# About Knights and Knaves and their consistency

On an Island of Knights and Knaves (where Knights always tell the truth and Knaves always lie), a Knight will never contradict himself unless some true fact changes. I was wondering: can a Knave contradict himself (regarding presently unchanging facts)? If he did wouldn't that mean he told the truth about 'something'?

• We're going to need to know more about the problem you're referring to. How is a 'knave' supposed to respond in this context? – Aza Sep 28 '14 at 6:44
• Can a Knave say some statement at say ,12 noon today and then some 'time' later say something that contradicts what he just said at 12 noon 'earlier' today? – user128932 Sep 29 '14 at 1:23
• This is only interesting if your knave is restricted to yes and no. Asked what is 2+2, he could say 3 one minute and 5 the next, which contradict while not requiring any truth telling. – Kate Gregory Oct 8 '14 at 13:47

A knave can contradict himself easily.

- Is the sky blue?
- No.
- Did you just answer no?
- No.

For example, let's take a set of facts:
Fact A, which is FALSE
Fact B, which is TRUE

If you ask a knave "what is A?" he would answer TRUE. Then "what is B?" - he would answer FALSE.
Then ask what A AND B is. He would answer TRUE (FALSE AND TRUE = FALSE).
But combining his previous answers logician would conclude that A AND B = FALSE (TRUE AND FALSE = FALSE).

• If you asked a Knave for two statements that contradict each other how might he answer? – user128932 Sep 29 '14 at 1:27
• @user128932, I do not know. Why would I ask him about statements? Usually you ask knaves about facts, which is not defined (can be true or false) and therefore can not contradict each other. – klm123 Sep 29 '14 at 6:18
• I mean if you ask a Knave to make two statement ( about info. he is aware of) and the two statements have to contradict each other could he do this? – user128932 Sep 30 '14 at 3:12
• @user128932, it depends on model of Knaves. In standard model they do not follow your wishes, just answer questions. – klm123 Sep 30 '14 at 6:22

The 'sky is red' and the 'sky is green' are contradictory, but don't require the speaker to be truthful at any point.

My friend suggested another interesting idea to answer this question.
Contradict himself means to say something illogical, independently of the perception of the reality. For example, "sky is not blue" would not be contradiction, may be our Knave is colorblind, or just crazy. But must leave here a criteria for what is logical and what is not anyway. So the logic provides us a facts, which are postulated to be true for all people.

Therefore one question is enough, just ask something like "Does A is true if and only if A is true?". Since the Knave should use the same logic as we do (otherwise it would not be a Knave in our definition), he will answer "No", and this way we would understand immediately that it is a Knave.

If we take general definition of the word: "contradiction is a situation in which inconsistent elements are present.". We can see that to contradict himself one need to say a set of statement, which can not be all true simultaneously (because of logic). Sometimes to create such a conditions one statement is enough.

• Do you mean by saying 'no' to this question the knave is contadicting himself? – user128932 Oct 6 '14 at 20:27
• @user128932, yes. – klm123 Oct 6 '14 at 20:54
• But wouldn't that imply he answered something similar to that question before in a different way? How could someone contradict themselves about 'something' if they only ever said one statement about that 'something'? – user128932 Oct 8 '14 at 6:17
• @user128932, in general sence "contradiction is a situation in which inconsistent elements are present.". To contradict himself one need to say a set of statement, which can not be all true simultaneously (because of logic). Sometimes to create such a conditions one statement is enough. – klm123 Oct 8 '14 at 6:27
• Does contradict 'mean' to say something ('dict' from a similar root to 'diction') that is 'against' ( or 'contra-') something? How can you say one statement that is against itself; isn't that just saying a paradoxical statement? If a set of statements that are not all true simutaneously is a set with just one statement then that one statement would be false ; is that right? – user128932 Oct 8 '14 at 6:39