## 163. The Court.

In the language of the tribe inhabiting the island located not far from the island of zombies, the words "bal" and "da" mean "yes" and "no," but words that sound the same do not necessarily have the same meaning. Some of the island's inhabitants answer questions with "bal" and "da," while others, breaking an ancient taboo, prefer to speak English (and answer with "yes" and "no").

For some unexplained reasons, all members of any family on this island are of the same type. In particular, any two brothers are either both zombies or both humans.

One of the island's natives has been accused of treason. Given the particular importance of the case, it was decided to call Inspector Craig from London. The three main witnesses, A, B, and C, were natives of the island. The following excerpt is taken from the court transcript. The questioning of the witnesses is conducted by Inspector Craig.

Question (to witness A). Is the defendant not guilty? Answer (from witness A). Bal.

Question (to witness B). What does "bal" mean?

Answer (from witness B). "Bal" means "yes."

Question (to witness C). Are witnesses A and B brothers?

Answer (from witness C). No.

Second question (to witness C). Is the defendant not guilty?

Answer (from witness C). Yes.

Is the defendant guilty or not guilty?
163. First, I will prove that witness C cannot be a zombie. Suppose that C is a zombie. Then A and B must be brothers. Therefore, they are either both zombies or both humans. Suppose A and B are humans. Then "bal" means "yes," so A gave an affirmative answer to the question of whether the defendant is guilty. Therefore, the defendant is not guilty. Now suppose A and B are zombies. Then "bal" means "no," and since A is a zombie and gives a negative answer to the question of whether the defendant is guilty, the defendant is not guilty. Thus, if C is a zombie, the defendant is not guilty (regardless of whether A and B are zombies or humans). On the other hand, if C is a zombie, the defendant must be guilty, since C claims the defendant is not guilty, leading to a contradiction. Therefore, C cannot be a zombie, and thus C is a human. Since C claims the defendant is not guilty, the defendant is indeed not guilty.