You’ve discovered a doorway to another realm, and now you and your brother are off exploring the wonderful world of Paradoxica. Fantastically paradoxical creatures crawl, run, and fly around you. And then you see the troll.
你發現一個 通往另一國度的出入口, 現在你和你的兄弟 出發前往奇妙的悖論世界探險。 奇異的悖論動物在你四周 爬行、奔跑和飛行。 然後你看到巨人, 牠正用一個極大的網子 捕捉所有的動物。
It’s catching all the creatures in an enormous net. You bravely step forward and demand it let them go. The troll laughs. “If you’re such a fan of paradoxes,” it says, “then I’ll make you an offer. If you say something true, I’ll release all these creatures." You’re about to say, “You are a troll,” but before you can, the troll grabs your brother. “If you say something false,” he continues, “then I’ll release your brother." Your statement can only be a single sentence. And as you can see, I hate paradoxes more than anything. If you try to cheat by saying something paradoxical, like, ‘this statement is false,’ then I'll eat your brother and the creatures."
你勇敢地走向前 要求牠釋放牠們。 巨人大笑,牠說: 「若你真是個悖論迷的話, 那麼我給你一個交換條件, 如果你說真話, 我就釋放所有動物。」 當你正要說:「你是個巨人。」 但話還沒出口, 巨人就抓起你的兄弟。 牠又說:「如果你說假話, 那我會放你兄弟。 你的話只能是單一句子。 如你所見,我最討厭悖論。 假如你試圖 說些矛盾的話來蒙騙我, 例如『這話是假的。』 那麼我會吃掉你兄弟和動物。」 你能說出哪句真/假的話,
What true/false statement can you say to force the troll to free your brother and the paradoxical creatures?
迫使巨人釋放你兄弟和悖論動物呢?
[Pause the video now if you want to figure it out for yourself!]
假如你想自己解解看, 現在將影片暫停。
Answer in: 3
答案即將公佈:3
Answer in: 2
答案即將公佈:2
Answer in: 1
答案即將公佈:1
This seems like an impossible situation, but incredibly, you can say something that will force the troll to release all its prisoners. This is an example of coercive logic, invented by the great logician and puzzle creator Raymond Smullyan.
這似乎是個不可能的任務, 但很奇妙地,你是可以說個 迫使巨人釋放所有囚犯的話。 這是個「強迫邏輯」的例子, 是由偉大的邏輯學家 及益智遊戲創造家 雷德蒙·斯穆里安發明的。
The trick Smullyan came up with involves saying a statement whose truth or falseness depends on what you want the troll to do.
斯穆里安提出解謎的訣竅 在於所用的句子是真或假
Your statement still has to be carefully crafted. For example, if you were to say, “You are going to free the creatures and my brother,” the troll could respond, “that’s false… I’m only going to free your brother.” Similarly, if you said, “You will free the paradoxes,” the troll could say, “That’s true,” and free the paradoxes.
是依你希望巨人做什麼而定。 你仍須小心斟酌所說的話。 例如,假如你說: 「你會放動物和我的兄弟。」 巨人可能回答: 「錯了…… 我只會放你兄弟。」 同樣地,若你說: 「你會放悖論動物。」 巨人可能說:「那是真的。」 然後釋放悖論動物。
But watch what happens if you say, “You will free my brother.”
但注意以下會發生什麼事, 假如你說:「你會放我兄弟。」
The statement can’t be false, because if it were, the troll, by its own rules, would have to free your brother. That would make the statement paradoxically true and false. But the troll hates paradoxes and would never willingly create one. So his only option is for the statement to be true. If “you will free my brother” is true, then the troll has to release your brother. And by its own rules, the troll has to free the creatures as well, since you said a true statement. By wielding just 5 words like a logical scalpel, you’ve forced the troll to free all its prisoners.
這句話不可能是假的, 因為如果是假的, 根據牠自己的規則, 牠就必須釋放你的兄弟。 那會使得那句話自相矛盾。 但巨人討厭悖論 且絕不願意去創造一個。 所以牠唯一的選擇 是把這句當真。 假如「你會放我兄弟」是真的, 那麼巨人必須釋放你的兄弟。 根據牠的規則 巨人也須釋放動物, 因為你說了一句真話。 僅用五個字, 如同用邏輯手術刀般, 你已迫使巨人釋放所有囚犯。
As the troll stomps off in anger, the paradoxes cheer you for winning them their freedom, and promise to lead you to the treasure at the top of the stairs. If you can reach it.
當巨人怒氣沖沖跺步離去, 悖論動物為你贏得牠們的自由喝彩, 而且答應帶你去拿樓梯頂端的寶藏, 只要你到得了的話。