I always lie...

[Kushan]

As you've probably guessed this is about the sith written test that is done on Korriban. the 4th question is: "which of these statements is *not* a paradox".

The options were (something along the lines of):

1) the master teaches the student who teaches the master

2) I always lie

3) this statement is false

4) to be powerful one needs an army, to have an army one must be powerful

5) is "no" the answer to the question?

 

I assumed the answer was 3), although it could be 1) (if keeping to Sith ideology of the student surpassing the master). Yet I discover, from the forums and a walkthrough, that the answer is 2)

Now, call me nit-picking, but that IS a paradox. By stating that "I always lie", I have just told the truth, therefore my original statement is incorrect. If I have not told the truth then I do not ALWAYS lie

 

found this on dictionary.com:

 

paradox

 

n : (logic) a self-contradiction; "`I always lie' is a paradox because if it is true it must be false"

 

 

Source: WordNet

[Aegis]

No, it's not a paradox.

 

We can conclude that the statement must be a lie. If it's true, then it contradict itself. That much is clear, right?

However, just because I lie in that statement, it doesn't mean I *always* lie, does it? That might be the only lie I've ever used.

[Nartwak]

Exactly.

[Orchomene]

It's a common mistake in mathematics : the opposite of

Forall x, A(x)=0

is

There exists x, A(x)<0 or A(x)>0

and not

forall x, A(x)<0 or A(x)>0

[Naso]

The first one isn't sufficiently qualified to be a paradox. They could be teaching different things, teacher and student are contrary, not contradictory, and thus can be combined in one person.

 

This statement is false is a paradox, because if it is false, it is also contradictory, because that means it is true, yet the statement claims to be false. No is the answer to this question is the same sort of thing as that. I always lie is also like this.

 

The army thing defines power as having and then says that you must be powerful to have an army. I think it's not technically a paradox because it only problematizes *becoming* powerful and *getting* an army.

[Angry Sherpa]

It's more of a catch 22 than a paradox.

[Kushan]

No, it's not a paradox.

 

We can conclude that the statement must be a lie. If it's true, then it contradict itself. That much is clear, right?

However, just because I lie in that statement, it doesn't mean I *always* lie, does it? That might be the only lie I've ever used.

<{POST_SNAPBACK}>

 

I see what you are saying. Yet, the statement on its own, without any context seems paradoxical. We can only assume it is a lie and that whoever said it has not always lied. Imagine a person who has never communicated to anyone in their life and they say this statement, with nothing else - it is then a paradox. (I know this is beyond the realms of possibility, but paradox's usually are)

 

In hindsight, "this statement is false" is a genuine paradox, it was a bit silly to contemplate it really...

[AlanC9]

I see what you are saying. Yet, the statement on its own, without any context seems paradoxical. We can only assume it is a lie and that whoever said it has not always lied. Imagine a person who has never communicated to anyone in their life and they say this statement, with nothing else - it is then a paradox.

<{POST_SNAPBACK}>

 

Yes, but you're bringing in extra information. We don't know if the speaker has always lied on the strength of the single statement given.

 

Leaving aside what is and isn't a paradox, the reason "I always lie" is different from the others is that it isn't completely self-referential.

[Darth Frog]

Yet, the statement on its own, without any context seems paradoxical.

<{POST_SNAPBACK}>

 

Yes, but it only seems to be paradoxial, and only if you allow yourself to think sloppily. The negation of "I always lie" is not "I always tell the truth", it is merely "I do not always lie" or "I sometimes tell the truth". You won't believe the number of programming bugs that are caused by similar 'thinkos'.

[Aegis]

The first one isn't sufficiently qualified to be a paradox. They could be teaching different things, teacher and student are contrary, not contradictory, and thus can be combined in one person.

 

This is technically true, but it would require an analysis of the words used. Or shall I say, in order for it not to be a paradox, you have to make additional assumptions beyond what information you're given in the statement. You'd have to assume that they teach different things. In a strictly logical use of the statement, it dictates that they are teaching the same thing.

 

This statement is false is a paradox, because if it is false, it is also contradictory, because that means it is true, yet the statement claims to be false. No is the answer to this question is the same sort of thing as that. I always lie is also like this.

 

"This statement is false" is a paradox, yes, because no matter where you start you will end up in a loop. However, "I always lie" is NOT, because you can start in a way so that it doesn't loop (as mentioned above).

 

The army thing defines power as having and then says that you must be powerful to have an army. I think it's not technically a paradox because it only problematizes *becoming* powerful and *getting* an army.

 

It is, because it 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's akin to the chicken and the egg paradox, which also requires a definition (more specifically, that a chicken egg is defined as an egg that comes from a chicken and results in a chicken).

 

I see what you are saying. Yet, the statement on its own, without any context seems paradoxical. We can only assume it is a lie and that whoever said it has not always lied. Imagine a person who has never communicated to anyone in their life and they say this statement, with nothing else - it is then a paradox.

 

It's what I like to call a partial paradox. A paradox is a statement that is logically inconsistent and have no "answer". "I always lie" can be such a statement, but only if you limit your examination of it to one side (more specifically, in this case that it is true). However, for it to be a true paradox, you have to make the assumpion that "I don't always lie" is the same as "I never lie". The two are not mutually exclusive of course, but you'd have to make an assumption without any information to back it up.

