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Passions in Poetry

Self-referential Paradoxes

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Ron
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0 posted 10-11-2002 03:05 PM       View Profile for Ron   Email Ron   Edit/Delete Message      Find Poems   Click to visit Ron's Home Page   View IP for Ron

How many mistakes are there in the sentence: 'Ther are three misteaks in this sentence'?
Cpat Hair
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1 posted 10-11-2002 03:52 PM       View Profile for Cpat Hair   Email Cpat Hair   Edit/Delete Message      Find Poems  View IP for Cpat Hair

none.... Mistakes does not appear in the sentence at all.
Christopher
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2 posted 10-11-2002 03:52 PM       View Profile for Christopher   Email Christopher   Edit/Delete Message      Find Poems  View IP for Christopher

Three.

I can even explain why, though i was stumped at first.
Stephanos
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3 posted 10-11-2002 03:54 PM       View Profile for Stephanos   Email Stephanos   Edit/Delete Message      Find Poems   Click to visit Stephanos's Home Page   View IP for Stephanos

Ron... there are no mistakes in that sentence.  They were all intentional.




But to play along...

there are two actual grammatical mistakes.  The "third" mistake is the screamer.  If the writer of the sentence was referring to the spelling errors he miscounted, but was inadvertently correct in stating three total mistakes ... but if we say this statement is correct, then it is not really a mistake, hence there are only two mistakes... which reaffirms the third mistake.  There is a referential problem somewhere.


Essorant
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4 posted 10-11-2002 04:48 PM       View Profile for Essorant   Email Essorant   Edit/Delete Message      Find Poems   Click to visit Essorant's Home Page   View IP for Essorant

I think there are six there!

1-spelling mistake "ther"
2-spelling mistake "misteaks"
3-no period
4-the question mark shouldn't be bolded
5-quotation marks should be double quotation marks
6-the sentence says it has 3 mistakes but it has more!


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5 posted 10-11-2002 05:25 PM       View Profile for Crazy Eddie   Email Crazy Eddie   Edit/Delete Message      Find Poems  View IP for Crazy Eddie


There are two mistakes in the sentence and one mistake concerning the truth value of the proposition which means there are a total of three which makes the proposition true and reduces the mistakes to two.

Which means the proposition is false and can be considered a mistake taking the total to three mistakes – minus the proposition, which is now proved not to be a mistake....

Was it an Englishman that wrote this? If it was we could simply ignore it - all Englishmen are liars.
Ron
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6 posted 10-11-2002 05:54 PM       View Profile for Ron   Email Ron   Edit/Delete Message      Find Poems   Click to visit Ron's Home Page   View IP for Ron

Actually, Ron, "mistakes" does appear in the sentence, though the letters aren't necessarily in that precise order. (Get technical with a programmer and expect the same in return! ) You do, however, raise the secondary effect of self-referencing language constructs. They can often be ambiguous.

Chris, are you sure?

Essorant, the lack of a period is grammatically correct, and even if the single quotes and bold question mark were errors, they are not part of the sentence in question.

Stephen, I saw that interpretation of the word "mistakes" and tried to think of a suitable synonym to eliminate the intentional angle. But I didn't try very hard after I realized "they were all intentional" is an assumption. We can't really know that for certain.

But, of course, your play-along conclusion and Eddie's post mark the point where things get interesting. There are only two spelling mistakes in the sentence, making the statement that there are three mistakes inaccurate. The content, thus, becomes the third mistake. But that realization then makes the content accurate, and we're back to just two mistakes.

This is really just a twist on the Epimenides or "liar" paradox we've explored before (ergo, Eddie's reference, which itself becomes a paradox when you know he lives in England). A self-referencing entity refers to itself before it even exists, and this process becomes essential to its existence. It can be fun to create self-referencing paradoxes, and even more fun to try to twist language into a solution to the paradox (even though Gödel mathematically proved, way back in 1931, that paradox forms an implicit and necessary part of every axiomatic system of logical reasoning.). Self-referencing paradoxes can also make excellent playgrounds for writers, as Kafka so delightfully proved again and again. But I also think self-reference can be a useful lens for examining many common "truths."

Every rule has an exception.
All generalizations are misleading.
Ignore all well-meaning advice.
Nothing exists.
Everything is subjective.
Truth is an illusion.

