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Double Liar Paradox (Jourdain's paradox)


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63 replies to this topic

#41 Sharon1301

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Posted 19 December 2009 - 03:41 AM

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!!!
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#42 iteasebrain

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Posted 24 December 2009 - 05:32 PM

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
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#43 phillip1882

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Posted 25 December 2009 - 10:37 PM

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 by phillip1882, 25 December 2009 - 10:40 PM.

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#44 DarthNoob

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Posted 26 December 2009 - 08:22 PM

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
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#45 Nox

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Posted 14 February 2010 - 09:55 PM

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 by Nox, 14 February 2010 - 09:56 PM.

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#46 PhoenixFromTheFlames

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Posted 11 March 2010 - 02:37 PM

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.
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#47 GUGHA

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Posted 16 March 2010 - 04:45 PM

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?

Spoiler for The answer is,... The Tennessee man said. You'll sentence me to ten years in prison." Now if this were true, then the judge would have to sentencing him to five years (which would make the man's statement false). However, if the judge were to sentencing him to ten years, then the man's statement would be true and he would have to sentencing him to five years! The man's statement had thus created a 'catch 22' situation...so rather than contradict himself, the judge set the man free!!!.

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#48 Thinker Girl

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Posted 29 March 2010 - 01:52 AM

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?
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#49 Thinker Girl

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Posted 29 March 2010 - 01:55 AM

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.)
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#50 shannonjk

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Posted 13 May 2010 - 06:10 PM

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.
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