Pinocchio Paradox

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wongrich
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Pinocchio Paradox

Postby wongrich » Sun Mar 08, 2009 3:39 am UTC

Posted on Digg ... was wondering if a solution/consensus was ever reached. Here's the problem

Pinocchio says "my Nose will grow now"

What will happen ?

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alias.exe
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Re: Pinocchio Paradox

Postby alias.exe » Sun Mar 08, 2009 3:58 am UTC

Wood is an organic material, with a very limited momentum of growth. Being non-sentient, the words that Pinocchio utters carry no weight with regards to the speed of the aforementioned growth of the wood.

Spoiler:
Okay, seriously, the keyword here is paradox.

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thomblake
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Re: Pinocchio Paradox

Postby thomblake » Sun Mar 08, 2009 4:31 am UTC

Pinocchio's nose grows when he lies, not when he says a falsehood, so there is not actually any paradox. Whether his nose grows depends upon the rules of magic, which perhaps are not worth speculation; however, since he doesn't know for certain what will happen in the future, it is unlikely that he can lie about it, unless his apparent certainty about what will happen counts as a lie. So, here are the possibilities:

1. He does not know the future and so can't lie about it. His nose doesn't grow. no paradox.
2. He is lying about how certain he is. His nose grows. no paradox.

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Re: Pinocchio Paradox

Postby eaglef2 » Sun Mar 08, 2009 8:29 am UTC

His nose grows an imaginary length. It will be xi + (current length) longer.
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Re: Pinocchio Paradox

Postby Vieto » Sun Mar 08, 2009 1:23 pm UTC

only the left part of his nose will grow, the other half won't, making what he said a 'half truth'.

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Re: Pinocchio Paradox

Postby Imagist » Sun Mar 08, 2009 6:54 pm UTC

thomblake wrote:Pinocchio's nose grows when he lies, not when he says a falsehood, so there is not actually any paradox. Whether his nose grows depends upon the rules of magic, which perhaps are not worth speculation; however, since he doesn't know for certain what will happen in the future, it is unlikely that he can lie about it, unless his apparent certainty about what will happen counts as a lie. So, here are the possibilities:

1. He does not know the future and so can't lie about it. His nose doesn't grow. no paradox.
2. He is lying about how certain he is. His nose grows. no paradox.


The problem with these solutions is that we are not aware of whether Pinnocchio has solved Pinnocchio's paradox. If he has solved Pinnochio's Paradox in one of these ways, then:

  1. He does know what will happen (his nose will not grow) and he lied about it.
  2. He is not lying about how certain he is (he is certain his nose will grow) and did not lie about it.
I realize this post will not endear me with most of its readers. If everything agrees with what you say, it's not worth saying.

++$_
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Re: Pinocchio Paradox

Postby ++$_ » Mon Mar 09, 2009 6:15 am UTC

There are several cases, and which ones can happen depends on exactly how the fairy made the spells work.

Case 1: Pinocchio is telling the truth (he knows that his nose will grow). Then his nose will grow. There's no stipulation that Pinocchio's nose grows only when he tells a lie, so this is quite possible. If that stipulation is in place, then Pinocchio's nose will not grow, contradiction.

Case 2: Pinocchio doesn't know whether or not his nose will grow, but this doesn't count as a lie. Then his nose will not grow (or it might grow for no reason at all; see Case 1).

Case 3: Pinocchio doesn't know whether or not his nose will grow, and this counts as a lie. Then his nose will grow.

Case 4: Pinocchio knows that his nose will not grow. Then his nose will grow, contradiction.

What we have proven is that Pinocchio can never know for sure that his nose will not grow when he makes the statement "My nose will grow." Under the additional condition that Pinocchio's nose grows only when he tells a lie, then it is also the case that Pinocchio can never know for sure that his nose will grow when he makes that statement. In the latter case, the magic that causes Pinocchio's nose to grow injects enough uncertainty into the system that we can never say he really "knows" what's going to happen when he makes certain statements.

