Peter or Paul

Peter and Paul are twin brothers. One of them (we don't know which) always lies. The other one always tells the truth. I ask one of them: "Is Paul the one that lies?" "Yes," he answers. Did I speak to Peter or Paul?

Answer:

I spoke to Peter. If a person always lies or alternately, always tells the truth, he cannot admit that he is lying (if this person were a liar, he would be telling the truth, and if this person were honest, he would be lying). Therefore, Paul could not have answered my question. Peter could answer about Paul without contradicting himself. What we don't know is who the liar is.