| A book of logic puzzles by Raymond Smullyan. Many of the puzzles involve reasoners on the island of knights who always tell the truth and knaves who always lie.
For example, if a native of the island says to a reasoner "You will never know that I am a knight", the reasoner (if she hears the statement and is sufficiently self-aware) will think the following.
"If he's a knave, then I will know he's a knight, but I can't know something false, so he must be a knight. Now I know he's a knight, which makes his statement false, so he must be a knave."
Now the reasoner believes both that the native is a knight and that he is a knave. She has become inconsistent. If the native had said "You will never believe that I am a knight" instead, things get more complicated, and it turns out that the reasoner cannot believe the native to be either a knight or a knave without becoming inconsistent. This is analogous to Godel's theorem and the statement "I am not provable in axiomatic system S".
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