You can also say that the person who says this will always either lie or tell the truth. However, if you do, you might as well rewrite the statement to reflect that, giving you a "this statement is false"-type of paradox.

[Cerebus]

5) is "no" the answer to the question?

Where is the problem with that, by the way?

 

In my oppinion, it would only be a paradox if it were phrased:

"Is 'no' the answer to this question?"

[Cerebus]

No, it's not a paradox.

 

We can conclude that the statement must be a lie. If it's true, then it contradict itself. That much is clear, right?

However, just because I lie in that statement, it doesn't mean I *always* lie, does it? That might be the only lie I've ever used.

<{POST_SNAPBACK}>

But don't we have to assume that a statement is valid for it to be a possible paradox? And isn't "I always lie" basically the same as "This statement is false"? Since, if the speaker always lies, as he claims, then this particular statement would be lie, too. Ergo: "This statement is false."

 

If we discard them as meaningless/false to begin with, then none of the alternatives above would qualify as paradoxes, if I understand you correctly.

We would simply assume them to be lies.

[AlanC9]

And isn't "I always lie" basically the same as "This statement is false"?

 

Only if the speaker has only made one statement, ever. Otherwise, you have to check the other statements he's made

[Darth Frog]

  But don't we have to assume that a statement is valid for it to be a possible paradox? And isn't "I always lie" basically the same as "This statement is false"?

 

These particular statements are self-referential and their validity becomes the object/focus of the paradox (if any). The first would be equivalent to the second if it were phrased "This statement is a lie", but it isn't.

 

The point of the statement is implied, and written out it would be something like: "I always lie, therefore this statement must be a lie." Such a statement is false if and only if the premise is true but the conclusion is not. In this particular case the premise can legally be false if the speaker sometimes lies, in which case the whole statement is trivially true ('automatic hit' :D) regardless of what the conclusion is. E.g., the statement 'if 1 == 2 then I am the smartest guy on this board' would be true even if I had the IQ of a potted plant.

 

The example in the dictionary quote a couple of posts back is wrong, but this is not surprising as not all linguists are automatically good in math/logic.

[Cerebus]

Only if the speaker has only made one statement, ever. Otherwise, you have to check the other statements he's made

<{POST_SNAPBACK}>

But assuming he had always lied before: Then the statement would be "the truth" and therefore a paradox because it disqualifies its own content. S: "This (S) true statement is false."

 

Assuming he had never lied before, or only ocasionally: Then the statement would be false and still be a paradox: S:"This (S) false statement is false".

 

Because the statement is refering to itself in an incorrect way.

[Cerebus]

<{POST_SNAPBACK}>

I see that you have got a point but I also see that I don't see it ... ehm, if that makes any sense (in my defence, I am a linguist)

 

This interests me. If you can provide a step-by-step explanation for dummies, I would apreciate it.

[Aegis]

I had written a lengthy explanation of all this, but I came to the conclusion that I'm horrible at explaining things. I think I'll leave that to other people, I can only tell you how it is, not why.

[Darth Frog]

"I never tell the truth" is a paradox but "I always lie" isn't, because in the second case the statement can be false (i.e. a lie) without becoming true.

 

P.S.: please disregard. This was just a brainfart of the first order and the first statement isn't any more paradoxical than the second. :"> I shouldn't have tried fancy stuff after slaving at work until 8 in the evening ... Mea culpa

[Darth Sirius]

5) is "no" the answer to the question?

Where is the problem with that, by the way?

 

In my oppinion, it would only be a paradox if it were phrased:

"Is 'no' the answer to this question?"

<{POST_SNAPBACK}>

"Is 'no' the answer to this question?"

 

"Maybe"

[Pog Mo Thoin]

A really interesting thing to consider is that the construction of a verbal paradox is only possible in self-referrential languages, i.e. languages that can refer to themselves.

 

In "This sentence is false" the subject of the sentence is the sentence itself. Some languages are unable to create these contradictions because sentences can't be assembled in such a way as to refer to themselves. (The speaker can be referred to - "I always lie." in most languages. The language itself cannot in some languages)

 

If you're a dork like I am, you may find this comic funny:

Self Referential Syntax

[Naso]

Yeah, a lot of logic derives from grammar. Parmenides went into a whole lot of stuff about what exists and what doesn't exist, but it all relied on the grammar of the word "to be". Unfortunately, I don't know enough about formal logic to know just how abstract and general it gets, but it will always have some axia, like math, which cannot be proven and simply must be assumed.

[Darth Sirius]

There was one from another game, cant remember which one:

 

Question:

"If you lie to me, I'll kill you with a sword!"

 

"If you tell me the truth, I'll kill you with a spell!"

 

Answer:

"You will kill me with a sword."

 

Which if I'm not mistaken is a true paradox.

[Aegis]

That's an old one, though it was hang or shot last time I saw it.

[The Great Phantom]

There was another logic puzzle somewhere... It was pretty cool... Maybe I'll try to find it.

[Darth Sirius]

That's an old one, though it was hang or shot last time I saw it.

<{POST_SNAPBACK}>

I know there are many, many variants.