“I am not a liar.” - Everbody

Part 1

There are three brothers: John, James and William. One day you meet one of them on the street and you want to know which of the brothers he is. You are allowed to ask him one question answerable by yes or no.

  1. John and James always lie. William always tells the truth. You wish to find out whether is he John.
  2. Now John and James always tell the truth, and William always lie. You wish to find out whether he is John.

Part 2

There are now only two brothers. One of them is called Arthur. One of them always lie and the other always tells the truth. One day you meet the two brothers together. You are allowed to ask one of them one question answerable by yes or no.

  1. You want to find out which one is Authur.
  2. You want to find out whether Arthur is the liar or the truth-teller.
  3. You want to find out which of the brothers you meet is the liar and truth-teller.
  4. Force the brother to answer “yes”

Solution

What if I tell you the there is a generic way to solve the different scenarios above? The key is self referential statements. That is the same principle that resulted in the Russell’s Paradox.

All of the above can be solved using the Nelson Goodman principle. It is a method invented by philosopher Nelson Goodman. Given an individual that always lies or always tells the truth, and given any proposition P whose truth or falsity you with to determine and whose truth or falsity is known by the individual, there is a way of determining this by asking one yes/no question.

Are you the type that would claim that P is true.

Both liar and truth teller will always give the correct answer.