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There Are Two Errors in the
is a correct statement

and

There Is One Error in the
is also a correct statement

I get the feeling that there is a confusion induced by the mathematical concept of function where one entry has only one result. Which is not even the case because the 2 statements are clearly different in syntax and in meaning.

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Ditch the doubled "the" to make things clearer and you are left with

"There is one error in this sentence"

Well, is there, or isn't there?

If there is, then there isn't but if there isn't then there is.

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The puzzle must be accepted as posed, not skewed by all sorts of possibilities outside the wording and boundaries stated in the original puzzle. Such as the liar deciding to only tell the truth, this defeats the whole objective of the prisoner finding out the right door to go through. Of course the guards must know which door leads to where, how can you mess up the whole idea of this logic question with all those meaningless assumptions?

No, the liar still always lies and the truth-teller is always honest. That still doesn't require that they give you good information. The liar may just say "The sky is yellow" while the truth-teller says "The sky is blue." The bad assumptions are that both guards will act in the best interest of resolving the puzzle, ie. helping the player. Usually with logic puzzles you want to do the exact opposite, and imagine that the puzzle is run by a demon who can manipulate things in order to produce the worst outcome possible that is still consistent with the rules and the information. This way you can be sure that if a solution is based on logic, there's no opportunity that a favorable outcome may also be arrived at by chance.

Here's another puzzle to show what I mean:

There are two wooden boxes with engraved messages on the top.

The first says "Only one of these boxes' messages is true."

The other says "The gold is in the other box."

Where is the gold? Or, which box do you open?

Ditch the doubled "the" to make things clearer and you are left with

"There is one error in this sentence"

Well, is there, or isn't there?

If there is, then there isn't but if there isn't then there is.

I think it's equivalent to "This statement is false," and asking if it's true or false.

However, if you ask how many errors there are in the statement "This statement is false", you might reasonably say 1, counting the logical inconsistency as an error. So I think that by playing with semantics there's room to count 2 errors in the original sentence. One is "the the", and the other is that the count of errors (while true!) is logically inconsistent. Or, "the paradox is an error." This treats differently whether a sentence is true, and whether or not it is in error. A true statement may have errors. This is probably subject to interpretation.

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No, the liar still always lies and the truth-teller is always honest. That still doesn't require that they give you good information. The liar may just say "The sky is yellow" while the truth-teller says "The sky is blue." The bad assumptions are that both guards will act in the best interest of resolving the puzzle, ie. helping the player. Usually with logic puzzles you want to do the exact opposite, and imagine that the puzzle is run by a demon who can manipulate things in order to produce the worst outcome possible that is still consistent with the rules and the information. This way you can be sure that if a solution is based on logic, there's no opportunity that a favorable outcome may also be arrived at by chance.

Here's another puzzle to show what I mean:

There are two wooden boxes with engraved messages on the top.

The first says "Only one of these boxes' messages is true."

The other says "The gold is in the other box."

Where is the gold? Or, which box do you open?

I think it's equivalent to "This statement is false," and asking if it's true or false.

However, if you ask how many errors there are in the statement "This statement is false", you might reasonably say 1, counting the logical inconsistency as an error. So I think that by playing with semantics there's room to count 2 errors in the original sentence. One is "the the", and the other is that the count of errors (while true!) is logically inconsistent. Or, "the paradox is an error." This treats differently whether a sentence is true, and whether or not it is in error. A true statement may have errors. This is probably subject to interpretation.

"A true statement may have errors."

You might struggle to explain that to a judge if you were in court.

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"A true statement may have errors."

You might struggle to explain that to a judge if you were in court.

This is a simple test of logic, nothing more, accept it as posed by the person who thought it up!

There Are Two Errors in the

and

There Is One Error in the

I get the feeling that there is a confusion induced by the mathematical concept of function where one entry has only one result. Which is not even the case because the 2 statements are clearly different in syntax and in meaning.

You stated that

There Are Two Errors in the

the Title of This Page is a correct statement. (No there is only one error, the extra "the" therefore, it is an incorrect statement)

Edited by Alan McDougall
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OK, back to basics.

"All cats are green and live at the bottom of the ocean" contains two errors.

They are not all green.

They do not all live at the bottom of the ocean.

Agreed?

"This sentence contains 143 errors" is false.

It contains one error- it is wrong about the number of errors.

Agreed?

Edited by John Cuthber
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I hope you plan to cover the difference between error-free and valid (true). A grammatical error does not necessarily change the logic of a statement. So we're dealing with at least 3 types of error here: grammatical/syntax errors, falseness of a statement, and inconsistency of an argument. Be careful not to mix different types of errors into one thing.

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Just because they are different types of errors doesn't mean you can't count them together.

Two apples and three oranges is still five fruits.

So "Some cats are the black" has two errors, one grammatical and one factual.

That's two errors.

