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.

Are you suggesting that A is actually ambiguous and not B?

A sometimes tells the truth, and his statement in this riddle just happens to be a lie. Presumably one can imagine a has told the truth at some other occasion. — flannel jesus

Exactly. That is why I questioned whether A contradicts his own assertion or if A, like B, is simply ambiguous. At least, we both believe that C is the lone truth-teller.
Then B is always false and ambiguous. But what happens to A?

That only leaves C as the guy who always tells the truth — flannel jesus

I had the same thoughts about C. A is a liar, and B is ambiguous , so I believe C is the lone truth-teller. But I was wondering if I had properly written those in logic language because the riddle statement requested if it could be formulated in first-order logic or not. Since you did not criticise my initial question, I assume I formulated it correctly.

The rest naturally follows — flannel jesus

The liar is B, but also A. Is it contradictory or ambiguous?

Okay. I will be more clear.

is he saying he's definitely not the guy who always tells the truth? — flannel jesus

Yes.

when he says he sometimes tells the truth, is he saying he's definitely not the guy who always tells the truth? — flannel jesus

B says the truth or not but not both. B says the truth often. B also lies often. B doesn’t say both. The ambiguity of B is the core of this riddle. I copied and pasted it as it is written on the internet. I haven’t altered anything. We can conclude he is not definitely the person who always tell the truth, yes. Nonetheless, A claims B always tells the truth.

This is a clear contradiction to the riddle. Right?

B is the liar — flannel jesus

Exactly.

'1+1 = 2' means that the value of the expression '1+1' is the same as the value of the expression '2'. — TonesInDeepFreeze

Why does it take so long to understand an axiom that appears so simple?

I once read Bertrand Russell's works, and one of them was Principia Mathematica. Well, it took him and another colleague of his more than 300 pages to prove that 1+1 = 2. I acknowledge that I struggled to understand some of their pages and axioms due to my lack of familiarity with logical language. There was even some criticism of the work of Russell and Whitehead because it seems the work was based on finding 'truth logic' 

I asked myself then. Is 1 + 1 = 2 a logical truth? And I found on the Internet big debates among mathematicians and logicians about whether it is a tautology, a logical truth, or a theorem.

In the following link (1 + 1 = 2) you will see similar answers to yours: 1 + 1 = 2 is a 'definition'.
2 is another way of defining '1 + 1' if I am not mistaken...

Angelos Sikelianos. Selected Poems. Translated and introduced by Edmund Keeley and Philip Sherrard.

Kazantzakis once said that if he were awarded the Nobel Prize in Literature, he would only accept it if he could share it with Sikelianos.

Identity. — TonesInDeepFreeze

The number of things is not the things. — TonesInDeepFreeze

:up:

And, in mathematics it is very clear that "=" is not defined as "is". — Metaphysician Undercover

Could it be defined as "equals to..."?

Mathematics adheres to the law of identity, since in mathematics, for any x, x=x, which is to say, for any x, x is x. — TonesInDeepFreeze

Are you referring to 'is' in terms of identity or value? For example: 5 is 5 in both mathematics and in our understanding of numerical systems. Meanwhile, £5 doesn't equal $5 or €5 because of the disparity in monetary value. Although every bill or note is represented by the payment of x5, it will depend on the value. So, x = x, doesn't equal to "is." To apply this, I need to carefully consider the specific context. Right? 

I'm sorry to be a bit abrupt, but if you don't keep your feet on the ground, you're bound to lose contact with reality. — Ludwig V

You are right. I am the one who apologises for derailing the topic in an inconsistent scenario. I thought the non-existence of a dog was a fascinating topic to discuss, but I admit that I overreacted.

Is there a non-existing dog? If there is, it doesn't exist. If there isn't, it doesn't exist. — Ludwig V

Don’t get me wrong. I explained myself mistakenly. It is true that you didn’t mention the non-existing dog, and I think Athena never thought about it either. But since this mysterious dog showed up in this game yesterday, I started to think about his interference in the counting. Well, if we imagine there is actually a dog who doesn’t eat anything, it means that it should be represented with a zero (0) in the counting. As ssu pointed out, it took a while for Western mathematics to accept zero as a number. According to this issue, maybe Plato would never have taken the dog who doesn’t eat anything into account, but yet it is clear we should take the dog into account, and thus, the dog exists. Right? 

