Paradoxes

[DominO123]

Sip, the first sentence is the truth, this person that is an Italian affirms that all Italians are liars... both are not inclusive in a logical test... how many times do I have to tell this? I already said that Armat first question could be misunderstood, I refered after my first answers after knowing which paradox it was, to the orginal with many other examples derived from the paradox.

 

I have to conclude that you are just playing the bonehead here and don't want to admit that you did not read my clarification of Armats poll question, and here you can not claim I was not clear, since my quote was derived from a work not from me.

 

If you don't understand which quotes I am refering to, it follows Sasun post, when I said that I will be braking heads... for some reason most people have ignored this clarification, and most of all, you ignored it, even if I clarified that the first given thing is a fact, and that this person is saying it... this was very soon in this topic...

 

Admit it Sip, you did not read the clarification, because on the first lines of it, you see exactly what I mean, and even the answer was given there.

 

Lets repost what I have posted in the first page of this thread.

 

 

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."

 

 

 

---------------------------------

 

 

 

Now Sip, will you finally admit you are playing the bonehead.

Edited December 7, 2003 by Fadix

[Sip]

I have to conclude that you are just playing the bonehead here and don't want to admit that you did not read my clarification of Armats poll question, and here you can not claim I was not clear, since my quote was derived from a work not from me.

Domino, I told you I did not read your long "clarification". How many times do I have to tell you that?

 

I stated my assumptions about the question, then I presented my solution. You keep saying I am wrong. Every time I ask for explanation, you present a different problem with a different set of assumptions. We are discussing DIFFERENT problems I think although I have no idea what you are trying to say. That's why I explicitly stated things to avoid this confusion.

 

I am DONE as of now about this. I have presented my answer above. If you think I am wrong, present an instance where my logic falls through under the set of assupmtions I have made.

 

 

"I am an Italian AND all italians are liars" ... if you want to discuss this particular problem under MY assumptions further, I'll be listening to what you have to say.

[Sip]

Domino, let me clear up you confusion about the two different problems you are mixing.

 

In the "Cretian" one you present, the "Cretianity" of the guy is taken for granted. It is not questioned ... thus the thing reduces to the "neither" case. In the problem that both MJ and I have been "solving", the "italianness" of the person is a predicate in the problem. That is why I am telling you to STICK to the problem and don't make such a confusing mess of everything. And if you do, at least have the decency not to call others bonehead.

 

I am sorry for getting mad at you but in this case you deserved it.

[DominO123]

Sip, if Azat is a bonehead, you are a metalhead.

 

You ask me to correct something, when I am telling you that your interpretation of the paradox is errenous... I presented the paradox into its context. The context is that you read I AM AN ITALIAN, the reason why you read this, and the reason why the author of the work wrote it that way(Armat changed Cretan for Italian), is for the reader to consider that he is an Italian(the reader is putting himself in the context), when you read I am an Italian, you are saying that you are an Italian, you are putting yourself in the place of an Italian which will say that all the Italians are liars. This is why I told you to replace the words, I am Italian with Sip, which will be you, this I will be you(like it was supposed to be in the first place).

 

You must consider the same way when you say I am an Italian, as you would consider when you consider yourself as Sip, which you are.

 

I AM ITALIAN(THIS IS A GIVEN FACT), as an ITALIAN I declare ALL ITALIANS ARE LIARS.

 

A last note, if you refuse to read the clarifications you can possibly not ask me to prove you wrong, when I am trying to tell you that your interpretation is wrong.

 

 

TB, where are you when I need you?.

[DominO123]

Domino, let me clear up you confusion about the two different problems you are mixing.

 

In the "Cretian" one you present, the "Cretianity" of the guy is taken for granted. It is not questioned ... thus the thing reduces to the "neither" case. In the problem that both MJ and I have been "solving", the "italianness" of the person is a predicate in the problem. That is why I am telling you to STICK to the problem and don't make such a confusing mess of everything. And if you do, at least have the decency not to call others bonehead.

 

I am sorry for getting mad at you but in this case you deserved it. 

Sip, first, I didn't realised what paradox Armat was talking about, i had the same conclusion as MJ and you, you'll see with the first answer I gave... when he presented the paradox, I understood of what he was talking about, he presented an existing paradox, so it was clarified that it was this paradox that was the center of the poll, by being such, we could just claim that Armat was not clear enought, but later, I have posted the carification, just read the two first lines of the quotation I made... It is very clear.... and the confusion had no place after this.

 

I can not stick to the problem, because Armat is talking about a specific paradox which has nothing to do with your interpretation.

Edited December 7, 2003 by Fadix

[Sip]

I can not stick to the problem, because Armat is talking about a specific paradox which has nothing to do with your interpretation.

