Truth and slander, and how we see ourselves

Raymond Smullyan, in his book “5000 B.C. and Other Philosophical Fantasies,” posits the question of two identical twin brothers, one who always lies and the other who always tells the truth. Whatever is indeed true, the truth teller believes to be true; the liar’s responses are always false, such that whatever is true he will always believe to be false and whatever is false he will always assume is true. 

Thus, posits Smullyan, each brother will always give the same answer to the same question, but for different reasons: 

“For example, suppose you ask whether two plus two equals four. The accurate truth teller knows that it is and will truthfully answer yes. The inaccurate liar will believe that two plus two does not equal four (since he is inaccurate) and will then lie and say that it does; he will also answer yes.” (Much like the case in which a schizophrenic patient is being considered for release from a mental institution. Asked if he was Napoleon, he replied “no” and the lie detector showed that he was lying!)

Smullyan says that if meeting one of the two brothers alone, you would only need to ask one question: Is he the accurate truth teller? If he is, he will know that he is (since he is accurate) and truthfully will answer yes. If he is the inaccurate liar, he will believe that he is the accurate truth teller (since he is inaccurate in his beliefs), but then he will lie and say no. So the accurate truth teller will answer “yes” and the inaccurate liar will respond “no” to this question.

Even though the two brothers give the same answers to the same questions, by asking each of them, “Are you the accurate truth teller?” they are really being asked two different questions since the identical word “you” has a different reference for each of them.