There cannot be a dog that eats the most - there's bound to be another one that eats more. Similarly for the dog that eats the least. Infinity doesn't follow the normal rules. — Ludwig V

Sorry, I was foolish in trying to follow usual norms when infinity is involved. :sweat:

Well, strictly speaking they are identified by the amount of food they eat, which determines their position in the line. — Ludwig V

Ah, the so-called non-existing dog is the one who doesn’t anything at all. I get it now. But I assumed every dog ate at least a bit.

So, since they are identical in every way, apart from the amount of food they eat, there is no other way to identify them.
It is easy to think that they must exist, but if the line is infinite, any specified dog has another dog after it. — Ludwig V

Yes, this is how I see the tricky game. If I'm not mistaken, the dog who eats less than the preceding dog would be represented by 0.00000000…, and so on. However, this dog does exist. It consumes something, even when it is infimum.

Thanks, ssu. A great and very well-written post. I appreciate your teachings. :up:
By the way, @Ludwig V has stated something interesting:

Your ordering means you have to start from a dog that you cannot identify. — Ludwig V

It is true that my knowledge of mathematics and logic is pretty limited.  Yet, if I understand the rules of this entertaining game correctly, the counting starts with two identified dogs. The one at the top (the dog who eats the most) and the one at the bottom (the dog who eats the least). Honestly, I think those two are always ‘there’ but it is a mistake to try to identify them with numbers. I follow Zeno’s point as indicative. This is why Plato was wrong in this game. He forgot to count the two 'axiomatic' or 'affirmative premise' dogs. I don't even sure what to call these two (maybe Teo and Sarah :lol: ). As ssu pointed out, the transcendental dogs are the sole obstacle in following Zeno's point. These exist, but everything becomes complicated if we are fixated with labelling the dogs in numerical sequence.

In casual conversation, the word 'elements' can be used that way. But if we are talking in a focused context about sets, 'elements' refers to members of a set. And the house is not a set. — TonesInDeepFreeze

Ah. Well, I think I have to agree with you. My arguments were based on casual and informal examples, and I can’t go further than that. Thanks for your explanations.

As all dogs do eat something, we have a problem with the non-existent dog that doesn't eat anything, — ssu

and @Ludwig V

I remember I referred to that specific dog in our previous exchange. I said that following Athena’s rule, it is not possible to think that there will always be a dog that will eat less than the previous one, and so on. Athena stated that there is enough food for every dog. So, let’s say, there is a dog who eats 15 pieces of meat, and there is another dog who eats only 0.0001 pieces of that meat. Those are the two dogs that Zeno was referring to: the dog at the “top” and the dog at the "bottom,” but why do you count a non-existent dog? If there is enough food for the dogs, there isn't a dog who doesn’t eat anything at all. 
I mean, following the premises of the OP it is not possible to imagine a dog who doesn’t eat anything.

What things separately? — TonesInDeepFreeze

All the things I previously referred to. The ‘objects’ or ‘elements’ that constitute a house: walls, ceiling, windows, door, etc.

Again, a house is a thing you live in. You don't live in a set; you live in a house. — TonesInDeepFreeze

Yes, yes. I understand that I live in a thing, but my point was different. I tried to explain that the ‘thing’ is based on different elements. Without these elements or 'objects', the principal thing (the house) is senseless, in my humble view. Maybe I was wrong in using those concepts in a confusing way. Yet I think we both agree that the house is senseless without furniture, unless you are minimalist. But even a minimalist house needs walls, a door, and a ceiling. Therefore, these three elements are necessarily elements of the house.

Order:

<door, roof, floor ... balcony> is one order

<floor, balcony, door ... roof> is another order — TonesInDeepFreeze

I see. Thanks. But then I wonder: what is the point of that order, or does it arise spontaneously? Obviously not. The house is what they relate to.

I would think of those as aspects of the house, not members of the house. I wouldn't think of a house as being a set. There are sets of aspects of a house. But that set is not a house. — TonesInDeepFreeze

If that isn't a house, what set are you talking about? Assume they are all 'aspects' of a set called furniture. We could agree on that. But what is the sense of doing those things separately? All of the 'aspects' I mentioned in my example follow a common logic. They'll end up in construction. A house or building. I can't envision a house without a wall or a ceiling as structural elements. Otherwise, this type of construction would be unsustainable. Perhaps I am misunderstanding the concepts of "set," "order," "members," and so on. I am aware of my limited understanding on the subject. But I still believe they are members a house.

