On Friday I set this puzzle….

Imagine that a man walks up to you and says, ‘Everything I say to you is a lie.’  Is he telling you the truth or is he lying?
If you have not tried to solve it, have a go now.  For everyone else, the answer is after the break.
The man is lying, but can you explain why?
I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

1. Anne Elk says:

Oh come on, Richard! Call that an answer!?!

I was pretty certain that he was lying but only because I remembered it from QI (I think). I can’t remember why…

1. who is Richard?

2. Anne Elk says:

The man who sets these puzzles. The man whose name is at the top of your screen right now.

3. Anonymous says:

Uh k

2. If what he says is true, then he is lying about that. Paradox! It cannot be true, so it must be false. However, if anything else he says is true, then he is lying. So it is possible that he lies, but it is not possible that he is telling the truth. So it is either a paradox or a lie. Even if it is a paradox, then it is not a lie, so it is a lie… Get it?

1. Anne Elk says:

Thanks! Yes, I think I get it. I’ve just come back from a holiday maybe I need more coffee first!

2. Dave says:

It isn’t even a paradox, but it reminds people of a famous paradox, so a lot of folks completely jumped the gun on Friday. Which was amusing.

3. Anton says:

how is it not a paradox?

3. Whistler says:

He’s lying because he is telling the truth. 🙂

4. Anders says:

If he is telling the truth, then he is lying, which is clearly nonsense, so he must be lying, and the paradox is resolved by realizing that the negation of “everything” isn’t “nothing, but “not everything”, so this statement is a lie, but he does sometimes tell the truth, which is entirely consistent and there is no paradox. Just as the resolution to the Cretan paradox “all Cretans are liars” is that “not all Cretans are liars”, so that one statement is false (though not necessarily a lie) and some Cretans are honest

5. Anonymous says:

he is lying because not everyhing he says is false… but he can still lie…..

6. kroketje says:

That he is lying, doesn’t mean that he has to tell the thruth all the time… he sometimes lies and sometimes tells the truth.

7. Danielle Kennedy says:

The lie is that EVERYTHING he says is a lie. Doesn’t mean he can’t lie sometimes, or tell the truth sometimes.

1. ctj says:

this.

a true statement would be, “some things i say are lies.” no paradox.

8. He is either a truthful or an untruthful man. If he is truthful he could not claim to be a liar, therefore he must be an untruthful man. The question is, as a liar, what does he really mean when he says, ‘everything I say to you is a lie’? Does he mean, ‘nothing I say to you is a lie’, which is inconsistent with him being a liar?, or does he mean, ‘everything I say to you is not a lie’?, which would make him an occasional liar.

1. Anders says:

In my semantic opinion, the two sentences you quote are logically equivalent. Nothing is a lie, or everything is not a lie say the same thing in my opinion.

NOT everything I say to you is a lie is not the same thing as everything I say is not a lie

None of these sentences speak of truth values though, only honesty (believed truth values). in the world of knights and knaves where these puzzles normally take place, it is not enough to know that a knight always speaks the truth and knave always lies to solve the standard puzzles, it is also necessary to assume perfect knowledge on all participants.

e.g. a knight saying “B is a knave” is normally taken to mean that the reader can assume that B is indeed a knave, but the knight could be honestly mistaken. For this reason, it is my (honest) opinion that most of such puzzles are really unsolvable, since the omniscience assumption is usually unstated

9. Ralf says:

Funny, that Richard seems so think that there is an easy answer to this. First question to be asked what is a lie? Any proposition that is intended to be a lie. Any “false” proposition”? Any proposition that is received as being intended to deceive about some fact? The sentence is obviously a meta language assertion that cannot give information about its own truth value.
It only says something about all other non-meta-language assertions. In this sense the truth value would be dependent on on the truth value of his other assertions. The answer to the “puzzle” is. One cannot say.

1. SimonP says:

Why can a “meta language assertion” not give information about its own truth value? The sentence “This sentence has five words” is true, or have I missed the point?

10. Anders says:

SimonP The idea that a sentence cannot speak about its own truth value is a cheapway to escape paradoxes like “this sentence is false”, and some people try to take it even further and say that a sentence cannot speak about itself in any way, but that way madness lies. and for this Friday puzzle it is completely unnecessary to go down any of those routes. about your counter example, “This sentence has five words” doesn’t speak about its own truth value. it speaks about its own structure. How about “this sentence six words” which fails on many counts, including not being a sentence

11. @Sceptic_Tank says:

I tend to solve this sort of puzzle graphically. This flowchart represents my thinking on Friday: https://www.dropbox.com/s/psq84vir5mhz4bq/Lies.jpg
and why my answer was that he is lying. It’s impossible for the statement to be true, so must be a lie, and the only way it can logically be a lie is if the only other variable – “everything” – is untrue.

12. Kristian says:

He lied about always lying. So we know he doesn’t always lie. This does not mean he always tells the truth, he could be telling 50% lies and 50% truths.

13. Anonymous says:

He’s a guy, proves my point, they all just lie!

14. Fotoflex says:

So it’s the Monday Puzzle now, is it?
Discuss.

