Good OP, Lionino. Switching logic into natural languages was a big handicap in my last thread. It seemed to be a simple riddle for everyone, until I asked to explain it with natural language and whether the concepts of ambiguity and contradictory are similar or not. I only got answers using logic language constantly until RussellA wrote a very good example using natural language.

I have to agree that statements like A∧B are universal, and I guess it helps people use logic quickly and easily. But, again, it is outstanding to see those logic formulas explained in language. It seems they are only allowed to use it with "A" and "B" in the premises.

So, what could one say about ¬(A→B) in English? — Lionino

I don't get it, but I'm confident I could get it using natural English. Is there a substantial difference?

On the flip side, can the English meaning of "A does not imply B" be converted to logical formulas? — Lionino

To what extent should it be converted into logic formulas?

I wouldn't call myself a fan in particular. — T Clark

Yes, I knew you were not a fan in particular, but I will consider you my partner when it comes to Japanese films, and I vow to recommend you some of them frequently. :smile:

The Eel is another good film by Shohei Imamura. Since I know Clarky (@T Clark) is another fan of Japanese films, I recommend you watch it whenever you can. Cheers.

Tomiichi Murayama who served as Prime Minister of Japan from 1994 to 1996. He is 100 years old and still living. Murayama led a difficult legislature and confronted a major crisis: the 1995 Great Hanshin Earthquake.

Yeah, that smells like bait. — Lionino

The $10,000 is in New Zealand Dollars. Seems legit. The prize is not in virgin-bitcoins or loser ‘ethereum’ scam at least. Everything that comes from NZ is rather reliable to me.

Yeah, a team of experts would be great, but I haven't got one, so I'm afraid you're stuck with me. — Dan

I wish I could help with this challenge, but I am far from being a trustworthy philosopher/thinker. I am a total novice. :lol:

Hello Amity! Happy to read posts from you again. :smile:

How can you not with that fantastic football result in Euro24 final!? Spain 2 - England 1. — Amity

It was a nice night, but I quickly went back to my normal life. Although it is always great to watch your country lift cups, it is, at the same time, quite sad that we only know how to stay together in football tournaments. In the rest of life aspects everything is messy here...

At least in the UK with Labour toppling the Tories. Yesterday, PM Keir Starmer hosted a European Political Community summit at Blenheim Palace - hopefully building stronger relationships...we will see... — Amity

Yes! I read similar news here, and we discussed it in the 'Brexit' thread. I am happy to know Sir Starmer wants to get closer to European countries and build stronger relationships. Yet, I wonder to what extent he has in mind another referendum to ask the British people to reunite the EU or not... Let's see what he does in his mandate. I wish him the best! The Tories deserved such a brutal loss. They cheated on people and their management of the country was outrageous.

But, of course, the hard right are still around. Boris, Truss and Farage hurrying off to support Trump. — Amity

U.S.A is becoming an extremely hazardous country. I hope we do not reach that point. Yes, there are still divisions across Europe, but not to the point of violence (with the exception of Slovakia's Prime Minister). Poor mate...

Oh, what is the deadline? Do we have all summer? A month? ... just a week?

Cool challenge! I am in. Let's see if I can solve it. It seems legit and interesting, but I have a few inquiries: 

* Whether a solution is successful will be determined exclusively by me and my decision is final. — Dan

Isn't this a bit unfair? In most contests or 'challenges', the final decision of who is the best applicant is usually determined by the vote of at least three members. The quality of each solution will only depend exclusively on your criteria. Don't get me wrong, I respect it.

On the other hand: If the winner happens to be a TPF member, could we know who of us won this challenge, or will the decision be kept confidential?

How the Japanese look at US politics. — javi2541997

I don’t get why the Republican shakes woman’s hands and in the Democrat cartoon there are apartments. Does this imply that Republicans are as friendly with women as Democrats are with town planning?

How the Japanese look at US politics. (comic in recent Tokyo newspaper)

If only I were able to understand such a beautiful language as Greek…

A noble soul. Rare nowadays, but being Greek it doesn't surprise me. — Lionino

I agree. Greeks are humble and loyal. God bless Kazantzakis and the souls of our Hellenic and Mediterranean brothers! 

The City and Its Uncertain Walls. by Haruki Murakami.

@praxis @T Clark et all Murakami fans.

His most recent book is fantastic. It is indescribable his talent to express a sweet sense of melancholy through his characters and places. I think Murakami is sentimental and nostalgic, and so am I. That’s why I like him so much. I can’t even express with words why I 'miss’ the characters of this novel and the ‘city’.
It may seem odd, yet when I read Murakami, this is the classic stimulus I grasp…

You're taking the game too seriously. But it is the attitude I've seen most people take in posts discussing logic, riddles, games, etc. When they interact with me I feel hugely overwhelmed.
They believe I am trolling, but I simply lack wording and reasoning.

New rule: The sum of the product of any two integers is omega minus (now corrected!) the double of Lionino’s integers. 

Beautiful poem of Angelos Sikelianos:

O when,
Huntress,
with naked foot beating the snow all night,
shall we see at last on the summit,
like Boreas
and the lion
rousing himself from sleep,
the rising sun?

for in that light
the contest will be decided,
and the new-fledged young men
will row their opponents from the cliff top
and, like the poppy beside the sheaf,
each life
will be harvested in the golden light
spontaneously, silently.