These aphorisms, and probably hundreds more, are all self-referencing. That doesn't necessarily make them paradoxical, though. "This sentence is true," is obviously self-referencing, but not a paradox. "This sentence is false," however, can only be true if it's false and will only be false if it's true. Instant paradox!

It seems to me that any statement that is self-referencing (such as this one?), must be put under the microscope a little longer than would a non-self-referencing statement. The question is, what should we be looking for? Is each such statement a unique case? Is our only course to examine every possible self-referencing statement for contradictions? Or is there a general rule that would help us determine when self-reference becomes paradox?


Cpat Hair
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7 posted 10-11-2002 06:01 PM       View Profile for Cpat Hair   Email Cpat Hair   Edit/Delete Message      Find Poems  View IP for Cpat Hair

Quite the contrary Ron,
( get technical with a database geek and get it in return )
the actual attribute Mistakes, does not appear in the sentence at all. A derivitive of the attribute appears but that was not the question, the question asked was literally how many mistakes appear in the sentence. While all the elements of the attribute appear, the actual ordered combination of attributes does not.

There are however several ways to interpret the meaning of the question as you point out it is ambiguos ( sure wish this thing had spell check)

Now the number of mistakes in the sentence truly depends on the rules applied to it. Therefore, mistakes needs a qualifier to make it more understandable. If for example you are going to query a table for a date, you can query it in numerous ways depending on the criteria you apply to the search. The sentence without additional qualifiers is indeed nonsense. If logic is to be applied, one needs to understand what is intended in the results set. We as humans ASSUME we understand and can answer a question or solve a problem based on ajust a few words ( such as your question that started this.) but often waste our time on blind runs because we do not ask for the specific result set thatis expected. We would therefore in my opinion be better off asking questions related to what it is the person asking the question is looking for, than to simply accept that the statement ( no matter how simple or how much it seems to make common sense) as truth and act on it.

[This message has been edited by Cpat Hair (10-11-2002 06:17 PM).]

Ron
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8 posted 10-11-2002 06:21 PM       View Profile for Ron   Email Ron   Edit/Delete Message      Find Poems   Click to visit Ron's Home Page   View IP for Ron

Ah, but you're seeing "mistakes" as an attribute, and I'm seeing it as a tuple composed of eight attributes. If the sentence is also composed of tuples, each consisting of one attribute, an inner join on each of the eight attributes will return at least one match for each of the eight queries.

SELECT DISTINCTROW [mistakes], * FROM sentence WHERE [M1] In (SELECT [S1] FROM [sentence] As Tmp HAVING Count(*)>1 );


Or, uh, something like that.

Cpat Hair
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9 posted 10-11-2002 06:29 PM       View Profile for Cpat Hair   Email Cpat Hair   Edit/Delete Message      Find Poems  View IP for Cpat Hair

(laughing).....

yes perhaps you are correct oh wise one... however we read not in letters, but in words. Some by recognition of the word itself and no effort made to sound out the letters, etc. While you are looking at the base elements that make up the word and your assumptions are based on the fact all the base elements are there, therefore the attribute is there. If this were true  then all the words that contain the same letters but in different orders, would be redundant.

Now... I have no reservations that you are much better educated in such things than I am and that while you can argue them quite eloquently, I do not.... I would however,
say that while one can break down the base elements into a query statement containing joins, one would be returned only the attributes that have the same base elements
which does not mean it is the same.... only similar.


Cpat Hair
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10 posted 10-11-2002 06:46 PM       View Profile for Cpat Hair   Email Cpat Hair   Edit/Delete Message      Find Poems  View IP for Cpat Hair

Post typing thoughts:

Yet.. you and I both write what is accepted as poetry. Because we do, we actually use the fact that while there is a finite number of definitions for any word, the combinations of words we use create or enhance the original. It is sometimes the very fact that words a range of meanings that we use them, so the reader may take from the things shared what they would. Poems in effect can and often become a pardox of meaning. Knowing this, do we not also then look at the words as the elements of understanding rather than the actual letters that comprise the words? But then, what about sign and sine? they sound the same, contain different letters, but change the understanding of the intent entirely. SO it would argue that similar is not good enough to understand what is being asked or stated. That would then say, your inner join might turn up similar attributes but does not insure the attribute returned is indeed the one requested.



