Double Liar Paradox (Jourdain's paradox)

[Guest]

It seems to me that the simple explanation to this paradox lies in it's title. "Double Liars"

Let F be the Face side and B be the Back. After you have read both sides, it seems that B declares opposite to that of F and vice versa. Therefore both statements are false (or if you prefer), the statement that: The two statements cancel each other.

Therefore neither statement is true and both are liars hence 'Double Liars'.

Edited March 30, 2008 by beyond-logic

[Guest]

wouldn't both sides be false?

[Guest]

If it isn't true that it's true..........then it's not true.

[Guest]

What is ironic is the fact that, because the front sentence is correct, the back sentence is incorrect, and the sentence on the back is also false. It also fails to mention which side of the card it speaks of; don't forget a card has three dimensions, the third is just very, very small. Think of that.

[Guest]

it is just like in math.

rule 1) 0 * anything is.... 0

rule 2) infinity * anything is... infinity

whats 0*infinity?

what is that absence of everything * the fulfilliment of everything?

its impossible to end the problem, unless u know calc.

i do believe that it is an infinit loop. but then again, it could be based on how u read it. and your thought process

This is not a paradox at all. It's absolutely simple.

Sure INFINITY TIMES ANYTHING = INFINITY.

But ZERO is NOT anything, it is NOTHING.

If I ask for something ZERO times, I get ZERO somethings in return.

If I ask for everything ZERO times, I get ZERO everythings in return.

If I ask for INFINITE somethings, I get INFINITE somethings in return.

If I ask for INFINITE nothings, I get INFINITE nothings in return.

ZERO, the absence of something, governs this equation, and therefore results in an answer of ZERO.

Keith

[Guest]

veryy niice.

[Guest]

If the front of the card reads that the sentence on the backside of the card is false then the sentence on the front side of the card would be true to as the sentence on the back of the card as being false.

THINK ABOUT IT

Front

THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS FALSE.

Back

THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS TRUE.

[Guest]

That's the first Paradoxe I ever heard

[Guest]

Maybe this will help, The truth is the absnce of a lie and a lie is the absence of truth.

So, when one side declares to be truth, it is declaring the absence of a lie. Then, when the other side declares the opposite site to be a lie, it is declaring the absence of truth in the opposite side. In conclusion both statements declare that there is a lie. So it is a lie.

[Guest]

THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS FALSE.

is TRUE

THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS TRUE.

is FALSE

Becouse THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS say [THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS FALSE.]

)IF FALSE is TRUE > TRUE is FALSE

IF TRUE is FALSE > FALSE is TRUE

IF TRUE is TRUE > FALSE is FALSE

IF FALSE is FALSE > TRUE is FALSE

...is TRUE or FALSE?

[Guest]

I don't quite understand the fascination with 'paradoxes' of this sort, which basically come down to which of the two statements are true, if any.

I am blue.

I am red.

Am I blue or red? Maybe I'm green. Doesn't matter, both cannot be true.

The truth is on the other side.

The other side holds no truths.

Or is that just it? We enjoy 'trapping' the mind in a room with mirrors on both the wall we are facing and the wall directly behind, and looking at the infinite reflections that result?

I just don't get it. Can someone tell me what I am missing?

I am reminded of the "bullet that pierces all vs. armour that cannot be pierced" contradiction. Similar situation, both just cannot exist. One is right, the other is wrong, or maybe both are wrong, but the contradictory elements cannot both be right.

The simple explanation is :

The two statements cannot be assigned a true or false value to make them consistent simultaneously

[Guest]

Back side

Inscription on the other side is true

Face side

Inscription on the other side is not true

this is not necessarily a logic paradox although it seems to be contradictory, True does not always mean correct that is only one possible meaning, therefore there it is logical to assume in a situation like this the intention is not to say weather or not the sides are correct...

here is some definitions for true

# consistent with fact or reality; not false; "the story is true"; "it is undesirable to believe a proposition when there is no ground whatever for ...

well... we know its not that one.

# accurately placed or thrown; "his aim was true"; "he was dead on target"

This one could work.

# devoted (sometimes fanatically) to a cause or concept or truth; "true believers bonded together against all who disagreed with them"

this one doesnt make much sense...

# truthful: expressing or given to expressing the truth; "a true statement"; "gave truthful testimony"; "a truthful person"

This one wouldn't appear to work but it implies intent also, so it may work especially with the common usage factor of this definition probably just being 'honest'

# conforming to definitive criteria; "the horseshoe crab is not a true crab"; "Pythagoras was the first true mathematician"

wouldn't work...

