Imagine you and your brother have stumbled upon a magical doorway that leads to a mysterious world called Paradoxica. This place is filled with amazing creatures that crawl, run, and fly all around you. Suddenly, you notice a troll capturing all these creatures with a giant net. You bravely step up and demand that the troll let them go.
The troll chuckles and says, “If you love paradoxes so much, I’ll give you a challenge. If you say something true, I’ll release all the creatures.” Just as you’re about to say, “You are a troll,” the troll grabs your brother and adds, “If you say something false, I’ll release your brother.” But there’s a catch: your statement can only be one sentence, and if you try to trick the troll with a paradox, it will eat your brother and the creatures.
This seems like an impossible situation, but there’s a clever way to make the troll release everyone. This puzzle is an example of something called coercive logic, a concept created by the famous logician and puzzle maker Raymond Smullyan. The key is to say something that forces the troll to do what you want.
Your statement must be carefully thought out. For instance, if you say, “You are going to free the creatures and my brother,” the troll could simply say, “That’s false… I’m only going to free your brother.” Or if you say, “You will free the paradoxes,” the troll might say, “That’s true,” and only release the paradoxes.
Here’s the trick: say, “You will free my brother.” This statement can’t be false because if it were, the troll would have to release your brother according to its own rules, creating a paradox. But the troll hates paradoxes and won’t create one on purpose. So, the only option is for the statement to be true. If “you will free my brother” is true, then the troll must release your brother. And since you said something true, the troll also has to free the creatures.
With just five words, you’ve cleverly forced the troll to release all its captives. As the troll stomps away angrily, the creatures cheer for you, grateful for their freedom. They even promise to lead you to a treasure at the top of the stairs, if you can reach it.
Imagine you are in Paradoxica and have to outsmart a troll with a clever statement. Write your own one-sentence paradox that would force the troll to release everyone. Share it with your classmates and discuss why it would work.
In groups, act out the scenario where one of you is the troll and the others are trying to save the creatures and the brother. Use different statements and see how the troll reacts. Discuss which statements work best and why.
Create a logic puzzle similar to the troll’s challenge. Use coercive logic to design a scenario where the solution involves a clever statement. Exchange puzzles with classmates and try to solve each other’s challenges.
Research more about Raymond Smullyan and his famous puzzles. Choose one puzzle that you find interesting and present it to the class. Explain the logic behind the puzzle and how it relates to the troll’s challenge.
Write a short story set in Paradoxica where you encounter another creature with a tricky challenge. Use your knowledge of paradoxes and logic to solve the problem in your story. Share your story with the class.
You’ve discovered a doorway to another realm, and now you and your brother are off exploring the wonderful world of Paradoxica. Fascinating creatures crawl, run, and fly around you. Then you see a troll 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. The troll warns that if you try to cheat by saying something paradoxical, it will eat your brother and the creatures.
What true/false statement can you say to force the troll to free your brother and the creatures? [Pause the video now if you want to figure it out for yourself!]
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. The trick involves saying a statement whose truth or falseness depends on what you want the troll to do.
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.
But watch what happens if you say, “You will free my brother.” 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 its 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 five words like a logical scalpel, you’ve forced the troll to free all its prisoners. As the troll stomps off in anger, the creatures 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.
Troll – A mythical creature often depicted as a giant or dwarf, known for causing trouble or being mischievous. – In the story, the troll tried to trick the travelers by asking them confusing questions.
Creatures – Living beings, often used to describe animals or mythical beings in stories. – The philosopher asked us to imagine a world where all creatures could speak and share their thoughts.
Paradoxes – Statements or situations that seem to contradict themselves but may reveal a deeper truth. – The paradox of the liar is a classic example where a statement contradicts itself by claiming to be false.
Logic – A system of reasoning used to evaluate arguments and reach conclusions. – In our philosophy class, we learned how to use logic to solve complex problems.
Statement – A clear expression of something in speech or writing, often presenting a fact or opinion. – The teacher asked us to analyze the statement to determine if it was based on evidence or belief.
True – In accordance with fact or reality; not false or incorrect. – It is true that critical thinking helps us make better decisions by evaluating information carefully.
False – Not in accordance with the truth or fact; incorrect. – The student realized that his assumption was false after reviewing the evidence presented in class.
Freedom – The power or right to act, speak, or think without hindrance or restraint. – Philosophers often debate the balance between freedom and responsibility in society.
Clever – Quick to understand, learn, and devise or apply ideas; intelligent. – The clever student used critical thinking to solve the puzzle that had stumped everyone else.
Challenge – A task or situation that tests someone’s abilities, often requiring effort and determination. – The challenge of understanding complex philosophical ideas can be rewarding and enlightening.
