
• 无不 + V ("none who doesn't") = all without exception: 听众无不感动 (the whole audience was moved). → strengthens.
Think of English "not without", "one cannot fail to".
Examples
他的批评虽然尖锐，但不无道理。
Tā de pīpíng suīrán jiānruì, dàn bù wú dàolǐ.His criticism is sharp, but not without merit.
网络上的个人信息安全问题，不可不重视。
Wǎngluò shang de gèrén xìnxī ānquán wèntí, bù kě bù zhòngshì.Online personal data security is something we cannot fail to take seriously.
听了这个判决，在场的人无不感到意外。
Tīng le zhège pànjué, zài chǎng de rén wú bù gǎndào yìwài.Hearing the verdict, everyone present was surprised.
Common mistakes
✗ Reading 不无道理 as "no sense": it's the opposite, "some sense".
✗ 无不 + another negation: ✗ 无不不感动 → one double negative is enough.