Nice to read a new post from you, Forrest.  :smile:

New rule: There is an integer that is neither a Fhorrest integers nor a Gill integer.

The sum of any two integers is zero. — jgill

The product of any two integers is omega. (Where omega is the first number bigger than any integers). — Pfhorrest

It must be a number smaller than omega, but not zero.

Something like this: x (the suspicious integer) < Ω.

It is 1. Why? Because it is the smallest integer greater than zero and the smallest of Omega.

Everything I wrote above is pure crank, right? :lol:

Oyarzabal (who scored the second goal yesterday) and his family have received threats from Basque nationalists. Oyarza is from a tiny town in Basque Country, so everyone knows where he and his mother live. The painting says: 'NO to play for the Spain National Team'

It's disgusting, but what can I expect from an issue that has existed since the 1960s? As well as Ireland had ‘The Troubles’ we have a big issue with ETA and his political lobby: EH Bildu.

https://www.elmundo.es/pais-vasco/2024/07/15/669506c6e9cf4a963f8b4581.html?cid=SIN26101&utm_source=marca.com&utm_medium=interno_bt&utm_campaign=SIN26101&_ga=2.37133860.509677226.1720796434-798002902.1719681135

There is nothing unclear. After the recent posts and examples (@RussellA’s one was very good), I now see the point of the riddle. It was funny to talk and debate about it. 

Basically, it was my first attempt to put logic into practice. I decided to start with a basic riddle. My intention is to level up in the future.

I understand it now, but not when I first posted this OP. Perhaps it is simple and clear for you, but not for me. One of the demands in my post was for someone to correct me if necessary because I wanted to learn and grasp everything through examples and "formulations."You thought I was trolling. I promise you I wasn't. I always posted with proper behavior.

I still don't get why the answer everyone else is giving isn't satisfying to you. — flannel jesus

Of course their answers (including yours) please me. But I'm keeping up with postings and questions because I want to learn how to apply logic. We are all welcome to ask questions. I promise that I am not trolling any of you.

I'm personally amazed that he's made such a simple riddle last 3 pages, when nobody else has any question about what the answer is. — flannel jesus

Be honest, you're having as much fun with this thread as a child in the park with a big red balloon. :smile:

Got it. :up:

A is either True or False, so A∨¬A. Therefore, A→B can be either True or False (in this case False). No inconsistency in the solution presented. — Lionino

What do you mean by ‘no inconsistency’? That A is coherent but ambiguous or what?

The problem with A is:

B -> A ∧ B = ¬A.

I don’t know whether is coherent or not. But the negation of “A is the truth-teller" means that “A is either the liar or the ambiguous person" Therefore, you are claiming he is the ambiguous and not B. Agree?

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". — RussellA

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.

Gotcha. :up:

Prima facie these might mean two different things:

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

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

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

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

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. — Michael

: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:

He can lie, I've said that explicitly — flannel jesus

Dude…

everyone here except you has understood that b must be the liar. Who else do you see claiming a might be the liar? — flannel jesus

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.

The three statements work on the understanding that A happened to be lying rather than telling the truth. — RussellA

A=can both lie and tell the truth — Igitur

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.

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

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

A sometimes tells the truth. — flannel jesus

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?

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.

I am trying to make an approach. I claim that A is just contradictory in his statement, but you are defending that A is precisely the ambiguous here because he ‘sometimes tells the truth’ and B is always the liar. I defend the opposite: B is ambiguous and A is contradictory for always telling the truth. It is B who often says the truth and others not, but not both. Then, when B tells the truth, A tells the truth as well. B is the ambiguous.

Excellent! :up: Thanks to your contribution to this thread. Also, to @flannel jesus for keeping the discussion alive. I am enjoying this.

The context where A is always true and not sometimes.

I thought B was ambiguous at first glance, but consider this, Michael:

Person A claims person B always tells the truth. Person B claims person B (himself) sometimes tells the truth. Okay, then, A tells the truth and B always lies. A is the ambiguous person here. I tried to explain that he is just contradictory and B is ambiguous.
But I am starting to realise that A is dragged down by the ambiguity of B. And then I asked myself: does this make A ambiguous or just contradictory with his statement?

Assuming either one of them is the truth teller leads to contradiction, so we don't. — flannel jesus

That’s what I tried to argue! If A is contradictory, then C is the truthteller, and B is ambiguous. I mean, according to this context, B could be the one who sometimes tells the truth.

Yes. I agree and I see the point. But what happens to A then? B is the only one who says he tells the truth sometimes. Nonetheless, it seems the riddle turned out with A being the ambiguous person, and this is very tricky to me. B cannot be the truth-teller. Therefore, A did not speak the truth  and therefore, A is not the truth-teller either. We all agree that C is the truth-teller. Then, is A the contradictory, ambiguous, or unreliable person here?

For me, it is like pulling a rabbit out of the hat. It is surprising that A is actually the problem and not B. Or did you see the point from the beginning? 

I back up your argument, and I also see A as ambiguous. A claims person B always tells the truth. B claims that person B (himself) sometimes tells the truth. Then, A tells the truth (ambiguous). But consider for a second this:

Assume A is true always, but he says B is true always. Is A still ambiguous or contradictory?

Assume B is always true, but he himself admits that he is ambiguous (because B stated that he sometimes tells the truth). Then B is the liar, though not always. He is ambiguous in this context.