Philosophy concepts and theories

Philosophy

First of all, because knaves always lie, the words of the always-truthful oracle must be consulted first. It says that 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. The oracle states that if there is one knight, at least one of the two must be a knight. The oracle also says that of Sam is the knight, either Alice is a knave or Bob is a knight.

Now the words of the knights and knaves must be consulted. Bob says that "Either Sam or Alice is a knave!" So, from what Bob says: if Bob is a knight and knights always have a partner, either Sam is a knight or Alice is a knight. But Alice said that at least one of them is a knight, and if Alice was a knave, that would have to be a lie. So this means that if Bob is a knight, Sam is the knave and Alice is also a knight.

If Alice is a knave, then all of them would have to be knaves, to make her statement false. Bob said that either Sam or Alice are knaves, so he could be a knave, as if they were all knaves, that would make his statement false as well. Sam cannot be a knight because to make the oracle correct if Sam is a knight than Alice is a knave or Bob is a knight, so then all three must be knights. But Bob said that either Alice or Sam is a knave, and he cannot be a liar and a knight, again underlining the fact that Sam cannot be a knight.

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.