Paradoxes

[Armat]

Please explain your answer

[Twilight Bark]

Please explain your answer

In terms of fuzzy logic, the statement's truth value is 0.5.

 

In more human terms:

 

The 2nd sentence negates the first one (he must not be Italian). But that means he might or might not be lying. We don't know.

 

However, this interpretation may be wrong, since being a liar does not mean that he lies all the time, in every sentence. So he may be Italian, and speak the truth about that, and lie in the second sentence. We don't know.

 

Also, he may be Italian, and be truthful about it, and think that all Italians are not necessarily liars, and "lie" about it in the second sentence. The second sentence may or may not be true depending on whether his information about Italians' ethics is correct. We don't know. So we also don't know its effect on the truthfulness of the first claim.

 

Or he may not be Italian. We don't know.

 

.

.

.

 

Conclusion: It is an information-free statement, and its truth value (on a scale of 0 to 1) is 0.5.

 

TB

 

P.S. Yes, I am looking for distractions today.

[Sip]

T.B. ... did I ever tell you I want to be just like you when I grow up?

[Armat]

Hi TB

the answer is rather clever and simple.You did not answer it but you are on something.

hint; exclude all if's

[Twilight Bark]

... when I grow up?

Oh no, don't. It will spoil everything.

Thanks. You might want to reconsider your wish.

[Twilight Bark]

Hi TB

the answer is rather clever and simple.You did not answer it but you are on something.

hint; exclude all if's

What? Is it "Domino two day hands off" ?

[Armat]

No, I know he knows it.

[Armat]

Ok a simpler version

 

This statement is false

 

true?

false?

other?

[ExtraHye]

How long are you going to keep us in suspense.... Come on what is it!!!

[Armat]

two days till Domino probation is over

[ED]

Ok a simpler version

 

This statement is false

 

true?

false?

other?

ok now Armat, put down that class of wine

 

That statment is not correct

[DominO123]

Hmmm... I just realised that this thread existed.

 

OK here is my answer, first of all, I do agree with TB, but with one differences, I think that you more meant that as "liar" they always tell lies, because if that would not be the cases, it would be a half truth like TB refered.

 

But supposing that Italians always tell lies. The answer would inevitably be false. because if you could always tell lies as an Italian, you could not claim to be an Italian.

 

This is like the Paradox of the Heaven door, with the one that tells always the truth and the other, always a lie.

 

But I still prefer TB answer. Admit that he surprised you. (thats like a programmer that finds a bug).

[DominO123]

BTW, I just have read that I had a probation.

[DominO123]

Wait a minute, I remember having read that paradox in a book... let me try to remember which one was it.

[DominO123]

Oh, I forgot to add, that if he would be a truth teller, he could possibly not claim that all Italians are liars, because telling *ALL* he is including himself in it.

 

Now, lets compare it with the Heaven one.

 

A person die, he goes to the purgatory, an Angel tells him to choose between 2 doors... he must know which of the doors to take. One of the doors will bring him to heaven, the other to hell. On each doors there is a gard, one of the gards always tell the truth and the other always lie. The person must ask one question, the same question he must ask it to the two gards, and from the answer he would know which door to choose...

 

What is the question?

 

If you compare to this paradox, it is of similair logic.

 

The person must ask... to each one of the two gards... If I ask to the other one which door I would choose, what will he tell me?

 

By doing such, you are forcing both to tell you a lie... because the truth teller will tell what the other(the liar) will answer, therefore, we could compare it to a lie, while if you ask to the one that lies the same question, he will say the contrary of what the truth teller will say, therefore he will as well lie. In both cases it will be a lie...

 

The same goes with this paradox, if it is not an Italian, and that really Italians are liars, the second statment would be true, but still by being a non-Italian, the first one will be incorrect... on the other cases, he may be an Italian and telling the truth about this, that would mean that he lies when he say all the italians are liars. On the other hand, if the second statment is true, the first can't be true... and we end up that even if he tells the truth in the first, he would lie by saying the second, if we take the second it will include him therefore he could not be an italian, if he would not be, he could not claim to be an italian etc... etc... etc...

 

When i say liar here, I suppose he always lie.

Edited December 6, 2003 by Fadix

[DominO123]

T.B. ... did I ever tell you I want to be just like you when I grow up?

According to TB, I am like he was when he was young, so following this path, I will be like him when i grow up.

[Armat]

Ok I had high expectations but...nobody nailed it.TB's .5 idea was the closest.

The name is Epimenides paradox

It is neither false nor true but rather goes in loop.One part supports the other and goes endlessly.

It is a statement which rudely violates the usually assumed dichotomy of statements into true and false,because if you tentatively think it is true,then it immeediately backfires on you and makes you think it is false.But once you've decided it is false, a similar backfiring returns you to the idea that it must be true.Try it.

Domino I thought you would nail it but....goes to show you are not alien after all.