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Re: Pinocchio Paradox

Postby Jedaz » Mon Mar 09, 2009 6:55 am UTC

Pinocchio catches on fire and is incenerated.

Pinocchio's nose is caught in a state of constantly growing and shrinking, this creates a massive amount of energy in a very small period of time (as small of a period as to how quickly the spell can rectify its own mistakes). This energy heats up the particals in his nose, therefore causing him to catch on fire. I think it is fairly self evident how the paradox is resolved from here.

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Re: Pinocchio Paradox

Postby jman03bx » Thu Jul 08, 2010 11:52 pm UTC

It would grow either way.
Long time lurker, first time poster. Registered just to put this one to an end.

Consider two scenarios:

Scenario 1: It's a lie, it would not have grown otherwise, and his nose grows as a result.

Scenario 2: It's true, but since it's a true statement, his nose wouldn't grow. The fact that his nose didn't just grow would, in fact, make it a false statement (just as if you said it is about to rain Jello, and it didn't), and as a result, his nose grows.

Keep in mind, in both scenarios, Pinocchio would appear to be right to observers. However, the rules only say that his nose grows if he lies. In both scenarios, his statements eventually achieve the status of a lie, and as a result, it grows, regardless the apparent truth to Pinocchio's statement.

Just as if you said "A blue car will drive by right now." without any prior knowledge of the car's impending arrival. If one does drive by, while you still appear to be right, however, you did not know ahead of time, so at the moment, it was a baseless prediction, or in other words, a lie.

The fact that Pinocchio does not know for sure whether his nose will grow or not means that his original statement is always a lie.

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thomblake
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Re: Pinocchio Paradox

Postby thomblake » Fri Jul 09, 2010 5:34 pm UTC

jman03bx wrote:The fact that Pinocchio does not know for sure whether his nose will grow or not means that his original statement is always a lie.


This would not convince us Bayesians. If by "for sure" you mean that he would assign a 100% probability, then every statement made by everyone is a lie, as one should never be 100% certain of anything; thus, the word "lie" becomes effectively meaningless. If by "for sure" you merely mean that he would assign a high probability, then it is not necessarily the case that his original statement is always a lie.

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Re: Pinocchio Paradox

Postby Patashu » Fri Jul 09, 2010 9:20 pm UTC

If Pinocchio's nose grew whenever he said a falsehood, he'd have immense divination powers - forget causing paradoxes, he could figure out the question of life, the universe and everything!

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Re: Pinocchio Paradox

Postby t1mm01994 » Sat Jul 10, 2010 5:58 pm UTC

Immense Necro LOSE!

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Re: Pinocchio Paradox

Postby Axidos » Sun Jul 11, 2010 1:22 am UTC

Nothing. I break his nose off.

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Re: Pinocchio Paradox

Postby undecim » Sun Jul 11, 2010 4:40 pm UTC

https://secure.wikimedia.org/wikipedia/en/wiki/Lie wrote:A lie (also called prevarication, falsehood) is a known untruth expressed as truth.


Keyword in the above definition: known.

It all depends on what he knows will happen. If he actually expects his nose to grow, then it won't. If he expects it to not grow, it will. Being wrong about something is not lying.

This logic would continue on indefinitely , meaning that he cannot determine if his nose will grow or not, and so he won't know. Since he doesn't know, he can't lie about it. It won't grow.
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Re: Pinocchio Paradox

Postby cypherjesus » Sun Jul 11, 2010 5:40 pm UTC

I'm just going to say it'll always grow, with no paradox. "Now" is an instant in time. At the moment he completes the sentence, it becomes a lie because it doesn't happen. Then the nose grows, following his lie. It appears he told the truth and still had his nose grow, but it grows only after it didn't initially grow. His foreknowledge seems immaterial--his nose will always grow as a result of the statement, but it will never grow exactly "now," only directly after. How long after depends on his animation speed. And, you know, magic.