Do you see that? — TonesInDeepFreeze

Yes, I do. I never claimed there was one and only “THE” order. I referred to the balls in the example of jgill because that was what I thought when trying to use logic. But I hadn’t in mind only one ‘ordering’.

There's plenty of detailed information and explanation posted in this thread.

If you have any questions, or wish to learn more, then it's as simple as asking. — TonesInDeepFreeze

I know. This long thread is very informative. I just didn’t want to ask because it is obvious that I don’t have the same high level of math and/or logic as you do, and my posts would interrupt the debate. But it is dreary to read such negative comments loaded with animosity. 

I came to this topic hoping to learn anything about set, order, infinite, and so on, but the responses seem like a shootout among the users. Just calm down a bit, folks. Your positions and answers are quite good; it is not necessary to reach personal animosity. :up:

If a set consists of concrete objects, then it has the order that those concrete objects have, and no other order. — Metaphysician Undercover

And exactly what order is that? — tim wood

‘Set’ and ‘order’ are very interesting concepts that I discussed in other threads, and it is not always clear what we can include in them. If I am not mistaken, I guess MU refers to those objects that are logically attached to an order and, therefore, make a set. For example, ground, bricks, walls, ceiling, windows, and a door altogether make a set, which is the house. 
Please keep in mind that I am not arguing about whether those are necessary order objects or not. However, it is evident that they create the order and set.

Set consisting of three balls colored red, white and blue. They also have differing weights. What is THE order? Just curious. — jgill

The order is how items are organised with one another based on a specific attribute. The only distinguishing feature is that they are spherical. The weight and colours are only accessories. The set would be spheres, and the order would be the three balls. Right?

I was listening to this yesterday afternoon because of the Euros feeling. I don’t usually watch football, but you know when our nations play against each other... I have butterflies in my stomach. :broken:

It will not be easy, that's for granted. But we all (EU members included, absolutely) need to fix something that couldn't have ever happened. Sometimes politicians lie to us, making us think one way is better than the other, but at the end of the day, the population ends up paying the price. I could understand that some EU bureaucrats can't be trusted at all. Germany has its own interests too, etc. I guess there will not be any issue on the Mediterranean nations side. I care about Europe. I also believe there is a possibility of getting through. The citizens are always the ones who sweep up the mess of the politicians. It is not the time to be divided. We already had that time back in past years. Wars of religion, nationalism, political ideologies, etc. It is something we no longer deserve. We are the candle of civilisation, and we don't need to be heavily dependent on the USA or China. We can do it on our own. If we couldn't reach it via politics, we could try it via culture, at least.

*That was a tiny excerpt from my address at Westminster. Sorry if there are any grammatical hiccups.

I am still so glad I left England when I did, that place is fucked up — Sir2u

It will no longer be a wrecked country. With Starmer as PM and my seat, everything will be OK. I see a re-accession to the European Union on the horizon.

Look, mates, hmm… 649 of the 650 possible seats are already declared, but there is one left. I don’t know if I am able to say this, but that seat is mine, actually. I won it to Liz Truss in East Londonderry. So, due to these exceptional circumstances and chaotic situation, I vow to declare my seat, if only His Majesty the King and Starmer allow me to do the following:

The VAT has to be reduced, and the price of a pint of beer will be £1 from now on.
@unenlightened will be the only real assessor for internal and external disputes. 
@BadenRob has to be the next Speaker of the House of Commons and appointed ambassador to Spain.
@Jamal has to be the next president of the Scottish Supreme Court. 
The full recognition of Palestine as a state.
No more pollution in the atmosphere. With the aim of achieving this, I plead with His Majesty the King to make the metro and bus free. 
@Sir2u has to be the next Chancellor of Oxford University to teach Spanish there.

This letter has already been sent to ‘The Telegraph’ …

Source: https://www.telegraph.co.uk/politics/general-election-2024/

Signed: Javier,

Thank you for your insight and explanations.