[DominO123]

Wait a minute, I remember having read that paradox in a book... let me try to remember which one was it.

Epimenides Paradox, I knew it was comming from a book.

 

So, where are you at "Goedel, Escher, Bach" (only Armat will understand that one. )

 

 

Ok! Ok!... I will go replace my avatar to the one of a donkey now.

 

 

The same goes with this paradox, if it is not an Italian, and that really Italians are liars, the second statment would be true, but still by being a non-Italian, the first one will be incorrect... on the other cases, he may be an Italian and telling the truth about this, that would mean that he lies when he say all the italians are liars. On the other hand, if the second statment is true, the first can't be true... and we end up that even if he tells the truth in the first, he would lie by saying the second, if we take the second it will include him therefore he could not be an italian, if he would not be, he could not claim to be an italian etc... etc... etc...

 

But I think this statment of mine was right on track, I just was too dumb to finally tell what it means.

[Sasun]

How about this? He is not Italian, and he also is a liar . So the answer will be "false", where both statements are false: "I am Italian" - false, he is not Italian but Czhekoslovakian, "All Italians are liars" - false, he is just lying because he doesn't like Italians.

Did TB's post also assume this possibility, I am not sure?

[DominO123]

OK! Since Armat will inevitably brake our head by posting something from the interesting work he is reading.

 

I decided to brake heads myself.

 

 

Our jumping off point is the famous Epimenides paradox. Epimenides the Cretan said, "All Cretans are liars." There are two relatives of this sentence: "I am lying" and "This sentence is false"

 

Consider these two:

 

This sentence claims to be an Epimenides paradox, but it is lying.

 

This sentence contradicts itself - or rather - well, no, actually it doesn't!

 

What should you do when told, "Disobey this command"? How about "This sentence contains exactly threee erors."

 

Consider:

 

You can't have "your cake" and spell it "too".

 

In order to make sense of "this sentence," you will have to ignore the quotes in "it."

 

This is a sentence with "onions", "lettuce", "tomato", and "a side of fries to go".

 

This is a sentence with vowels, consonants, commas, and a period at the end.

 

I should begin with a capital letter.

 

I am not the person who wrote me.

 

I am thinking about myself right now.

 

You are under my control because you will read until you have reached the end of me.

 

As long as you are not reading me, the fourth word of this sentence has no meaning.

 

Hey, out there - is that YOU reading me, or is it someone else.

 

Thit sentence is not self-referential because "thit" is not a word.

 

While you are not looking at it, this sentence is in Spanish.

 

I had to translate this sentence into English because I could not read the original Sanskrit.

 

The sentence now before your eyes spent a month in Hungarian last year and was only recently translated back into English.

 

If this sentence were in Chinese, it would say something else.

 

siht ekil ti gnidaer eb d'uoy ,werbeh ni erew ecnetnes siht fi

 

If I had finished this sentence,

 

What would this sentence be like if Pi were 3?

 

If the subjunctive was no longer used in English, this sentence would be grammatical.

 

This sentence would be seven words long if it were six words shorter.

 

Because I didn't think of a good beginning for it.

 

This sentence was in the past tense.

 

This sentence has contains two verbs.

 

This sentence contains one numeral 2 many.

 

This is not a complete. Sentence. This either.

 

This sentence contains only one nonstandard English Flutzpah.

 

It feels so good to have your eyes run over my curves and serifs.

 

This sentence is a !!!! premature punctuator.

 

This sentence, though not interrogative, nevertheless ends in a question mark?

 

If you meet this sentence on the board, erase it.

 

This sentence no verb.

 

I have nothing to say and I am saying it.

 

Do you read me?

 

I have been sentenced to death.

 

This sentence will end before you can say "Jack Rob"

 

Does this sentence remind you of Agatha Christie?

 

What is a question that mentions the word 'umbrella' for no apparent reason?

 

This sentence is graffiti. (But only when on the rest-room wall).

 

How do you keep a turkey in suspense? (Answer follows)

 

One day a father and son go for a walk. The son had told a big lie and his father warns him about the "Liars' Bridge" which they were approaching. This bridge always collapses when a liar walks across it. After hearing this frightening warning, the boy admits his lie and confesses the truth. What happened at the bridge? It collapsed under the father, who had lied, since in fact there is no Liars' Bridge.

 

If the meanings of "true" and "false" were switched, then this sentence wouldn't be false.

 

This sentence every third, but it stil comprehensible.

 

This would easier understand fewer had omitted.

 

I'm just a girl who can't say 'n...', 'n...', 'n...'.

 

The following sentence is totally identical with this one, except that the words 'following' and 'preceding' have been exchanged, as have the words 'except' and 'in', and the phrases 'identical with' and 'different from'.

 

The preceding sentence is totally different from this one, in that the words 'preceding' and 'following' have been exchanged, as have the words 'in' and 'except', and the phrases 'different from' and 'identical with'.