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Re: Pinocchio Paradox

Postby Patashu » Sun Jul 11, 2010 11:41 pm UTC

I never knew that truth values propagated at relativistic speeds. Maybe there's a physical theory to built out of this.

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Re: Pinocchio Paradox

Postby ++$_ » Mon Jul 12, 2010 3:09 am UTC

Patashu wrote:I never knew that truth values propagated at relativistic speeds. Maybe there's a physical theory to built out of this.
I can't remember where I heard this (maybe it was Martin Gardner):

Imagine you have a list of statements as follows:

1. Exactly one statement on this list is false.
2. Exactly two statements on this list are false.
3. Exactly three statements on this list are false.
...
1,000,000,000,000,000,000. Exactly 1,000,000,000,000,000,000 statements on this list are false.

It's possible to determine the truth values of all the statements. Now, a computer scientist sneaks up to the top of the list and adds:

0. None of the statements on this list is false.

And instantly the truth value of a statement way down near the other end changes! Spooky action at a distance! (Or not.)

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Re: Pinocchio Paradox

Postby undecim » Mon Jul 12, 2010 7:04 am UTC

cypherjesus wrote:I'm just going to say it'll always grow, with no paradox. "Now" is an instant in time. At the moment he completes the sentence, it becomes a lie because it doesn't happen. Then the nose grows, following his lie. It appears he told the truth and still had his nose grow, but it grows only after it didn't initially grow. His foreknowledge seems immaterial--his nose will always grow as a result of the statement, but it will never grow exactly "now," only directly after. How long after depends on his animation speed. And, you know, magic.


I think you're just trying to interpret the question wrong.

If someone says "my nose will grow" the word "will" implies something int the future.

A better way to say this might be "my nose will grow as a result of this statement"
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Re: Pinocchio Paradox

Postby Mike_Bson » Mon Jul 12, 2010 12:51 pm UTC

wongrich wrote:Posted on Digg ... was wondering if a solution/consensus was ever reached. Here's the problem

Pinocchio says "my Nose will grow now"

What will happen ?

With a little bit of simple logic, it is obvious:

Spoiler:
There was no reason for his nose to grow, at first. There was no reason to have anticipation of such; therefor, when he said his nose was abut to grow, he was lying, which would proceed to cause his nose to grow, but this event does not pertain to his previous knowledge of whether or not his nose will grow.

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Re: Pinocchio Paradox

Postby graatz » Wed Jul 14, 2010 5:01 pm UTC

undecim wrote:A better way to say this might be "my nose will grow as a result of this statement"


That does remove the time element from this dilemma. Perhaps some unmentioned part of the spell is that his nose will poke him in the eye every time he tries to cause a paradox? Another option might be to resolve a paradox as a false, seeing that the spell is meant to teach Pinocchio proper manners/morals. Nothing saying that his nose won't grow from telling a truth but being an ass about it.

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Re: Pinocchio Paradox

Postby Jammerjoint » Thu Jul 15, 2010 5:37 pm UTC

This is such a silly question. Much like "this sentence is false." You are assuming an illogical premise and expecting a logical solution. The very premise that pinnochio's nose can determine the truth of a statement unfailingly is a violation of logical possibility, due to such an instance. The mistake is that you are trying to predict the truth of a statement about the future, however, that statement cannot possess a truth until the future actually arrives. By then, you'd have to time-travel back to the past to evaluate the statement, because once the future has been reached, the truth you were trying to ascertain is null. This apparent paradox arises only from a misleading manipulation of time.

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Re: Pinocchio Paradox

Postby Xias » Fri Jul 16, 2010 1:36 am UTC

If Pinocchio says "God exists as Christians believe him to exist," would his nose grow?