So, for example, in my local constituency, labour won the seat comfortably with just over 33% of the vote. — unenlightened

Let me guess. Your constituency is Chatham and Aylesford. :smile: https://www.theguardian.com/politics/ng-interactive/2024/jul/04/uk-general-election-results-2024-live-in-full

Given this situation, the fact that there are over 100 third, fourth, fifth party and independents is highly significant. I hope this will persuade Labour towards some electoral reform. — unenlightened

Although, it is not in the same context, be careful with those small parties. We have independent parties in our Congress, and they persuade the main party (PSOE, that is the Labour Party), but just for personal benefits, forgetting the common and national goals. 

TA-DA.

Say good morning to your new Prime Minister, lads.

Yes. The whole point of the topic is about when human demarcation is absent. — noAxioms

:up:

But it isn't even furniture without humans to name them so. They serve purpose to humans. Your examples are of human made artifacts, which serve a specific purpose to a human. — noAxioms

I agree. All of those objects serve a purpose for humans, but I think this is not the main point of my argument. Although they are dependent on human purposes, they are necessarily part of a house. I mean, you would not put a sofa or a fridge in the moon, just as a twig would not flourish randomly in a corridor. We can imagine in the abstract, but I think there should be a basic sense in order to attach things to others. You claim (if I am not mistaken) that their ‘attachment’ serves human purposes, but I still believe they have intrinsic value. I will not light up a candle in the sun. Would you? How will the latter satisfy my purpose? 

A sofa 'knows' it is a sofa, or at least where its boundaries are, or that it is useful to humans? in what way does that make sense? — noAxioms

But why should everything be useful to us? Didn’t you ever think of the pure lonely existence of that sofa?
Consider what happens if a nuclear bomb destroys all of human life and leaves only that sofa. Do you believe the sofa will lose its sense since it will no longer meet a human need?

I had no idea you were joking about Biden's dementia until I read @Benkei’s post. I am naïve about politics. :snicker:

The 2024 United Kingdom general election is today! Are you ready, mates?
Most of the opinion polls say Labour will win a large number of seats. Let’s see what happens.

Here’s a mediocre 20 minute read that you could be currently reading… — Fire Ologist

Spamming your OP is not allowed. :roll: We talk about books and literary recommendations in this thread.

Samurai trilogy

The Book of Five Rings by Miyamoto Musashi.
Hidden by the Leaves by Yamamoto Tsunetomo.
Bushido: The Soul of Japan by Inazō Nitobe

No, I asked where 'this' stops. I never said 'building'. — noAxioms

Are you really sure? ...

Where does the building stop? — noAxioms

Still, purpose is defined by the humans that find utility in the 'object'. The topic is about an object in absence of such ideals such as purpose. — noAxioms

I agree. Human convention defines 'purpose,' and the building exemplifies this. What I don't understand is why you wish to eliminate such principles. As far as I can tell from this thread, most objects and things are defined by human conventions or other categories that make them 'interesting.' Are you arguing that there could be an intriguing object that lacks human ideals?

I don't think a beam of energy say 'knows' anything about human purpose. — noAxioms

Obviously, and I don't think it is necessary to go too far. What I tried to argue is that there are objects which are dependent upon others just for need. The furniture, walls, ceilings, etc. are attached objects to the principal which is the building. Otherwise, where would you put furniture? In middle of the forest? That would be senseless. You claim this is due to human purpose, but I think those 'objects' know the destination of its utility.

The word invokes a convention, and the convention typically includes all those parts, but how about the piles or the utility hookups? Where does the building stop? Does it include the furniture and people? That question was asked in the OP where I explore the concept of what you weigh, and exactly when that weight changes. — noAxioms

Yes, I follow you and the sense of your OP. I remember when we talked about chopping the twig off, for instance. I know that it would sound silly to say that without a twig, the tree no longer exists, and therefore, the forest either. But this is exactly the trace I want to keep up! I think the example of the house is better.
You asked me: Where does the building stop? Does it include the furniture and people?
Of course, it includes furniture and people. :smile:
What would be the point of constructing a building, then? The building, as an object, precisely stops when it lacks everything above. The combination of the walls, furniture, ceiling, roof, and people makes the 'building', and when an element of the set is left, the building as an object is senseless. I wish I could go deeper regarding the example of the twig and the forest because I still see symmetry in both cases. 

But in the absence of language, how does anything 'know' that 'building' is the object of interest? — noAxioms

The object of interest is inherent in the building. The remaining 'things' are attached to it. They ‘know’ that the building is of interest to them.