1. Island of Knights and Knaves Jack says: “At least one of us is a knave.” Question: Is Jack a knight or knave? What about Jill? Answer: If Jack is a knave, then none of them is a knave since his statement is not true. A contradiction. So Jack can’t be a knave. Jack is a knight, then Jill must be a knave since he tells the truth. No contradiction.

2. Disjunctive syllogism Jack says: “ I am a knave, or Jill is a knight.” Question: Is Jack a knave? Answer: No. If Jack is a knave, then his statement would be true. That can’t be since he is a knave. Jack must be a knight. Then Jill is also a knight, because what Jack said must be true. Disjunctive syllogism: p or q, but not p, so q. Not a paradox.

3. Truth table statement: “ I am a knave, or Jill is a knight.” JackJillStatementConclusion Knight Truepossible KnightKnaveFalseNot possible KnaveKnightTrueNot possible Knave TrueNot possible.

4. Barber example (paradox) Statement: In a small town [a closed community], there is a barber who shaves those and only those who do not shave themselves. Question: Who shaves the barber? Answer: If the barber shaves himself, then he cannot shave himself. On the other hand, if the barber does not shave himself, then he has to shave himself. Either case, it is a contradiction.