That is why I made sure I clarified exactly what problem I was referring to. That is the ONLY way to prevent being a bonehead

[Twilight Bark]

Phew. Glad I didn't get involved in the hostilities. Also glad that the version of the ambiguous original problem I "solved" was not considered by any of the warring factions. Please leave it at that.

 

A few quick thoughts to add:

 

Since we are asked to choose "true" or "false" (or "other"), we are forced to start with taking the statement at face value ("true"). If the question were "I am a redhead", or any other simple assertion, the only reasonable answer would be "other" since we really don't know. But that's not in the spirit of the question. The fact that the statement was more complex does not detract from the necessity to start with the assumption that it is true. So, while it is perfectly reasonable to test two assumptions and see where they lead, the spirit of the question really dictates that we only start with assuming the statement to be true and see where it leads. The statement is true unless you prove it false. Or you may arrive at a paradox.

 

Which brings me to the second point. A paradox does not imply that the statement is false. It implies that the statement is useless (i.e. without any usable information). In terms of fuzzy logic, something that isn't true isn't necessarily false. And in terms of binary logic, a paradox isn't false per se; it's not even false, it's nonsense. I think this point might have been overlooked here.

[Twilight Bark]

“Those who speak, know nothing.”

 

Let’s assume that it is true.  Then the above speaker knows nothing, therefore he would not know what those who speak may know or not. Therefore, him/her being a speaker, that statement cannot be true.

... , that statement may or may not be true. Knowing nothing implies that he has no information. But even with no information he will be right half the time (about true-false problems).

 

.... Therefore, those who speak may know something.  This is the only valid implication of the quoted statement with absolutely no built-in paradoxical structure.

That conclusion (that the given statement is false in the strict sense) is correct, but not because of contradicting the initial assumption (which it does, and in the absence of other logical results, that would make it paradoxical, not false), but as a matter of simpler linear deduction.

 

I have a feeling that fuzzy logic experts would find a way to make it half-right (after all the statement is false not because we know for sure that those who speak may know something, but because we have no idea if they may or not).

But I won't go there.

[MJ]

... , that statement may or may not be true. Knowing nothing implies that he has no information. But even with no information he will be right half the time (about true-false problems).

 

 

That conclusion (that the given statement is false in the strict sense) is correct, but not because of contradicting the initial assumption (which it does, and in the absence of other logical results, that would make it paradoxical, not false), but as a matter of simpler linear deduction.

 

I have a feeling that fuzzy logic experts would find a way to make it half-right (after all the statement is false not because we know for sure that those who speak may know something, but because we have no idea if they may or not).

But I won't go there.

[Sasun]

Domino, breaking my head with a paradox? hmm... I doubt, my head is paradox-proof

[Twilight Bark]

That conclusion (that the given statement is false in the strict sense) is correct, but not because of contradicting the initial assumption (which it does, and in the absence of other logical results, that would make it paradoxical, not false), but as a matter of simpler linear deduction.

 

I have a feeling that fuzzy logic experts would find a way to make it half-right (after all the statement is false not because we know for sure that those who speak may know something, but because we have no idea if they may or not).

But I won't go there.  

 

Upon further reflection, I am not sure the statement "Those who speak know nothing" qualifies as "false" even under binary logic. It cannot be proven to be false. And it cannot be proven to be true. We appear to have decided in this thread that what is not proven to be true must be false. I don't think that's quite right. It's a statement whose truth cannot be determined. It's either a paradox or an "indeterminate" statement. In both cases it has a complete lack of information.

 

Those who speak know nothing --> I know nothing --> Those who speak may know something -->

--> Possibility 1: The speaker of the original statement knows something (paradox) (fuzzy truth value = 0.5)

--> Possibility 2: The speaker of the original statement knows nothing

--> Possibility 2.1: The original statement is true by chance (truth value = 0)

--> Possibility 2.2: The original statement is false by chance (truth value = 1)

--> Fuzzy truth value of Possibility 2 = (0+1)/2 = 0.5

---> Fuzzy truth value of the statement: (0.5+0.5)/2=0.5

 

 

I would like to end my contribution to this amusing thread (thanks Armat), by maintaining that it is important to distinguish falsehood from paradox, and to know why we regard something as not true (is it because we know it to be false, or is it that the statement is not justified but not necessarily false?). Failing to master those "niceties" allows us to be manipulated, or become unwitting participants in manipulation.

 

Even if we make mistakes in our logical process, the act of striving for logical judgement already makes us less prone to manipulation.

[Armat]

I got kick out of reading this thread again.

Kind of sad nobody much posts here anymore. During this thread 2003 wow this place was hot!