# dependable: worthy of being depended on; "a dependable worker"; "an honest working stiff"; "a reliable source of information"; "he was true to his word"; "I would be true for there are those who trust me"

This one actually works very well, to be dependable in general does not mean you are always completely correct

# genuine: not pretended; sincerely felt or expressed; "genuine emotion"; "her interest in people was unfeigned"; "true grief"

This one also works very well in the way that implies intent and beliefe in the statement rather than whether or not it is factual.

# true(a): rightly so called; "true courage"; "a spirit which true men have always admired"; "a true friend"

doesnt really work well...

# true(a): determined with reference to the earth's axis rather than the magnetic poles; "true north is geographic north"

once again doesnt work well...

# true(a): having a legally established claim; "the legitimate heir"; "the true and lawful king"

also doesn't work well...

# on-key: in tune; accurate in pitch; "a true note"

does'nt work unless the coin doubles as 2 tuning forks. lol

# accurately fitted; level; "the window frame isn't quite true"

works in the sense that the text may not be straight on one side lol

# as acknowledged; "true, she is the smartest in her class"

doesn't work

# proper alignment; the property possessed by something that is in correct or proper alignment; "out of true"

also works in the sense that the text may not be straight on one side lol

# make level, square, balanced, or concentric; "true up the cylinder of an engine"

another that works in the sense that the text may not be straight on one side lol

I dunno i might be completely out there with this comment i thought lateral thinking could help solve a logic problem by using logic in a paradox discussion I shall call this latogic or maybe logeral

[Guest]

lets look at this in a very basic algebra way

cross multiplying

the saying on the other side is true

the saying on the other side is false

this can be said as

Father = what mother says is true

Mother = What father says is false

so therefore mother is true and father is false

so we simplify into

- = +

------

+=-

we cross multiply and get

2+

---

2-

which brings us to

+

--

-

if you think of it as a fraction then the whole solution is negative

when everything is negative it means that everything is false

therefore what they both say is false

simple math

Credits to PlayTheMindGame fr the mother father thing

Edited December 22, 2008 by lil-xander

[Guest]

This is like a never-ending paradox

1. The sentence on the other side of this card is false

2. The sentence on the otherside of this card is true

If side 1 is true by saying side 2 is false, doesn't it also mean that side 2 is false by saying side 1 is true, which would make side 1 false even though it is true. This reminds me of when an unstoppable force meets an immovable object. You just can't win.

[Guest]

it is just like in math.

rule 1) 0 * anything is.... 0

rule 2) infinity * anything is... infinity

whats 0*infinity?

what is that absence of everything * the fulfilliment of everything?

its impossible to end the problem, unless u know calc.

i do believe that it is an infinit loop. but then again, it could be based on how u read it. and your thought process

Well... wouldn't it be infinitely nothing? zero for infinity? Like the classical idea of a blackhole, to find infinite mass, look for the least of anything?

[Guest]

i think that discussing about a paradox will be a endless discussion simply because a circle has no start no end!!! its all the same with this kind of circular thinking!!! its paradoxal thats all!!!

[Guest]

it is just like in math.

rule 1) 0 * anything is.... 0

rule 2) infinity * anything is... infinity

whats 0*infinity?

what is that absence of everything * the fulfilliment of everything?

its impossible to end the problem, unless u know calc.

i do believe that it is an infinit loop. but then again, it could be based on how u read it. and your thought process

actually, infinity * anything except zero is infinity

so zero * infinity is zero

[Guest]

infinity is not a number, it's a limit.

limit 0*x = 0

x->infinity

however this does not mean that 0*infinity = 0. it just means that, as you go higher and higher, value stays the same or approach zero.

Edited December 25, 2009 by phillip1882

[Guest]

Er, actually guys, zero*infinity and many other similar forms (zero/zero, infinity - infinity, etc.) are indeterminate. So if you're dealing with a problem and you hit something that's indeterminate, then I'm guessing you just have to attack the problem in a different way or circumvent it. I'm basing this guess on having solved limits that are indeterminate via method of substitution by using L'hopital's rule (which is very simple and easy to do - this is all very basic calculus).

On the other hand, something like 1/0 or infinity/0 is not indeterminate, because their limits obviously approach infinity.

Relating it to the paradox:

Say in order for a statement to be true, its limit has to approach 0 as x goes to some number. One side of the paper is true given that the other side is true, so its limit approaches 0 as something else approaches 0. This something else only approaches 0 when the other side does not. So the other side is approaching infinity, so that means both sides are not approaching 0, which means both are false and neither are true.

Okay, scratch that. *scratches it*

Algebraic math means nothing here, sooo...