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Just because they are different types of errors doesn't mean you can't count them together.

Two apples and three oranges is still five fruits.

So "Some cats are the black" has two errors, one grammatical and one factual.

That's two errors.

So doesn't that make the statement (eg. "There are 2 errors in this this sentence.") true? Is there any way to make the statement not true?

Now I must flipflop... I think you may be right. I looked it up and all I could find was that if a formula is valid, it's negation must be inconsistent (incapable of being true). Since "There are not 2 errors in this this sentence," can be true, then the original must not be valid.

HOWEVER I must flipflop again. Since the sentence is self-referencial, its meaning changes in a way that negating it does not make it a logical negation of the original. So I think it might require interpretation of the meaning of the sentence, and the rules of logic can't be applied naively.

Edit: The logical negation should be "There are not 2 errors in the original sentence."

Is there an interpretation of the original sentence that is not true? Is there an interpretation where there are not 2 errors in the sentence?

All I can think of is that the mix-up of the count of errors is not itself an error if the count turns out to be right, and that any paradox that that creates is not an error either. Personally I don't think that's an acceptable interpretation.

Edited by md65536
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1. Johnny’s mother had three children. The first child was named April. The second child was named May. What was the third child’s name?

Johnny

2. A clerk at a butcher shop stands five feet ten inches tall and wears size 13 sneakers. What does he weigh?

Meat

3. Before Mt. Everest was discovered, what was the highest mountain in the world?

Mt. Everest

4. How much dirt is there in a hole that measures two feet by three feet by four feet?

None

5. What word in the English language is always spelled incorrectly?

Incorrectly

6. Billie was born on December 28th, yet her birthday always falls in the summer. How is this possible?

Southern Hemisphere

7. In British Columbia you cannot take a picture of a man with a wooden leg. Why not?

It isn't a camera

8. If you were running a race and you passed the person in 2nd place, what place would you be in now?

2nd

9. Which is correct to say, “The yolk of the egg is white” or “The yolk of the egg are white?”

Neither both are not correct

10. A farmer has five haystacks in one field and four haystacks in another. How many haystacks would he have if he combined them all in one field?

1

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So doesn't that make the statement (eg. "There are 2 errors in this this sentence.") true? Is there any way to make the statement not true?

Now I must flipflop... I think you may be right. I looked it up and all I could find was that if a formula is valid, it's negation must be inconsistent (incapable of being true). Since "There are not 2 errors in this this sentence," can be true, then the original must not be valid.

HOWEVER I must flipflop again. Since the sentence is self-referencial, its meaning changes in a way that negating it does not make it a logical negation of the original. So I think it might require interpretation of the meaning of the sentence, and the rules of logic can't be applied naively.

Edit: The logical negation should be "There are not 2 errors in the original sentence."

Is there an interpretation of the original sentence that is not true? Is there an interpretation where there are not 2 errors in the sentence?

All I can think of is that the mix-up of the count of errors is not itself an error if the count turns out to be right, and that any paradox that that creates is not an error either. Personally I don't think that's an acceptable interpretation.

Trust me, it's a paradox: just like this one

especially if you ignore the additional error of the stuttered "the".

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Trust me, it's a paradox: just like this one

especially if you ignore the additional error of the stuttered "the".

But is the paradox an error? And if so, is there any interpretation in which the paradox wouldn't be counted as an error?

This one is different than the liar's paradox, because this one is a statement about errors while the liar's paradox is a statement about validity.

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No, Both are statements about truth.

If it's wrong, it's wrong.

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No, Both are statements about truth.

If it's wrong, it's wrong.

What is the truth value of a wrong sentence?

What is the truth value of "This this sentence has a syntax error"?

Edited by md65536
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I saw 'the Enigmatic Giant', an anime episode, on tv the other day that describes the mechanics of an interresting dilemma.

The giant in the title guards a bridge and only allows people to cross if they answer his question correctly.

His question is "If you lie, I will run you through with my sword, but if you tell the truth, I will strangle you with my bare hands, what do you say?"

The correct response is "You will run me through with your sword".

If the giant runs the answerer through with his sword then, by his own stated rules, he implies that the answerer lied but if that was the case then the answerer was telling the truth in the original answer and should not be run through with the sword but should be strangled by the giants bare hands.

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Τhen the giant runs the answerer through with his sword and says:

"Ooops, sorry, my mistake."

Edited by michel123456
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Τhen the giant runs you through with his sword and says, "It seems you told the truth", pulls the sword out, and responsibly strangles you with his bare hands.

If the giant is known to be honest, why not just say nothing (neither lying nor telling the truth)? The "correct" answer is still a lie if you live. It seems that the implied goal is just to make the giant's statement a lie, and then he'll let you pass. I guess as it was mentioned before, it's totally up to the puzzle maker to decide how a giant or guard will act, and in this case the "correct" answer works if the giant is mainly concerned with reasoning alone, which seems to be the point of the puzzle. But reality doesn't work on reasoning, and it is dangerous to think that something physical like your death can be prevented just by making a semantic statement about it logically impossible.