Really the growing nose is a way of punishing Pinocchio for being dishonest, not for making false statements. Honesty vs. Dishonesty is different from Truth vs. Falsehood. The core of the growing nose rule comes from his heart, not his head. Saying "My nose will grow as a result of this statement" would not do anything, his nose will not grow.

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Re: Pinocchio Paradox

Postby BoomFrog » Fri Jul 16, 2010 7:15 am UTC

jman03bx wrote:It would grow either way.
Long time lurker, first time poster. Registered just to put this one to an end.


This is so ironic because A) it was already at an end before you necroed it. And B) You restated ++$_'s Case 3 so you didn't add anything new at all.
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Re: Pinocchio Paradox

Postby bobleboffon3 » Fri Jul 16, 2010 8:08 am UTC

Spoiler:
The answer to this question/paradox is as simple as it is unfunny.

Pinocchio's nose is supposed to grow when Pinocchio's tells lies.

This puzzle brings a situation where if pinocchio's nose grow, he told the truth ( so his nose shouldn't have grown ) and if his nose don't grow, he lied so it should've grown ).

The solution, as boring as it is, is that Pinocchio's nose doesn't grow when he tell lies. Even if it was possible to create a real Pinocchio, it wouldn't work like this. It's just impossible. This statement ( his nose will grow when he tell lies ) bring a logical impossibility : This very problem IS that logical impossibility.

It's a bit complex, but it's just not any more logical than saying "His nose will grow when it doesn't grow", or "2+2 = 4 only if 2+2 =/= 4".

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Re: Pinocchio Paradox

Postby crazyiscool899 » Sat Jul 31, 2010 9:02 pm UTC

thomblake wrote:Pinocchio's nose grows when he lies, not when he says a falsehood, so there is not actually any paradox. Whether his nose grows depends upon the rules of magic, which perhaps are not worth speculation; however, since he doesn't know for certain what will happen in the future, it is unlikely that he can lie about it, unless his apparent certainty about what will happen counts as a lie. So, here are the possibilities:

1. He does not know the future and so can't lie about it. His nose doesn't grow. no paradox.
2. He is lying about how certain he is. His nose grows. no paradox.


1. His nose didn't grow so he lied whether intended or not.
2. His nose grew so he told the truth so his nose would shorten rather than lengthen, hence the term paradox.

The only thing I see hapening, would be his nose grows (truth) because he lied and his nose shortened first (false). Whether that made sense or not to you is not really a concern of mine, because in my mind it made sense. So essentialy nothing would happen to his nose.

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Re: Pinocchio Paradox

Postby Mazuku » Sat Aug 28, 2010 8:25 am UTC

I always figured that Pinocchio's nose only grew when he intentionally told what he believed to be false.

Example: Inside this box, there is an apple.

1/ Pinocchio knows there is an apple inside (he peeked) and told someone that there is an apple inside. Knowingly told the truth = Nose stays short.

2/ Pinocchio knows there is an apple inside (he peeked) and told someone that there is an orange inside. Knowingly told a lie = Nose grows.

3/ Pinocchio believes that there is an apple inside (he guessed) and told someone that there is an apple inside. Believed he told the truth = Nose stays short.

4/ Pinocchio believes that there is an apple inside (he guessed) and told someone that there is an orange inside instead. He believed that he told a lie = Nose grows.

5/ Pinocchio believes he knows that there is an apple inside (he peeked earlier) and told someone that there is an apple even thou someone changed it to an orange after he peeked. Believed he told the truth = Nose stays short.

6/ Pinocchio believes he knows that there is an apple inside (he peeked earlier) and told someone that there is an orange not knowing that someone changed it to an orange after he peeked. He believed that he told a lie = Nose grows.
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Re: Pinocchio Paradox

Postby RonWessels » Sat Aug 28, 2010 2:10 pm UTC

There are also implicit statements made. When Pinocchio says "there is an apple inside the box" (in so many words), there are two statements actually being made. He is saying "I know what is inside the box" as well as "there is an apple inside the box". So, if he makes that statement based on a guess, he lied.