--

This paradox attempts to assign a boolean value of some abstract concept (a sentence) based on the boolean value of some other abstract concept. So let's look at it from a programming perspective:

boolean sentence1;

boolean sentence2;

sentence1 = sentence2;

They obviously haven't been initialized, so there's two different ways to look at it:

situation A)

boolean sentence1, sentence 2;

//code that initializes the sentences to random values

sentence1 = sentence2;

sentence2 = !sentence1;

This means that whatever sentence2 was will now be sentence1, and sentence2 will change to its opposite value.

What does this show about the paradox?

axiom 1) whether you look at each statement once, in succession, or you look at both statements simultaneously and try to make them both work, matters. Humans tend to do the latter, but in the case of the former...

2) there is no paradox (given you look at each statement once, in succession), both sentence just have an unknown, or rather undefined (but not indeterminate) boolean value

situation B)

You have an object called Sentence that has a data field holding a boolean value. Its constructor may have an empty parameter or a boolean, Sentence parameter.

Sentence sentence2 = new Sentence2();

Sentence sentence1 = new Sentence(true, Sentence2());//sentence1's boolean value is currently null, I think

sentence2 = new Sentence(false, Sentence1);

What this object does is try to determine its own boolean value based on the value of other Sentences... which means this program will go into an infinite loop (or maybe an error).

What does this show?

3) Given that there is a simultaneous, or rather objective, perspective for the two sentences, then there is no answer: the two statements, when combined, simply do not work, and if you search for a solution, you will go in circles. And in this case you could also say that the boolean value of the sentences are both undefined and indeterminate.

So HA! I did relate it to math. =P

[Guest]

Both statements are wrong. Why?

Because they are correct inside a limited spectrum. And that is not being correct.

You glue this card to another surface(a book page,an appliance etc.) with such glue that the card would tear if you were to separate it. Or what if I modify the text on one side of the card ?

Or you just give it to japanese people, unchanged.

In other words, this paradox holds true for as long as the "ingredients" stay untouched.

Moral:

You can't fight somethings in their own territory.

Edited February 14, 2010 by Nox

[Guest]

Based on the two staements in short. Simple answer, One would be truth and the other would be a false but based off limited info of what makes one truth and one false is irrational to try to figure out. For the math proving this? Mathmatics can only give you an idea. An idea is what is agreed on by MOST. Presribed schooling. What they think you should learn. Majority so to speak. Majority only takes 51% What about the other 49% Is there a such thing as truth? Any giving situation can have an unknown outcome. It's simply called a calulated guess. What the odds would be.

Mathmatics are even flawed. Take this riddle for example: Do the riddle before looking at the so called answer.

Riddle:

Three friends check into a motel for the night and the clerk tells them the bill is $30, payable in advance. So, they each pay the clerk $10 and go to their room. A few minutes later, the clerk realizes he has made an error and overcharged the trio by $5. He asks the bellhop to return $5 to the 3 friends who had just checked in. The bellhop sees this as an opportunity to make $2 as he reasons that the three friends would have a tough time dividing $5 evenly among them; so he decides to tell them that the clerk made a mistake of only $3, giving a dollar back to each of the friends. He pockets the leftover $2 and goes home for the day! Now, each of the three friends gets a dollar back, thus they each paid $9 for the room which is a total of $27 for the night. We know the bellhop pocketed $2 and adding that to the $27, you get $29, not $30 which was originally spent. Where did the other dollar go????

So called answer: The Answer to the Riddle

The facts in this riddle are clear: There is an initial $30 charge. It should have been $25, so $5 must be returned and accounted for. $3 is given to the 3 friends, $2 is kept by the bellhop - there you have the $5. The trick to this riddle is that the addition and subtraction are done at the wrong times to misdirect your thinking - and quite successfully for most. Each of the 3 friends did indeed pay $9, not $10, and as far as the friends are concerned, they paid $27 for the night. But we know that the clerk will tell us that they were charged only $25 and when you add the $3 returned with the $2 kept by the bellhop, you come up with $30.

**SEE WHERE IT IS FLAWED: EVEN SIMPLE MATH YOU HAVE TO USE A DIFFERENT METHOD TO FIX WHAT IS FLAWED!!!! It is not an exact science or mathmatical Equation out there that is in complete truth. TO KNOW COMPLETE TRUTH IS IMPOSSIBLE!!! YOU JUST GET A GOOD IDEA BUT DOESNT MAKE IT FACT OR FICTION. Just peices of truth. JUST LIKE SAYING YOU CAN"T HAVE NIGHT WITHOUT DAY. Let the world stop turning and ask yourself that question. They are still trying to find answers to multiples of things So if it made simple math which to most to be fact a false statement then what are the more advanced mathamaticains messing up because of search for complete truth. You can't measure truth. Following bread crums in an endless journey. Please read what I got off the net about calculus alone and get a laugh and where in definition it is wrong. Not Completely wrong but no absolute truth. Just a good idea. I have my thoughts in parentheses***

