"Which of the following statements is NOT a paradox?" - Lets discuss the answer to my previous question

[Janson]

So this will be a discussion on the paradox question I asked earlier. If you missed it, look here ( link ) I'm making a new page for this since I want to go in depth with the answer. Just so you guys know, I got this from a game I was playing and it stumped me for a moment until I did some more research. Most of you said (1), which wasn't correct. "I always lie" was the right answer as it is not a paradox. I'll try to explain

Paradox: "a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth." (ie. A paradox can be described as a statement which can be neither true nor false. This is key)

link

1 is a paradox because a student teaching his master who then teaches his student has some contradiction. The only way for it not to be a paradox is by throwing in additional assumptions about what they're actually teaching each other, which the statement never gave us. If the statement wasn't a paradox, it would have detailed that the student and the master were teaching each other different things. However, using the definition of a paradox above, the statement fits what a paradox is perfectly. It "seems"self-contradictory, yet in reality it expresses a possible truth (ie. It's not impossible for the student to teach the instructor if you make a few assumptions, but strictly looking at the information provided, it seems contradictory. A master isn't a master in their field anymore if they are being taught by the person they are supposed to be teaching). The problem is that you can make an argument for both sides depending on your point of view, just as in the chicken and the egg paradox. I can understand why people picked it though.

2 is not a paradox because there exists an answer that eliminates any contradiction. The answer is that the person is telling a lie. Just because the person is lying in that statement, it doesn't mean they always lie. That might be the only lie they've ever made. Had the statement been: "I lie at every opportunity, and therefore not a word of truth is ever spoken by me", a case could have been made for the existence of a paradox. If you still don't get it, imagine someone who was trying to trick you into believing that they always lied, so they make that statement in order to fool you. They said it, but in truth, they were lying to you when they said it. They don't always lie, but in this case, they were. Looking back at our paradox definition, the statement does seem contradictory, but when you think about it, it doesn't express a possible truth. A person who always lies could never make the statement "I always lie" because that in itself would be the truth due to the nature of the person always having to lie. This is the main difference between the 1st and 2nd statements. The 1st one is neither true nor false (like the chicken-egg paradox)

Updates

+1 y

For easy reference, here were the options to my original question


(1) The student teaches his instructor who teaches his student


(2) I always lie


(3) This statement is false


(4) To be powerful, one must have an army - to have an army, one must be powerful


(5) Is "no" the answer to this question?

Updates

+1 y

3 is a paradox because if "this statement is false" is true, then the sentence is false, which is a contradiction. Conversely, if "this statement is false" is false, then the sentence is true, which is also a contradiction. This statement is highly contradictory but it does express a possible truth because its simply a statement which is not self- referring.Google the Quine's paradox (or Liars Paradox) It's a paradox which shows that a sentence can be paradoxical even if it is not self-referring

Updates

+1 y

4 is a paradox because the statement defines power as having an army and getting an army requires power. No matter what you start with (power or army), you'll end up in a loop. It is very similar to the chicken and the egg paradox, which also requires a definition. There is contradiction here, but the statement does reflect some truth.

[noumenon]

I think you're wrong and more than one of your answers is not a paradox. (4) is not a paradox - you can imagine a possible world in which this statement is true and serves as an explanation for the fact that nobody has ever been powerful and nobody has ever had an army. Of course, in the actual world there have existed people with power and there have existed people with armies, and sometimes (but not always) these have been the same people. This shows only that (4) is false in the actual world. It does not show that it is a paradox.

BTW in your original question you said "I wonder how many people get this RIGHT". Your emphasis on right/wrong led me to assume you had set a logic puzzle, in which case the correct definition of paradox is the second one in your link - viz. "a self-contradictory and false proposition". Surely (1) is not a paradox in this sense? And all your explanations of why other statements are or are not a paradox seem to use this logic-sense of the word?

Not wanting to be harsh, but I think you might not really be qualified to set a puzzle about paradox. But it was an interesting question nonetheless.

[Janson]

as I said, it was not my possible. it was from a game

[Janson]

puzzle*

[noumenon]

Fair play then and thanks for sharing it. In my excitement at finding a mistake I forgot it was not your puzzle. lol

[Janson]

no worries. It's possible that the game got it wrong.