Of course, this is getting rather pedantic for the target audience of the Pinocchio story.

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Re: Pinocchio Paradox

Postby Mazuku » Sun Aug 29, 2010 3:55 am UTC

RonWessels wrote:There are also implicit statements made. When Pinocchio says "there is an apple inside the box" (in so many words), there are two statements actually being made. He is saying "I know what is inside the box" as well as "there is an apple inside the box". So, if he makes that statement based on a guess, he lied.

Of course, this is getting rather pedantic for the target audience of the Pinocchio story.


The nose thing also depends on whenever the inference of "I know what is inside the box" when he doesn't actually know truly counts as a lie or not according to the magic spell.
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Re: Pinocchio Paradox

Postby Axidos » Sun Aug 29, 2010 3:10 pm UTC

Well I guess that's a neat solution. Pinocchio's nose cannot grow unless he knowingly tells a lie. If it could grow in reaction to him telling lies about things he doesn't even know, his nose would be an absolute truth engine capable of determining the exact nature of the universe, and that doesn't really tie in with the whole "don't tell fibs" moral of the story.

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Re: Pinocchio Paradox

Postby thomblake » Wed Sep 01, 2010 4:16 pm UTC

RonWessels wrote:When Pinocchio says "there is an apple inside the box" (in so many words), there are two statements actually being made. He is saying "I know what is inside the box" as well as "there is an apple inside the box".


Only if you're comfortable with infinite recursion.

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Re: Pinocchio Paradox

Postby ChaosR » Wed Sep 01, 2010 10:24 pm UTC

First time he says it, he would be unsure, thus not telling a lie, result: nothing happens
Second time he says it, he would think nothing will happen, thus telling a lie: nose grows

From there on, when he says it, he would be unsure what will happen, thus telling a lie: nose grows
Until, he thinks it must always grow and the second time was just a fluke, in which case it not telling a lie: noes does not grow, and situation will loop back to the previous line.

What will happen depends on what Pinocchio believes will happen. The internal conflict growing from this situation will drive him mad to the point where he will refuse to say it, or keeps saying it forever with spurious results.

Only missed case: Pinocchio thought up this reasoning before hand, thus he tells a lie knowing it depends on his belief rather on the statement he makes, result: nose grows.

Q.E.D.

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Re: Pinocchio Paradox

Postby Mazuku » Thu Sep 02, 2010 4:02 am UTC

Laconic Answer: His nose will only grow when intentionally deceives with his words.
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Re: Pinocchio Paradox

Postby voidistant » Wed Sep 15, 2010 7:38 pm UTC

Spoiler:
When is now? Is that a specific moment in time?

What's Pinocchio's motivation for saying "now"? Did he just tell a lie? If so, he's telling the truth and his nose will grow, perhaps at the same time as the assumed "now" moment if the timing is right. If he didn't, he's lying when he says "now" and his nose will grow, but it won't grow at the moment in time that Pinocchio deems as "now". So in order to have the nose grow at the exact "now" moment, he would have to be telling the truth about his nose growing.

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Re: Pinocchio Paradox

Postby LMeire » Wed Sep 29, 2010 12:57 am UTC

On the outside, his nose does not grow; but on the inside, his nose does grow.

Schrodinger's Nose has created a fourth dimension!

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Re: Pinocchio Paradox

Postby ericgrau » Fri Oct 01, 2010 5:59 am UTC

Disney-type answer: He isn't deceiving anyone so nothing happens. After all, the whole thing was about lying being bad.

Time paradox answer: The nose is hardwired into whether or not a statement is true, and responds accordingly. This is amazingly useful, because now Pinocchio may say statements about anything in the universe whether he knows them to be true or not, and find out which it is. It also requires an omniscient nose, which is a far more notable contradiction than a silly paradox.

