Monday, February 13, 2017

The Second Trial (Some Unusual Knights and Knaves Part II)

Another suspect was arrested and brought to trial. Here is a transcript of the trial:

CRAIG: The last suspect was a queer bird; he actually claimed to be Arthur York! Did you ever claim to be Arthur York?
DEFENDANT: No.
CRAIG: Did you ever claim that you are not Arthur York?
DEFENDANT: Yes.

Craig's first guess was that the defendant was not Arthur York, but are there really sufficient grounds for acquitting him?
(Source: To Mock a Mockingbird and Other Logic Puzzles: Including an Amazing Adventure in Combinatory Logic by Raymond Smullyan)

If the defendant is a knight, then the issue of deciding whether he is Arthur York is as simple as taking his words at face value, which would mean he is not Arthur York. If, however, he is a knave, then he is lying about his claim that he never claimed to be Arthur York. This would mean that the defendant claimed to be Arthur York in the past but is lying. So he is not Arthur York. This impression is confirmed by the defendant's claim that he claimed he is not Arthur York in the past. If he is a knave, what that would really mean is that he did not ever claim he was Arthur York in the past. That's good for completing the case that the defendant is not Arthur York, because any claim by a knave defendant that he is not Arthur York would of course be false. Fortunately no such claim has been made and we can let this defendant off the hook for the unnamed crime York was accused of (although possibly not for perjury).

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