[palek]

"I am a liar" is paradoxical if by "liar" we mean someone who always lies, as in this case from the statement we would deduce "I am lying now", the liar's paradox. If "liar" is taken in a wider sense, the statement would be true if uttered by somebody who lies occasionally. And false if the speaker weren't a liar, but in this case he would have uttered at least one false sentence. I would suggest removing the last sentence. - Calypso

Since the party in question is professing to always lie, we have no basis to assume they DON'T always lie, and thus the paradox exists.

[palek]

As you said yourself, if the speaker had said "I lie at every opportunity, and therefore not a word of truth is ever spoken by me". How does "I lie at every opportunity, and therefore not a word of truth is ever spoken by me "differ in any form from "I always lie"? The word "always" is defined as 1. At all times; invariably. 2. For all time; forever

[Janson]

The difference is that "I always lie" is not a contradiction if the person saying it is a liar. They don't need to always be a liar, but in this case, they are lying. All it takes is a few lies for someone to be a liar. They don't need to always lie. I see the 2nd statement as more specifically removing the subjects ability to lie about always lying. Anywho, the answer to this question came from a game so I don't know, maybe they got it wrong. I was just curious to see the responses

[palek]

Well, it certainly IS a revolving door, but such is the nature of parodoxes. I just recall the so-called "liars parodox" to be widely accepted as same. Though "always" to me is "always". At any rate, I'll leave it to the logicians to argue about. Bowel maintenance is more to my liking. ; - )

[toulouse]

theres no contradiction in#5 . there is no subject in #5. if the answer WAS no it would be a contradiction because in order to say no youd have to say yes. though not really because you could just say 'the answer to the question is no. you don't have to respond with a yes. or w/e the answer is. the answer to the question is blank. you do not have to say 'no' the answer is not no.

but you dud not ask anything in the question. not knowing the content doesn't count as a contradiction. its insufficient information.

[confugirl]

In the other question, you used the word "instructor" for paradox one instead of master. If you use instructor, it has different implications than if you use master. It wasn't a paradox in the other question. The other things you named are undoubtedly paradoxes.

[Janson]

Ah in the game they said instructor. I said master here by mistake. I think the dynamics are the same though. An instructor isn't an instructor anymore if they are being taught in the subject they are supposed to be instructing.

[confugirl]

So instructors never make mistakes? Or does correcting your instructor when he makes a mistake strip him of his title? If you loosely define an instructor not as someone who is being paid to teach, but someone who teaches in general, then it is a paradox and it means the title of instructor gets shifted between the two persons involved, depending on who has more knowledge about the subject. But in the real world it is not a paradox, since "instructor" is an official title.

[Janson]

Well the statement itself doesn't really specify how long the student is teaching the instructor. Without any specifics, the student could be teaching the instructor indefinitely. At that point, is that instructor really an instructor, or a student? Slip ups every now and then are okay, but would you take a second lesson from someone whom you had to constantly teach in the first lesson? I think the problem is that it can be argued both ways like the chicken and the egg paradox

[confugirl]

Its problem is that it is not defined enough, so it can be argued to be both a paradox and a non-paradox. Maybe THAT is the paradox. But I'm going to lean toward it not being a paradox, simply because, by that logic, any situation with too few parameters can be a called a paradox.

[Janson]

fair enough. I got this from a game and it had me stumped for a while. But on a multiple choice, (2) would probably be the better answer

[confugirl]

Why do you think that?

[Janson]

because its more clearly not a paradox

[confugirl]

I really don't see how you came to that conclusion. You don't have to tell me if you don't want to, I'm just curious.

[Janson]

Well I gave the explanation already. Paradoxes have no "answer" that perfectly solves the problem. Think chicken and the egg scenario, where you can argue for either side, but none is 100% correct. In the second statement however, you have an answer that eliminates any contradiction. The person who made the statement lied.

[confugirl]

Oh I see now. You mean that the person does not always lie, just in this instance and maybe a few others, making the statement incorrect and the person a liar in this instance. Clever

[Janson]

yup!

[Cromartie]

#1 is incorrect since mutual interactions are not paradoxial. As a matter of fact your explaantion is backwards, it requires a specific subject in order to be a paradox. I.E.: "The Math Teacher was learning from the student as he was being taught." The reason the word "master" is used is specifically to indicate that whatever the subject is the person who is teaching it has 100% grasp and the paradox lies in the idea that there is nothing MORE to learn.

