# Non self-referential statement in answering truth-liers puzzles.

As it goes, there are knights, who always tell the truth, and knaves, who always right. Suppose, a question is that there are a knight and a knave, and we have to find out if a Statement S is true or not [0] .

So, instead of asking:

"What would the other guy reply if I asked if S is true ?" Or something like that

What's wrong, if I ask simply:

If you're a knight, then answer "Is S true ?" and if you're a knave, then reply "Is S false ?"

Then, (If I don't make any dumb mistake), that would tell the truth value of S.

What's wrong with that (If this is true, then this should answer any knight-knave puzzle like in condition X, there are knight and knaves, and you pick n randomly, and ask them yes/no questions to find truth about S ?

0: S has no reference to knight/knaves, just casual ones like "This island contains treasure", "X is the correct maps", not meta ones like "This statement is false" or "I am a knave" (His head will explode if he says it)

• "Knaves, who always right"? Was "right" a typo for "lie"?
– bof
Oct 22, 2016 at 7:23
• There are plenty of similar questions on the puzzling site. See e.g. here Oct 22, 2016 at 7:26
• Your solution sounds good to me. Maybe you could put it a little bit more clearly/elegantly (or maybe not) by asking: "Is it the case that you are a knight and the island contains treasure, or else you are a knave and the island contains no treasure" or "Is it the case that you are a knight if and only if the island contains treasure".
– bof
Oct 22, 2016 at 7:26
• I think your solution is considered "cheating". It's a command and not a statement and they are answering different questions. You might as well say "If you are a knight stamp your feet. If you are knave wave your hands." I suppose someone can argue that when a knave "lies" it means they are dishonest. "If you are knight answer "What color is the sky"; if you are a knave answer "what texture is a bunny"". The knave would "lie" and answer the knight question and answer "green". Or not. It really depends an the rules. Oct 22, 2016 at 7:52
• Actually the solution to all knight/knave questions is: "If I asked you X what would you answer?" Knights would be honest and tell you that that will give the right answer. knaves will lie and tell you they will give you the right answer. Oct 22, 2016 at 7:55

## 1 Answer

While it's logically sound reasoning, the problem is that it's not posed as a question. The proper way to phrase it is

Is it true that either $$S$$ and you are a knight or $$\neg S$$ and you are a knave?

This will always return the truth value of $$S$$.