Logic puzzle about knights and knaves

Joe asked:

The philosopher chose the correct door and safely entered the Inner Sanctum. Seated on two diamond thrones were the two greatest priests in the entire universe. It is possible that at least one of them knew the answer to the Great Question: ‘Why is there something instead of nothing?’.

Of course, each of the two great priests was either a knight or a knave. (Whether they were human or monkey is not relevant.) So we do not know of either whether he is a knight or a knave, or whether he knows the answer to the Great Question. The two priests made the following statements:

First Priest: I am a knave, and I don’t know why there is something instead of nothing.

Second Priest: I am a knight, and I don’t know why there is something instead of nothing.

Did either of the priests really know why there is something rather than nothing?

Answer by Craig Skinner

Yes. The first priest really knows; we can’t say as regards the second priest.

In this kind of logic puzzle, the two rules are: 1. Knaves always lie, knights always tell the truth. 2. A statement is a lie if part (or all) of it is a lie (so part of a lying statement may be true)

First priest can’t be a knight (a knight can’t say ‘I am a knave’). So he is a knave. So his statement must be a lie. But the first part is true (he is a knave), so the second part must be false. So he really does know why there is something instead of nothing.

The second priest could be:

(a) a knight who doesn’t know why there is something instead of nothing (the statement is true) (b) a knave who doesn’t know why there is something instead of nothing (first part of statement false) (c) a knave who does know why there is something instead of nothing (all of statement false).

This is one of many logical puzzles found in the Penguin book What is the Name of this Book? (1990) by the logician and magician Raymond Smullyan. They are all good fun, help you to think straight, but are of limited value for systematic learning of either symbolic logic or philosophical logic.

2 thoughts on “Logic puzzle about knights and knaves

  1. No. A knave always lies, but if part of a statement is a lie, this counts as a lie. So she can say, for example, “I am a knave and grass is red” (second half a lie), but she cant say “I am a knave and grass is green”. Of course she can say “I am a knight and grass is green”(first half a lie) or “I am a knight and grass is red” (both parts a lie).
    Yes, a knight must say “I am a knight” if he comments on what he is.

    Craig Skinner

  2. ‘I am a knave’ is an impossible statement because if knaves always lie then this knave must say: ‘I am a knight’. The knight, always telling the truth, must also say, ‘I am a knight’.

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