Both Knaves

Logic Level 1

On an island, there are only 2 types of people: knights who only tell the truth and knaves who always lie.

Interestingly, no islander can ever make the statement "I am a knave."

However, can a married islander make this statement?

"My wife and I are both knaves."

Note that this is considered a single statement that is either true (as a whole statement) or false (as a whole statement).

Yes No

11 solutions

Kaushik Chandra
Jun 16, 2017

The islander might be a knave and her wife may be a knight.

He said that ' Both He and his wife are knaves ' which can be incorrect if wife is a knight. And it also proves that the Husband is a knave.

Moderator note:

Interpreted mathematically, the statement "My wife and I are both knaves" can be broken apart such that $A$ is the statement "I am a knave," $B$ is the statement "My wife is a knave," and the combined statement is simply $A \wedge B$ (that is. A AND B).

An AND statement in logic is true if and only if both parts are true. In truth table format:

$A$	$B$	$A \wedge B$
T	T	T
T	F	F
F	T	F
F	F	F

Therefore, while "I am a knave" is impossible for a knave to say as an individual statement, they can do it as long as they simultaneously claim something that's false.

I agree answer should be no because he calls himself a knave. If he is a knight then he is lying and if he is a knave then he is claiming to be a knave which knave can it do.

Jose Marquez - 3 years, 11 months ago

This problems seems kinda self contradictory.

Anuj Shikarkhane - 3 years, 11 months ago

Well...what if a partial lie within a statement means that the entire statement is a lie? Then it won't matter what he says about himself. If, within a single sentence, he lies about his wife, then if that's a partial lie, it would allow him to say whatever he wants about himself, I think. A knave never admits to being a knave, but he can says a lie about his wife...so if his wife were a knight and he a knave, he'd be lying about her but allowing himself to claim himself a knave.

But on the surface of what's simply written in the problem above, the answer should be "no".

David Smolar - 3 years, 11 months ago

In the logical statement A AND B, the statement is true if and only if both A and true and B is true. It is false in any of these cases: A is false; B is false; or both A and B are false.

Jason Dyer Staff - 3 years, 11 months ago

@Matthew Pharr It is not sufficient for him to lie. He has to deny his knave identity too.

Dimitri Boscainos - 3 years, 11 months ago

can there be a moment when a knave considers himself as a knight?

Shreya bheemarasetti - 3 years, 11 months ago

That raises the philosophical or psychological question of whether the knave is honest with himself.

Richard Desper - 3 years, 11 months ago

He said that ' Both He and his wife are knaves ' which can be incorrect if wife is a knight. And it also proves that the Husband is a knave.

Kaushik Chandra - 3 years, 11 months ago

Oh that makes sense, because he is lying about one so it's a lie still.

Matthew Pharr - 3 years, 11 months ago

The answer surely is NO.

Mrinal Agarwal - 3 years, 11 months ago

This has turned out be quite of a controversial problem.

Anuj Shikarkhane - 3 years, 11 months ago

As a knave he cannot say it as he always lies and the statement is said to be true or false in entirety. As a knight he can't lie.

Phil Erup - 3 years, 11 months ago

The question says that the knave cannot say the *statement * i.e only "I am a knave "but logically other than this statement a knave can make any statement to justify that he/she is a knave hence....

Animesh Ãñí - 3 years, 11 months ago

Arjen Vreugdenhil
Jun 25, 2017

Although, should a marriage based on a lie be considered legally binding?

Presumably, the wife would figure out her husband always lies and, therefore, would craft her questions accordingly. How about the question, "When did you stop having an affair with our neighbor?" ;-)

SizemoresScience Sizemore - 3 years, 11 months ago

It's an interesting proposal, but a bit complicated, and it doesn't work: if he didn't have an affair, could he answer at all? If he doesn't answer, either as a knight or knave, it means that he didn't have an affair, therefore he can't tell a time for the event, since it didn't exist to begin with. Then again, if he's a knave, even if he had an affair, he could answer with a wrong date and it would be a lie if he had an affair, and also a lie if he didn't. So there's nothing to gain from this kind of question, if you know the other one is a knave, and you can't find out if he is, if you don't. The direct approach is much more effective, just ask anything objective (are you 3 years old, for instance), and then treat all other answers with the same truth value that the answer to this question had.

József Inczefi - 3 years, 11 months ago

good one ,bro

sam dave - 3 years, 11 months ago

This is not a sociology question...🤣

Ben John Toms - 3 years, 6 months ago

But logically, they either said "I do" while not intending to get married, or "I don't". :D

Arjen Vreugdenhil - 3 years, 6 months ago

@Arjen Vreugdenhil My opinion is that it should not, since persons who are not deemed trustworthy should not be able to enter into legally binding contracts. Still it can, since by common law the knave is permitted to conceal his or her identity and a secret agent is invested with rights under color of law.