So, yeah, #1 is not a paradox. Also #2 IS a paradox. "I always lie", if True, is a Lie, therefore it is a paradox. It's actually classic liar's paradox. The only way this ISN'T a paradox is if you you were to change the statement to reflect the opposite. "I always tell the truth" can be true and never create a paradoxical state.

The only answer is one, but that a mistake, so you posted no answers.

[Janson]

#2 is not a paradox because a paradox doesn't have a side of the argument that is 100% correct. Like the chicken and the egg scenario, you are in a loop no matter what side you take. In the statement "I always lie"...there is no perpetual never ending loop no matter what side you take. The person is simply lying

[Cromartie]

The statement is a paradox because it has only one viable answer despite having two viable answers. If that doesn't make sense that's why it's a paradox. This is the inherent contradiction. It only works under one condition that assumes by reference to itself that it must hold a specific state which creates a false conclusion.

It suffers a contradiction paradox for the exact reason you list; only one of the answers that is possible is allowable.

[Cromartie]

Basically to change terms the phrase "I always lie" is the same for "A strawberry is a thing that is always red." It double-backs by defining it's own nature which is circular logic creating a false conclusion. In order for a thing to be a strawberry it must be red; if you find one that is not red then that would disprove the statement, but because all things that are strawberries are red, the item that is not red but is a strawberry is, simultaneously, not a strawberry.

[wpmason]

I'm with you Cromartie... If "I always lie" is a lie, then I NEVER tell the truth. Therefore stating "I always lie" becomes a truth in itself. Contradictory.

As for 2, there are multiple ways out it... one instructor, 2 students. Differing lessons, etc. you're not trapped in a loop. QA's just wrong.

[wpmason]

I messed up my own explanation. I can't fix it right now. Gotta run.

[palek]

You are correct.

[palek]

Correction: I believe you're correct about everything except the last sentence, since the QA has shown himself to be a man of integrity.

[Cromartie]

It isn't an attack on his integrity. I only addressed the original arguments not any corrections made to them or expressions of intentions. I'm in no place to be attacking others.

[palek]

Me either.

[ElijahCynicism]

Ahhhhhh. Damn, that's really clever. The answer is to simply reject the seeming contradiction. It seems like a play on the old 'This statement is false?' I thought it was just lifted from, as I said, the two doors scenario. 'One of us always tells the truth, the other one always lies.' Of course, that's not a paradox, it's a riddle, and it's not contradictory... Huh...

[Nicolas]

If (3) is a paradox then by the same reasoning (2) is a paradox as well. It has the same structure and the same meaning. If you "always lie" then the statement will not be a lie which is contradictory. If you do not always lie then the statement is false and since, well you do not always lie!

On the other hand (5) is not a paradox, the only one I see that you have not commented upon.

[noumenon]

It's a difficult one to call. Especially since the word "always" is ambiguous. "I always lie" could be analysed to mean "for any proposition P I utter, P is necessarily false" in which case you certainly get the paradox you get in (3). But you do not HAVE to analyse it this way, and if the utterer of the sentence "I always lie" is lying when he says this, then this need not be a paradox just because it is false. To be honest, I don't know if QA is right or wrong about (3), but...

[noumenon]

... I know he's wrong about (4) being a paradox

[noumenon]

Or should I say "the puzzle is wrong". He has just pointed out to me - and it was in the original post - that this was not his puzzle but one from a game.

[Nicolas]

I am not sure about (4) but (5) is surely not one...

[sa230e]

Have you been playing Portal 2 lately?

link

[Janson]

No I haven't haha. Funny

[sa230e]

I highly recommend it.

[Janson]

I imagine its cheap on steam by now so perhaps ill pick it up

[sa230e]

Actual play the first one before you play Portal 2.

[Koldhearted]

Kotor as in Xbox kotor or the mmo?

I always lie

Hmm. I only see it if always doesn't actually mean always.

[Janson]

yeah that kotor. kotor2 actually

[OpenClose]

Well, that was kinda a cool puzzle to think about. Thanks!

[Vandal]

I get it, haha. Very clever. What game did you get it from, BTW?

[Janson]

Knights of the Old republic - of all places haha. It was in a minigame and I was like wtf!

[Vandal]

Classic bioware...

[Janson]

it was kotor 2 actually so Obsidian gets the credit ^_^