"Don't despair," said Craig to the chief of the island police, "we may find our man yet!"
Well, a third suspect was arrested and brought to trial. He brought with him his defense attorney, and the two made the following statements in court.
DEFENSE ATTORNEY: My client is indeed a knave, but he is not Arthur York.
DEFENDANT: My attorney always tells the truth!
Is there enough evidence either to acquit or convict the defendant?(Source: To Mock a Mockingbird and Other Logic Puzzles: Including an Amazing Adventure in Combinatory Logic by Raymond Smullyan)
If the defense attorney is a knight, then it is the case that the defendant is a knave. Then the defendant's claim that his attorney always tell the truth (i.e. is a knight) is false, which means that the defense attorney is actually a knave! There is a contradiction here and the defense attorney cannot be a knight.
When I initially tried to solved this, my reasoning was that the defense attorney could not be a knave either, and no verdict could be attained. This conclusion was based on the belief that, for the defense attorney to be a knave, both conjuncts of the statement "My client is indeed a knave, but he is not Arthur York" would have to be false. In other words, "My client is indeed a knave" and "He is not Arthur York" would both have to be false. This assumption would lead to another contradiction: "My client is indeed a knave" would mean that the defendant is actually a knight, which would in turn mean that the defense attorney is a knight.
But in Smullyan's knights and knaves puzzles, being a knave really has the weaker meaning that at least one of the conjuncts of an "and" statement—"but" is a form of "and"—is false, though not necessarily both. In this case, the first conjunct of his statement is true (i.e., the defendant is a knave) but the second must then be false. This means the defendant is in fact Arthur York.
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