## Ambiguous Teller Riddle

• 1.8k
I don't know why you're defending that. If C always tells the truth, and C says B always lies, then B always lies.

That seems pretty simple and straight forward to me. Which part of that logic do you disagree with?
• 5.4k
We already know C is the truth-teller. But I was wondering what happened to A. Some claim he is ambiguous, others he is contradictory. If he is ambiguous, A sometimes tells the truth and sometimes lies. If he is contradictory, A always tells the truth because B is always true.

Am I missing something in that attempt to use logic? As I asked at the beginning of the OP I wonder whether I am correctly formulating the logic or not.
• 1.8k
Some claim he is ambiguous, others he is contradictory.

Who claims these things? As far as I can tell, everyone here except you has understood that b must be the liar. Who else do you see claiming a might be the liar?
• 1.8k
Am I missing something in that attempt to use logic?

Yes, you're overcomplicating something very simple. C tells the truth. C says B is the liar. Therefore, B is the liar.

But I was wondering what happened to A.

You keep asking this, and everyone else keeps giving the same answer. A sometimes tells the truth.
• 5.4k
Yes, you're overcomplicating something very simple. C tells the truth. C says B is the liar. Therefore, B is the liar.

Yes, I understood it at the first glance, but:

A sometimes tells the truth.

If Person A is the person who sometimes tells the truth, then it means he sometimes lies. Person A could be a liar as well. Yes or no?
• 1.6k
Who is the liar?

I agree with @flannel jesus that A sometimes tells the truth, B always lies and C always tells the truth. (admittedly my solution is more convoluted).

Presumably, a person who always tells the truth is different to a person who sometimes tells the truth, and in this sense are mutually exclusive.

IF A always lies - B always tells the truth - C sometimes tells the truth
THEN B would not say of himself "B sometimes tells the truth"

IF A always lies - B sometimes tells the truth - C always tells the truth
THEN C would not say about B "B always lies"

IF A always tells the truth - B always lies - C sometimes tells the truth
THEN A would not say about B - "B always tells the truth"

IF A always tells the truth - B sometimes tells the truth - C always lies
THEN A would not say about B - "B always tells the truth"

IF A sometimes tells the truth - B always tells the truth - C always lies
THEN B would not say about himself - "B sometimes tells the truth"

The only remaining possibility is - A sometimes tells the truth - B always lies - C always tells the truth.

On the occasion that A was lying rather than telling the truth, A would say one of two things about B, either "B always tells the truth" or "B sometimes tells the truth"
B would say one of two things about himself, either "B always tells the truth" or "B sometimes tells the truth".
C would say of B, "B always lies"

The three statements work on the understanding that A happened to be lying rather than telling the truth.
• 1.8k

Person c always tells the truth, and he says B is the liar. Therefore a can't be the liar. I can't tell if you're trolling.

A can sometimes tell lies, but he can't be the person who always lies.
• 40
If the statement that B sometimes tells the truth could also mean that they always tell the truth (sometimes be a subset of always) then there are multiple solutions.
Otherwise, B cannot only tell the truth sometimes because that would make both A and C liars. This makes B the liar, because they stated that they sometimes told the truth.

Therefore, A must sometimes tell the truth but isn’t in this situation, because A cannot be the truth teller, having lied. This makes C the truth teller.

A=can both lie and tell the truth
B=liar
C=truth teller
• 5.4k
The three statements work on the understanding that A happened to be lying rather than telling the truth.

A=can both lie and tell the truth

Thank you so much for your posts. You explained very well what I tried to explain, but I couldn’t find the correct premises due to my lack of wording and logic skills.

Do you see it now, @flannel jesus? Because you claim A can’t be a liar emphatically. While, as Igitur noted, if A sometimes tells the truth, A can be both a truth teller and a liar. Therefore, there is the possibility for A to be a liar as well as B.
• 15k

I think you are confusing matters by being imprecise with your descriptions.

There are three types of person:

1. The person who always tells the truth
2. The person who always lies
3. The person who sometimes tells the truth

Person A can tell the truth but cannot be the person who always tells the truth.
Person A can lie but cannot be the person who always lies.

Person A is the person who sometimes tells the truth. If Person C is the person who always tells the truth then Person A is lying. If Person B is the person who always tells the truth then Person A is telling the truth.
• 40
Person A cannot be the person who always lies.
I think this is what was trying to say. That A is lying, but doesn’t always lie (because B always lies). A only sometimes lies, and has the capacity to tell the truth.
• 5.4k
I have never said that A always lies. It is obvious and that would make the riddle senseless. As far as I can understand the relationship between the three, my statement goes as follows:

A: Sometimes tells the truth. Therefore, he can lie often.
B: always lies.
C: Always tells the truth.

Therefore, A and B are liars and C is the only truth teller. If A sometimes tells the truth it means he can also lie as well as B.
• 1.8k
Because you claim A can’t be a liar emphatically.

I think you're confused about what I've claimed. I've only claimed he can't be THE liar, as in, the one who always lies. He can lie, I've said that explicitly
• 5.4k
He can lie, I've said that explicitly

Dude…

everyone here except you has understood that b must be the liar. Who else do you see claiming a might be the liar?
• 1.8k
ok you must be trolling at this point

The answer is apparently obvious to everyone but you.
• 5.4k
Person A is the person who sometimes tells the truth. If Person C is the person who always tells the truth then Person A is lying.

:clap:

I couldn’t have said it better. Michael, frame that post please because @flannel jesus is not capable of seeing that A can actually be a liar too.