15. edwardv says:

Does lying mean the man has to know he’s lying? Would it be more accurate to ask if what he is saying is true or false? He might not be lying if he doesn’t understand what he is saying.

16. Steve says:

I think lie in this case means for the statement to be untrue and says nothing about the intent of the person making the statement.

If we assume that “Everything I say to you is a lie” is true then the ‘truth’ of “Everything I say to you is a lie” contradicts itself. If we assume that “Everything I say to you is a lie” is false then that also contradicts itself. Therefore if there are only two answers allowed are yes or no (or truthfulness or falseness) then the answer can be neither of these then there is no answer.

Just because a question can be asked does not mean that it has an answer.

1. “If we assume that “Everything I say to you is a lie” is false then that also contradicts itself.”

Where’s the contradiction then?

17. Fotoflex says:

He always says the opposite of what he knows to be the truth.
So he’s always lying.

18. Cocky Jockerson says:

Someone else may have said this–I haven’t read through all of the comments–but, here is my take on the riddle.

First, let me say, the phrase (“Everything I say to you is a lie.”) only SEEMS to be a paradox. A paradox is a (for our purposes here) self-contradictory statement.

Second, although this may be obvious it is helpful to think about, a LIE is a statement that is FALSE and that the speaker KNOWS to be false.

Third, there are some things we need to understand about the Statement: 1. there is a FACT OF THE MATTER (FotM) (i.e. it is either true or false, despite what the guy is saying) 2. the FotM is independent of the content of the statement (i.e. just because the statement itself is false does NOT mean that the FotM is also false. It could be true and vice versa.)

Another way to look at it is that just because he SAYS its true, doesn’t mean it actually IS true.

OK, so, the best way to understand whether or not its an intractable paradox is just tweak each of the variables and try out the different options.

Option 1: The FotM is that the guy is a COMPLETE LIAR. Everything he says is false. This would be a paradox because that would mean the statement is false. If the statement is false, then it is true that at least SOME stuff he says is true. But that contradicts the FotM that everything is a lie. [I.e. ALL statements are False AND this one is True. These are contradictory statements.]

From Option 1, we know that the FotM CANNOT be that the guy lies about everything. So, he MUST be lying when he makes the Statement.

OK, so we’ve answered the question (“Is he telling you the truth or is he lying?” This is called a dilemma–it must be one or other other. He can’t be telling the truth, so he must be lying.)

BUT, you might be thinking that a similar paradox could rule out the alternative (i.e. He can’t be lying, so he must be telling the truth). This is the TRICK of the question. Let’s try out our other options. Unlike the Option 1 (where the statement is a truthful one), these alternative options are scenarios in which the statement is a lie.

Option 2: The FotM is that the guy TOTAL TRUTH TELLER. Everything he says is true. Like Option 1, this leads to a paradox. [ALL statements are True AND this one is False. These are contradictory statements.]

So, we know from Option 2, that there is at least one case where if the Statement is false, then it leads to a paradox. Does this mean that we’ve answered the question? (“Is he telling you the truth or is he lying?” He can’t be lying, so he must be telling the truth.) Well, no. For one, we’ve already ruled out the possibility that he is telling the truth.

Now, we come to the third option. In this final scenario, we need a few things to be true: (A) It must be the case that he is lying when he makes the Statement (i.e. the Statement is false). (B) The FotM must be that he is NOT a COMPLETE LIAR. [(A) needs to be true, because if the Statement is True then it leads to a paradox. (B) must be true because if he IS a COMPLETE LIAR, then it leads to a paradox.]

Option 3: The FotM is that he is an OCCASIONAL TRUTH TELLER. Sometimes what he says is true, but sometimes he lies. And, in this case, when he makes the Statement he is lying.

Do you see how Option 3 escapes the paradox? It works, because we’ve shown a perfectly valid example of a situation in which the statement is a false (If he sometimes tells the truth, then everything he says CANNOT be a lie) but does not lead to a self-contradictory conclusion. [SOME statements are NOT lies AND this thing IS a lie.]

I hope this helps! To explain the trick in a sentence: If a statement is NOT true, then it logically must be false. BUT if NOT ALL of the things are a certain way, then it can be that NONE are that way but it can ALSO be the case that only SOME are.

[One last note: Option 3 is ONLY possible, because he said EVERYTHING. If he said, “What I’m saying right now is a lie” then there are only two options. This is because if you have only have one thing you’re talking about and the thing can only be one way or another, then SOME of its can’t be one way and SOME of it another. But If you have multiple objects (e.g. statements) then they don’t necessarily have to be ALL one way or ALL another way. SOME can be one way and SOME can be another way.]

1. Cocky Jock says:

Man, you have a lot of spare time on your hands. Try going for a walk, visiting an art gallery, or doing some chores for someone who needs a little help.

19. L.Long says:

He is lying because as House says ‘Everyone lies”

20. The lie is found in the word “everything”. Not “everything” I say is a lie, but “some things” I say are a lie. Interesting that most of the comments seem to focus on the fact that either “everything” is a lie or “nothing” is a lie and don’t consider the most obvious.

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22. Udit says:

he is lying