 

This sentence refers to every sentence that does not refer to itself.

 

This paper is dedicated to all those who did not dedicate their papers to themselves.

 

Proper writing - and you've heard this a million times - avoids exaggeration.

 

I used to think I was indecisive, but now I'm not so sure.

 

In this sentence, the last three words 'were left out'.

 

You have, of course, just begun reading the sentence that you have just finished reading.

 

This sentence offers its reader(s) various alternatives/options that he or she (or they) is (are) free to accept and/or reject.

 

If you were me, who would be reading this sentence?

 

You have, of course, just begun reading the sentence that you have just finished reading.

 

If you think this sentence is confusing, then change one pig.

 

The purpose. Of this paragraph. Is to apologize. For its excessive

use. Of. Sentence Fragments. Sorry.

 

Every last word in this sentence is a grotesque misspelling of "towmatow". (Very interesting - two meanings)

 

If this sentence had been on the previous page, this very moment would have occurred approximately 60 seconds ago.

 

The whole point of this sentence is to make clear what the whole point of this sentence is.

 

A very sad poet was Jenny--

Her limericks weren't worth a penny.

In technique they were sound,

Yet somehow she found

Whenever she tried to write any,

She always had one line too many!

 

As long as I have you, I can endure all the troubles you inevitably bring.

 

Remember me? I'm the one who never made any impression on you.

 

Hofstadter's Law: "It always takes longer than you think it will take, even if you take into account Hofstadter's Law."

[DominO123]

How about this? He is not Italian, and he also is a liar . So the answer will be "false", where both statements are false: "I am Italian" - false, he is not Italian but Czhekoslovakian, "All Italians are liars" - false, he is just lying because he doesn't like Italians.

Did TB's post also assume this possibility, I am not sure?

Sasun, this is not what Armat is after, I do believe that he didn't asked the right question, because in its form about the sentence, it takes a false to claim it is false, what the point here is that when you consider it as a lie, it become a truth... as being such, it become a none issue, but if in fact it is a truth... it can't because it become a false... it will continue continue in this never ending cicle.

Edited December 6, 2003 by Fadix

[Sasun]

Sasun, this is not what Armat is after, I do believe that he didn't asked the right question, because in its form about the sentence, it takes a false to claim it is false, what the point here is that when you consider it as a lie, it become a truth... as being such, it become a none issue, but if in fact it is a truth... it can't because it become a false... it will continue continue in this never ending cicle.

What..??? come again Domino, I know you can do it

[Armat]

it takes a false to claim it is false, what the point here is that when you consider it as a lie, it become a truth... as being such, it become a none issue, but if in fact it is a truth... it can't because it become a false... it will continue continue in this never ending cicle.

Domino yes it is from the book.It really got me excited about logic and how easy it is to miss the meaning.

The paradox is great example of loop theory.

[Armat]

Domino this one is a masterpeice

 

I am not the person who wrote me.

this made my night

[Twilight Bark]

The statement in this poll is not exactly equivalent to the Epimenides paradox, but it is messy just like that one. Assuming a "strong" definition of a liar (always lies)

 

I am Italian AND All Italians are liars --> I am a liar --> I am not Italian AND not all Italians are liars --> Since I am not Italian, now I may or may not have been a liar (my being a liar was based on my being Italian) AND depending on whether I lied, all Italians may OR may not be liars --> Complete lack of information

 

truth value: 0.5 (no information)

 

 

In Epimenides' paradox, the first question is not in the loop; it's a given. We know that he is Cretan.

 

With a "strong" definition of a liar (always lies), we end up in an infinite loop in only one branch:

All Cretans are liars --> I am a liar --> Not all Cretans are liars --> I may or may not be a liar (i.e. I may or may not be telling the truth about Cretans)

Possibility 1: He is telling the truth about Cretans (i.e. the statement is TRUE) (go back to the beginning of the loop, which goes on forever);

Possibility 2: He is lying about Cretans (go back to "Not all Cretans are liars", and it is perfectly consistent for him to be a liar and not all Cretans to be liars) and there is no loop. The statement is FALSE

 

truth value: (0+1)/2 = 0.5

 

 

With a "weak" definition of a liar (lies often but not always), we end up with:

 

All Cretans are liars --> I am a liar --> Not all Cretans are liars (although I might be)

Possibility 1: He is telling the truth about Cretans just this time (but he tells lies often, just like all of them) --> His statement is TRUE (no loop)

Possibility 2: He is lying about Cretans (Not all Cretans are liars) --> His statement is FALSE (i.e. He is a liar, but not all Cretans are) (no loop)

 

truth value: (0+1)/2 = 0.5

 

Now a statement like "This statement is false" is a nice, little, clean paradox with a tight little loop. But the poll question and the Epimenides paradox are not as simple.

Edited December 6, 2003 by Twilight Bark