That sentence is impossible for anyone on that island to say—if they worship Satan they can’t say it because it would be true, and if they worship God they can’t say it because it would be false. On the other hand, both can (and would) say they worship God.
I actually thought about including that: similarly, in American logic, you can’t take an arbitrary claim P and come up with a sentence S such that you can derive P from “S is true” and also from “S is false”.
I found a different solution to the initial puzzle, which I won’t spoil here, but post as a follow-on:
Same scenario, except after you hear the statement, you know the person is single—but you don’t know who they worship!
What was the statement?
My solution (rot13′d): “Vs lbh nfxrq zr vs V nz fvatyr, V jbhyq fnl lrf”
This is the Godel Escher Bach solution :)
I like it!
I didn’t think of that one!
“I’m a rationalist.”
JKJK
“I am single if and only if I worship God.”
If I worship God, then the sentence reduces to “I am single”, and since I worship God, it must be true.
If I worship Satan, it reduces to “I am not single”, and since I worship Satan, it must be false.
That was my solution.
This was my solution! :)
Oh, I thought that was the version in the post. So I guess my solution to the post version is also my solution here.
“V jbefuvc fngna naq V’z zneevrq.” ?
That sentence is impossible for anyone on that island to say—if they worship Satan they can’t say it because it would be true, and if they worship God they can’t say it because it would be false. On the other hand, both can (and would) say they worship God.
A single satanist could say it.
Oh, right, if you treat it as one statement then it’s possible. But then it fails the modified question because you discover who they worship.
I actually thought about including that: similarly, in American logic, you can’t take an arbitrary claim P and come up with a sentence S such that you can derive P from “S is true” and also from “S is false”.
“I worship God XOR I am married.”
rot13
Jnf lbhe nafjre fbzrguvat nybat gur yvarf bs “V jbefuvc Tbq be V nz zneevrq, ohg abg obgu”?