Jul

28

My friend Russ Sears and I were talking, and he was differentiating between "crooks" who behave with rational motives and "pathological liars."

He told me, "in 6th Grade I had a friend that was a pathological liar. He would lie even when telling the truth would have been more beneficial to him. He simply could not help himself, when he was asked a question he had to lie. He had a platform to showcase his "talent" and he could not tell the truth no matter what."

Without regard to whether politicians are necessarily pathological liars, his 6th grade friend brings to mind Smullyan's "Knights and Knaves " logic puzzle — which (as opposed to a meal for a lifetime) can cause indigestion for a lifetime. That is because a pathological liar is vastly preferable to an "alternator" who alternates between lying and telling the truth; and is also preferable to a "normal" who says whatever they want.

Knights and Knaves is a type of logic puzzle devised by Raymond Smullyan.

On a fictional island, all inhabitants are either knights, who always tell the truth, or knaves, who always lie. The puzzles involve a visitor to the island who meets small groups of inhabitants. Usually the aim is for the visitor to deduce the inhabitants' type from their statements, but some puzzles of this type ask for other facts to be deduced. The puzzle may also be to determine a yes/no question which the visitor can ask in order to discover what he needs to know.An early example of this type of puzzle involves three inhabitants referred to as A, B and C. The visitor asks A what type he is, but does not hear A's answer. B then says "A said that he is a knave" and C says "Don't believe B: he is lying!" To solve the puzzle, note that no inhabitant can say that he is a knave. Therefore B's statement must be untrue, so he is a knave, making C's statement true, so he is a knight. Since A's answer invariably would be "I'm a knight", it is not possible to determine whether A is a knight or knave from the information provided.In some variations, inhabitants may also be alternators, who alternate between lying and telling the truth, or normals, who can say whatever they want (as in the case of Knight/Knave/Spy puzzles).

A further complication is that the inhabitants may answer yes/no questions in their own language, and the visitor knows that "bal" and "da" mean "yes" and "no" but does not know which is which. These types of puzzles were a major inspiration for what has become known as "the hardest logic puzzle ever".


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