1 / 4

Island of Knights and Knaves

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.

ardith
Download Presentation

Island of Knights and Knaves

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 tablestatement: “ I am a knave, or Jill is a knight.”

  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.

More Related