You edited your posts after reading the arguments of Michael and Igitur :lol:
• 15k
If A sometimes tells the truth it means he can also lie as well as B.

That is unclear. Prima facie these might mean two different things:

1. I sometimes tell the truth
2. I only sometimes tell the truth

Strictly speaking (1) might be true even if I always tell the truth. It is ambiguous as to whether or not (1) entails (2).

If it doesn't then the question is even more problematic as the person who sometimes tells the truth might always tell the truth, and so we have two people who always tell the truth.
• 1.8k
I didn't edit my posts. What edit do you think I made?
• 5.4k
Prima facie these might mean two different things:

1. I only sometimes tell the truth
2. I sometimes tell the truth

I agree. That’s about what happens to A.

Strictly speaking (2) might be true even if I always tell the truth.

Yes. And reaching (more or less) that conclusion, we can (perhaps) say that A is the ambiguous here. Right?
• 15k
Yes. And reaching (more or less) that conclusion, we can say that A is the ambiguous here. Right?

No, because if "sometimes tells the truth" doesn't mean "only sometimes tells the truth" then "sometimes tells the truth" is consistent with "always tells the truth", and so there may in fact be two people who always tell the truth.

In such a scenario it would be that both A and B always tell the truth and C always lies.
• 1.8k
Or one of a and B sometimes, and the other one always tells the truth
• 15k
Or one of a and B sometimes, and the other one always tells the truth

What I was getting at is that if "sometimes tells the truth" doesn't mean "only sometimes tells the truth" then the original claim "one person sometimes tells the truth and one person always tells the truth" is consistent with the claim "two people always tell the truth".

So our initial setup is that two people always tell the truth and one person always lies.
• 5.4k
Gotcha. :up:
• 1.8k
yes I'm actually talking about the same interpretation, and what I'm saying is a possibility within that interpretation
• 1.8k
just to be fully clear:

You're saying "I sometimes tell the truth" and "I always tell the truth" can be simultaneously true - which I brought up in the second comment in this thread, I get the idea.

You're saying, that means A and B could both always tell the truth, and C always lies - that's good, that's one possibility.

Another possibility the is, A sometimes tells the truth and B always tells the truth. Test out the validity of everyone's statements in that case and let me know what you think.
• 15k

I think it’s clearer to phrase it like this:

Scenario 1
A sometimes lies (and is lying)
B always lies
C always tells the truth

Scenario 2
A sometimes lies (and is telling the truth)
B always tells the truth
C always lies

Scenario 3
A always tells the truth
B always tells the truth
C always lies
• 1.8k
yeah, scenario 1 is the more obvious one, scenario 3 was what you came up with with the alternative interpretation of sometimes, and scenario 2 is what I was offering as another alternative.
• 1.8k
You edited your posts after reading the arguments of Michael and Igitur :lol:

For the record, I did in fact edit exactly one post, but I edited it within a minute of making it and it had nothing to do with the arguments of Michael and Igtur - I had already made my initial answer, which was entirely the same as theirs, back at the very start of page 1.

The only post I edited was this one: https://thephilosophyforum.com/discussion/comment/917024 I slightly misworded something, and I edited it very shortly after posting.
• 1.6k
Is it possible to formulate it using first-order logic?

Person A claims person B always tells the truth.
Person B claims person B (himself) sometimes tells the truth.
Person C claims person B always lies.

Knowing that person A sometimes lies, person B always lies and person C never lies.

Perhaps in order to formulate in First Order logic, one should start with a set of statements, where each statement is either a lie or not a lie, and where the variable x stands for a statement.
∃x (Lie (x) ∨ ¬ Lie (x))

Perhaps one should also try to avoid the problem of Russell's Barber Paradox, where the person is named after their occupation. If someone always barbers, they can be called a "Barber". If someone never barbers, they can be called "Not a Barber". But if someone at one moment barbers and at a later moment doesn't barber, they can neither be called a "Barber" nor "Not a Barber"

Similarly, it seems that a problem with First Order Logic would arise if someone who always lies is called a "Liar" and someone who never lies is called "Not a Liar". Within the logic of First Order Logic, a "Liar" is not "Not a Liar". There is no middle ground to account for person A , who is neither a "Liar" nor "Not a Liar".

Therefore, given a set of statements, some of which are lies and some aren't:

Person A is someone whose statements are sometimes lies and sometimes not lies, not that person A makes every possible statement within the set that is a lie and every possible statement that is not a lie.
Person B is someone whose statements are always lies, not that person B makes every possible stalemate within the set that is a lie
Person C is someone whose statements are never lies, not that person C makes every possible statement within the set that is not a lie

How First Order Logic achieves this is beyond my pay grade.
• 5.4k
A very well written and informative reply. Every kind of help is appreciated here. Thank you, lad.

There is no middle ground to account for person A , who is neither a "Liar" nor "Not a Liar".

This is the core of the riddle, indeed. I tried to pin A’s state, but it turned out to be more difficult than I expected. If I am not mistaken, we need some statements to ensure that the truth-teller and the liar are different people. "There is exactly one liar" turns into a similar trio of statements. if x is true, A cannot be the liar. if x is false, A cannot be the truth teller.

But the debate on A is that he is able to be three different positions: truth teller, liar, and ambiguous. Can I get away with one proposition for A? No, I can’t. Since A “sometimes tells the truth”, it means he can also lie. Therefore, A can be in another position (liar/person who sometimes lies). Then I asked yesterday if A was ambiguous or just contradictory. The debate remains.
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