Off the web:

Calculus in defination: may refer to any method or system of calculation guided by the symbolic ""manipulation"" (Did you notice the word manipulation)of expressions. Historically, calculus was called "the calculus of infinitesimals", (Hint:Infinate means on going or never ending)or "infinitesimal calculus". More generally, calculus (plural calculi) may refer to any method or system of calculation guided by the symbolic manipulation (Theres that word again!!!)of expressions. Some examples of other well-known calculi are propositional calculus, variational calculus, lambda calculus, pi calculus, and join calculus. (Do you see how many forms of calculus?!?!) Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics (Have to point this out. The more advanced courses are just advanced at the present. They will keep trying to find ways to come up with definate answers. Making more advanced math and calculus will be equivant to counting on ones fingers in near future. Not nessesary truth!!!!) devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.(Did u catch that Algebra alone is insufficient?!?!)

CALCULUS ONLY MEASURES THERORY!!!!! Doesn't make it fact. It's just a tool of calulating the odds. Reading, writing, math, science. Everything you use just is a tool to make life a little easier at somethings and more complicated in the end. If you would have never learded to read. You wouldn't be trying to kill yourself over finding the answer. It's like asking is technology a blessing or a curse. It's both!!! Depending on the situation.

I'm 33 years old. 7th grade education. Genius iq. (If you want to base off of that the majority thinks is intelligent.) (What the ones making these test thinks is smart) Please don't let that form your decision. Please always question things and not look to others for absolute truth. Use the information you get as possiblities and throw out what doesn't seem right to you. Put it this way. We never would have made it into space by believing the majority. It was impossible. Except the one's that didn't believe in absolute truth.

Just for fun. Go to youtube and pull up "doctor quantum split screen test.: It's a cool cartoon easy for everyone to follow. Then ask yourself how can something act so strange as if having secrets that it doesn't want figured out. That it seems to literally mocks science. Science can't figure it out and science relies on math to prove it. Sooo, Go quantum.. Quantum is the study of that defies the laws of science. So, truth is untruth givin the situation. It's not fun being intelligent. Life would be easier believing in someone elses truth. Sorry I took up so much time. Life is a brain teaser.

[Guest]

Hey it's a loop..

I know a puzzle just like this one..

A Tennessee man was in court to be sentenced for theft.

The judge told the man, "You may make a statement. If it is true, I'll sentence you to five years in prison. If it is false, I'll sentence you to ten years in prison."

After the man made his statement, the judge decided to let him go free. What did the man say?

[Guest]

The question is, what is a paradox?

Dictionary definition:

1.a statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory : a potentially serious conflict between quantum mechanics and the general theory of relativity known as the information paradox. See note at riddle .

2. a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true : in a paradox, he has discovered that stepping back from his job has increased the rewards he gleans from it.

So basically, a paradox is something that condradicts itself. Recently, in math class, there was a question about the opposite of zero. I wrote that it did not have an opposite , and I wrote a mathematical formula. However, this is not a paradox because it has an answer.If it had been a paradox, I could have written "There is no answer." THIS WOULD CAUSE A PARADOX, BECAUSE I WROTE AN ANSWER! This proves paradoxes are possible. So, paradoxes can happen many times every day without you knowing about them! THIS MUST MEAN THERE IS AN ANSWER TO AL THESE PARADOXES!

Ok, this might not even work, but as my teachers say, I do have a unique way of thinking! Anyways, what do you expect from a 10 year old?

[Guest]

Ok, let me clarify the post above a bit. This is philosophy! There is no right or wrong answer to philosophy! So my answer isn't wrong. (That doesn't mean it's right, but I'm going to think some more.)

[Guest]

The fact of the matter is, what is true and what is false, and subsequently what is a paradox are all human superimposed concepts. If humans did not exist then there would be no true or false (or other life forms with this concept but that is another discussion). Mathematics, despite it's common use is still an abstract concept. We are assigning arbitrary values to the universe so our brains can interact with it logically. The 'paradox' is our mind's attempt to solve conflicting human concepts. The purpose is to achieve a higher understanding of things non-conceptually by forcing our minds to think 'outside the box'. In Zen Buddhism they call these Koans, and students are to sit and meditate on an answer. The point is however, there is no 'answer' since they are still human concepts, and what is conceived as an answer is still a concept. If your mind is contrite, skeptical, and stern, then you will only find contrite, skeptical, and stern answers (such as previous statements of "Oh that's easy." or "That's not a paradox." followed by that persons own perception) If you allow your mind to open up and contemplate all plausibilities then despite an answer you have expanded your mind.