Here are some of the famous language paradoxes. Inspect each carefully and strive to answer the questions asked. If you cannot answer these questions, explain why you think answering these questions are not possible.
1. Plato: Socrates is a liar.
Socrates: Plato speaks the truth.
Who is telling the truth?
All statements in this square are false.
Is this statement true or false?
3. Once upon a time there lived in a tiny kingdom a ruler named Vero. He was a good king and ruled his people with much wisdom. So concerned was the king with truth that he declared all those who told the truth and only those who told the truth would be allowed to live in his kingdom. At the gate to the kingdom Vero stationed a guard who was granted a most peculiar power; he was able to tell when someone was telling the truth and when someone was lying. To those who told the truth he graciously permitted entrance to the kingdom. But to those who lied he vigorously denied entrance. And with this procedure the little kingdom prospered greatly and the inhabitants lived together in peace and harmony.
One day a man came to the gate of the kingdom and before the guard could question him to determine whether he was a truth teller or a liar, the man said, "You are going to deny me admission to your kingdom?"
Should the guard grant or deny him entrance to the kingdom?
4. Statement A: Statement B is false.
Statement B: Statement A is true.
Which statement is true? Which statement is false?
5. In this small town there is one cook. This cook cooks for everyone who does not cook for himself. Who cooks for the cook?