The real answer those two were leading towards: Ok fine, pinocchio's nose grows only when he knows it's a lie. He doesn't, so it doesn't.

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Evidence from the novel

Postby tepples » Tue Nov 09, 2010 12:41 pm UTC

Necro in response to a Google search after reverting some vandalism on Wikipedia's article about Pinocchio.

++$_ wrote:There's no stipulation that Pinocchio's nose grows only when he tells a lie

The text of Collodi's novel The Adventures of Pinocchio supports your case 1. Part of chapter 3 strongly implies that it grows whenever he is under stress. This includes pain: "Poor Geppetto kept cutting it and cutting it, but the more he cut, the longer grew that impertinent nose. In despair he let it alone." Growth in response to lying doesn't enter the picture until halfway through the novel, at chapter 17. So I'm guessing it's a chemonasty in response to stress hormones.

graatz wrote:Nothing saying that his nose won't grow from telling a truth but being an ass about it.

Being an ass about it comes later, in chapter 32.

RonWessels wrote:Of course, this is getting rather pedantic for the target audience of the Pinocchio story.

Once the author has been dead for 70 years, the target audience expands to include those who would write fan fiction. Finding the rules of magic that apply in this universe helps avoid inconsistency among works.

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Re: Pinocchio Paradox

Postby iroZn » Fri Nov 12, 2010 1:04 am UTC

Pinocchio's nose will not grow. You cannot lie about something that will happen in the future, only make predictions. Since Pinocchio's nose only grows when he tells a lie, it will not grow.

If Pinocchio had said "My nose just grew" when it hadn't that would be a lie and would cause his nose to grow. Basically his nose does not work retro-actively.
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Re: Pinocchio Paradox

Postby Jimmigee » Mon Nov 15, 2010 11:23 am UTC

iroZn wrote:You cannot lie about something that will happen in the future, only make predictions.


Doesn't this somewhat invalidate pretty much any legal contract ever? You clearly can lie about something in the future, if you have control over it (or in this case if you know the mechanisms by which it works).

Having constructed a magic puppet I can conclusively answer that the entirity of Pinocchio, apart from his nose, get's smaller.

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Re: Pinocchio Paradox

Postby Tirian » Mon Nov 15, 2010 3:45 pm UTC

Jimmigee wrote:
iroZn wrote:You cannot lie about something that will happen in the future, only make predictions.


Doesn't this somewhat invalidate pretty much any legal contract ever? You clearly can lie about something in the future, if you have control over it (or in this case if you know the mechanisms by which it works).


I think this is, again, a semantic argument about what a "lie" is. Let's say I borrow money from you and tell you that I'll pay you back tomorrow. Even if I didn't believe that I would, I don't think that statement is a lie, at least at that time. Tomorrow, when I consciously make the decision to violate the conditions of our agreement, it's the decision that is impeachable and not my statement from the day before.

One could argue about a statement that couldn't possibly be true in the future, like if I said that I would spin straw into gold tomorrow or two plus two would equal five tomorrow. But that's getting pretty deep into modal logic and I'm still not certain that I'd categorize those as false statements without the evidence that tomorrow would provide.

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Re: Pinocchio Paradox

Postby iroZn » Tue Nov 16, 2010 2:18 am UTC

Jimmigee wrote:
iroZn wrote:You cannot lie about something that will happen in the future, only make predictions.


Doesn't this somewhat invalidate pretty much any legal contract ever? You clearly can lie about something in the future, if you have control over it (or in this case if you know the mechanisms by which it works).


Signing a legal contract is equivalent to saying "I will do my absolute best to uphold this contract according to the rules it states, if I do not uphold this contract, I will subject myself to the penalties or face prosecution." Simply put a legal contract allows for multiple possibilities in the future because no one can foresee the future.

Equating the Pinocchio paradox to a legal contract Pinocchio would have had to say "My nose may or may not grow after I say this, depending on whether or not the circumstances would necessitate that my nose grows."
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