Inspector Craig of Scotland Yard-of whom you will read much in this book-was called to the Island of Knights and Knaves to help find a criminal named Arthur York. What made the process difficult was that it was not known whether Arthur York was a knight or a knave.(Source: To Mock a Mockingbird and Other Logic Puzzles: Including an Amazing Adventure in Combinatory Logic by Raymond Smullyan)
One suspect was arrested and brought to trial. Inspector Craig was the presiding judge. Here is a transcript of the trial:
CRAIG: What do you know about Arthur York?
DEFENDANT: Arthur York once claimed that I was a knave.
CRAIG: Are you by any chance Arthur York?
DEFENDANT: Yes.
Is the defendant Arthur York?
If the defendant is Arthur York, then, if he is a knight, he would not have claimed that he is a knave (even in the third person). If, on the other hand, he is a knave, then he would have not claimed this of himself either. It's not clear whether Arthur York is a knight or a knave, but in either case the defendant isn't Arthur York.
He can't be a knight. If he were, then when he answers the second question, he would have to be telling the truth. But that would mean he is Arthur York, and as you have pointed out, he can't be Arthur York. So he has to be a knave.
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