Philosophy First of All, Because Essay

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Assuming that a 'plain' letter represents knighthood but a ~ represents being a knave representations go as follows.

Representation;

A: Alice says at least one of them is a knight.

B: All knights tell the truth

C. If Alice is a knight then at least one of them must be a knight, and Alice must be one of the knights.

C: The oracle always tells the truth

D: The oracle says if there is one knight, there are at least two knights and if Sam is a knight, then Alice is a knave or Bob is a knight.

E: Alice cannot be a knave or all are knaves.

F. If Bob is a knight either Sam or Alice must be a knave

G. Alice cannot be a knave if Bob is a knight, as Alice's statement must be valid.

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H. Sam must be a knave.

I. Bob must be a knight.

So a, B, ~S or all are knaves

All three cannot be knights, as this would make Bob's statement that either Sam or Alice is a knave inaccurate, and knights tell the truth. However, all could be knaves because the oracle's statements are dependant upon two being knights, and Bob and Alice's statements are invalid if they are both knaves -- none of them are knights (invalidating Alice's statement, as she is then a knave and knaves always lie) and if all are knaves, not 'either' Sam or Alice, as Bob….....

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