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Τhen the giant runs you through with his sword and says, "It seems you told the truth", pulls the sword out, and responsibly strangles you with his bare hands.

If the giant is known to be honest, why not just say nothing (neither lying nor telling the truth)? The "correct" answer is still a lie if you live. It seems that the implied goal is just to make the giant's statement a lie, and then he'll let you pass. I guess as it was mentioned before, it's totally up to the puzzle maker to decide how a giant or guard will act, and in this case the "correct" answer works if the giant is mainly concerned with reasoning alone, which seems to be the point of the puzzle. But reality doesn't work on reasoning, and it is dangerous to think that something physical like your death can be prevented just by making a semantic statement about it logically impossible.

Very good point.

I have seen the same reasoning with pedestrians crossing the road without even looking left or right, just because they have the right to cross when it is green for the pedestrians. The fact that you are right may kill you in the circumstances.

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What is the truth value of a wrong sentence?

What is the truth value of "This this sentence has a syntax error"?

There is no syntactical error in that sentence.

There is neither a syntactical nor factual error in the sentence

"Thursday is purple".

Since it is not possible to demonstrate that thursday has a colour that differs from purple.

In this case the error is semantic.

And, if you like, you can have a linguistic error too.

if you really put your mind to it, you could combine all those errors in one sentence.

Then you could count the errors.

And, finally, if you make the sentence self-referential and include a negation, you can generate a paradox.

Like you did.

BTW, the correct response to the giant on the bridge is to walk away.

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Those test of mental acuity were obviously too easy, I will come back with more difficult tests later

These tests strongly rely on perfect English language knowledge.

IMHO to truly test somebody mental acuity we need tests that will work without having to know language perfectly. That's why IQ tests looks like they look.

Try beating chimps in this:

They must love these drops..

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Brilliant video - thanks Sensei +1

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I read that, on average, the Japanese (or was it Chinese?) score higher on the IQ tests than even native English speakers.

Edited by Trumptor
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• 1 month later...

I will give the link later!

1. Johnny’s mother had three children. The first child was named April. The second child was named May. What was the third child’s name?

2. A clerk at a butcher shop stands five feet ten inches tall and wears size 13 sneakers. What does he weigh?

3. Before Mt. Everest was discovered, what was the highest mountain in the world?

4. How much dirt is there in a hole that measures two feet by three feet by four feet?

5. What word in the English language is always spelled incorrectly?

6. Billie was born on December 28th, yet her birthday always falls in the summer. How is this possible?

7. In British Columbia you cannot take a picture of a man with a wooden leg. Why not?

8. If you were running a race and you passed the person in 2nd place, what place would you be in now?

9. Which is correct to say, “The yolk of the egg is white” or “The yolk of the egg are white?”

10. A farmer has five haystacks in one field and four haystacks in another. How many haystacks would he have if he combined them all in one field?

1 Johnny

2 meat

3 Mt Everest

4 none

5 incorrectly but that is not right since incorrectly is sometimes not spelled correctly.

6 Souther hemisphere

7 You need to use some sort of camera

8 second place

9 neither

10 one

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• 2 years later...

3. ask either guard which door he/she thinks the other guard will say leads to freedom.... take the opposite door assuming the guards know each other well.

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• 2 weeks later...

In an experiment,you shoot a bullet , down a level flat plane, and drop a bullet at the same moment.

A) At the exact moment bullet A) leaves the barrel of your gun, your friend dropped another bullet B) from his hand at exactly the same height and moment the bullet was expelled out of the end of your gun..

1) Which bullet hits the ground first?

If the gun shot was level, they hit at the same time.

You are rowing up river against a flow of 5 miles per hour, after 1 hour of rowing you notice you have dropped your hat and immediately turn around and row at the same rate down river to retrieve it (Discard the time needed to actually turn your boat around)

2) How long will it take to catch up with your hat and retrieve it from the river?

It's being nit picky, but if you start mixing logical riddles with word play riddles, it's just not a good mix. And people will assume the wrong meaning when looking for more word play.

For instance, it sounds like a wordplay riddle for traveling at the same speed as the hat.

You are in a room with just 2 unmarked doors, one door leads to the hangman and death, the other leads to freedom and life.

There are 2 guards in the room with you, one can only lie the other can only tell the truth. You have no idea which is which.

You are allowed just one question to one of the guards, you chose which, by just by asking this one question, you must establish exactly which door is the one leading to freedom or you die

3) What is the correct question?.

This one is a classic, I answered back in the 80s. I have a bunch of logical riddles from back then, though how many of them I can recall may not be considered a bunch.

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