Dimitri Boscainos - 3 years, 11 months ago

That escalated quickly

Mehdi K. - 3 years, 11 months ago

You are implying that there can be a law that supersedes truth or false values of the problem. The thing is, this is a theoretical question, and as such its premises are absolute, everything aside from that is just speculation on your part. The problem clearly states that a knight can only tell the truth, and a knave can only tell a lie, so in this scenario there wouldn't be any law that permits them to do otherwise, since that would overwrite the premise. This is a problem with mixing emotions with logic, you end up with false logic. The problem clearly states that they can marry, and if you think that knaves will say stuff like "I don't love you", and at the altar, "I don't", if they know about each other whether they are knaves or not, it really isn't much of a problem. You see, when somebody always tells a lie, and you know that about him/her, it's really the same as if he/she would be speaking only the truth. The problem in our world is that any person can do either, and that is way worse regarding marriage and legally binding contracts.

József Inczefi - 3 years, 11 months ago

Mohammad Khaza
Jun 25, 2017

i think the husband is a knight and the wife is a knave.but the husband loves her wife so much. so he is telling life only for his wife which he thinks isn't a lie.

that means he truely isnet a knave, because knaves ALLWAYS lie

Sarathy Jayakumar - 3 years, 11 months ago

yes sir,you are both right and wrong.cz this is a confusing flawed question.

Mohammad Khaza - 3 years, 11 months ago

It doesn't matter if he thinks it is a lie or not, as the problem states "knights only state the truth", not that the "knights always state what they think is the truth". Truth is universal, not subjective. And the truth is, that if he is a knight, and states what he stated, he isn't stating the truth, thus he isn't a knight. Don't try mixing in emotions with a logic question, you'll only end up with false logic. The truth always prevails :D

József Inczefi - 3 years, 11 months ago

But this would mean that the husband told a partial truth.

henry isham - 3 years, 11 months ago

The problem explicitly states there is no such thing, either the whole statement is taken as truth, or taken as lie.

József Inczefi - 3 years, 11 months ago

Timmy Kostolansky
Jun 28, 2017

The islander saying this must be a knave married to a knight. If both were knaves, the statement is not allowed under the rules. If the islander saying this was a knight, then he would be lying, thus also being impossible under the rules of the island. Thus, the islander must be a knave married to a knight.

Ash H
Jun 27, 2017

The statement suggests that both the Islander and his/her wife are Knaves. A knave is unable to tell the truth, therefore one part of that statement must be a lie. He can't be a knight as they always tell the truth. Therefore, the lie must be that his/her wife is the knight.

I think you are all overthinking it so far. The Knave could be single.

Camille Lee - 3 years, 11 months ago

Colin Matthews
Jun 28, 2017

I think the bigger issue is, if at least one of them is a knave, during the marriage ceremony, their 'I do' affirmation would come out as 'I don't' or would potentially be paradoxical.

Matthew Warwick
Jul 1, 2017

Let's look at all the possible combinations: (husband, wife)

Knave, Knave
"My wife and I are both knights"

Knight, Knight
"My wife and I are both knights"

Knight, Knave "I am a knight. My wife is a knave."

Knave, Knight
"I am a knight. My wife is a knave." or
"My wife and I are both knights" or
"My wife and I are both knaves"

Why can he make this statement. Because it's a statement. If he said "I am a knave. My wife is also a knave" he would be telling the truth.

Gary Hanson
Jun 30, 2017

They are a married couple but if the wife is speaking then the statement that the other party is also a women is a lie (unless they are same sex couple) makes the statement a lie so the fact that both members of the couple are knaves being true does not matter.

Stephen Bush
Jun 30, 2017

I looked at this problem from a stochastic view point - there are three possibilities in a set S {knight knight; knight knave; knave knave}. The probability of an islander saying "I am a knave" = 0. The knave knave couple could claim the second statement, as well as the knight knave couple - since the knave would lie. So there is a greater than 50% chance a couple could make the claim.

No, this question has nothing to do with probability.

Pi Han Goh - 3 years, 11 months ago

Munem Shahriar
Jun 30, 2017

The islander is a knave and his wife is a knight. The statement is 'My wife and I are both knaves' since his wife is a knight the statement is true.

Saya Suka
Apr 25, 2021

Knave husband + Knight wife = husband's "My wife and I are both knaves."

Both Knaves

11 solutions

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