Now I hush... and leave philosophy to those smart enough to debate and understand it... for philosophy is indeed not an exact science but one based on interpretation and study of actions and reactions without the benefit of metrix to measure the actual results.

[This message has been edited by Cpat Hair (10-11-2002 06:56 PM).]

Ron
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11 posted 10-11-2002 07:06 PM       View Profile for Ron   Email Ron   Edit/Delete Message      Find Poems   Click to visit Ron's Home Page   View IP for Ron

Responding technically, if you didn't want "only the attribute that have the same base elements" you would just change to an outer join - but that would be pretty useless. As to similarity, the "m" in mistakes isn't similar to an "m" in the sentence, it is identical. It's no different than asking a database to give you all the customers with a zip code of 49040. The results returned don't represent customers living in similar zip codes; it is the same identical zip code. And unless your customers have hooves or paws, you'll probably get more matches in the sentence than you will in my zip code.  

Less technically? You're absolutely right, of course, and on several different levels.

I find myself wondering if Brad is going to move this thread to a technical forum if we're not careful?
RSWells
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12 posted 10-11-2002 07:29 PM       View Profile for RSWells   Edit/Delete Message      Find Poems  View IP for RSWells

You fellas lost me several bumps ago and perhaps in that miasma the question was answered. But in addition to the two obvious spelling errors would not the quotation mark need be outside the question mark?
Nan
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13 posted 10-11-2002 08:05 PM       View Profile for Nan   Email Nan   Edit/Delete Message      Find Poems   Click to visit Nan's Home Page   View IP for Nan

ROTFLMBO... You guys are making me dizzy - and I'm going to have to read this at least three times to makes heads & tails of it...

But Richard.. I'm giggling the most at your question. Ron and I have gone around on this one... The answer is NOPE - NADA - In this particular case, the question mark goes on the outside... True fact..
Ron
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14 posted 10-11-2002 08:55 PM       View Profile for Ron   Email Ron   Edit/Delete Message      Find Poems   Click to visit Ron's Home Page   View IP for Ron

What Nan kindly failed to mention, Richard, is that our discussion centered around an edit I made to one of her poems at the main site. Like you, I was wrong.  

http://webster.commnet.edu/grammar/marks/question.htm  (This is the best site I've ever found for English grammar and punctuation. Highly recommended, but it only works in Internet Explorer.)

I think I'll change the title of this thread to "Tangents." Anyone got any ideas yet on what makes a self-referencing sentence paradoxical?  
Christopher
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15 posted 10-11-2002 09:47 PM       View Profile for Christopher   Email Christopher   Edit/Delete Message      Find Poems  View IP for Christopher

Yup - I'm sure.
  1. "Ther" should be "There"
  2. "misteaks" should be "mistakes"
  3. there should be a period following "sentence."
This would make the sentence read as follows:
quote:
There are three mistakes in this sentence.
The above is correct in spelling and grammar.

Because - I disagree that the lack of a period is grammatically correct. The question mark outside - i agree with that. However, as you mentioned, the statement inside the quotation marks is what we are looking at, the quotes and question mark being outside (the container). This would require the statement inside to be completed with a period to make a true and grammatically correct statement... unless you wished to include the container, which would increas the mistake level.

[This message has been edited by Christopher (10-11-2002 09:48 PM).]

Essorant
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16 posted 10-11-2002 09:48 PM       View Profile for Essorant   Email Essorant   Edit/Delete Message      Find Poems   Click to visit Essorant's Home Page   View IP for Essorant

I still think the lack of a period is a mistake!
The reader should know that the sentence ends there and isn't including a question mark or any other mark.  Same with a question mark--Would you omit that?  
It would make a difference wouldn't it if the question were:

How many mistakes are there in the sentence: 'Ther are three misteaks in this sentence?' ?


[This message has been edited by Essorant (10-11-2002 10:02 PM).]

Essorant
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17 posted 10-11-2002 09:50 PM       View Profile for Essorant   Email Essorant   Edit/Delete Message      Find Poems   Click to visit Essorant's Home Page   View IP for Essorant

Hey Christopher you must have posted right when I was posting. I agree, the period should be there!

[This message has been edited by Essorant (10-11-2002 09:53 PM).]

Christopher
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18 posted 10-11-2002 10:06 PM       View Profile for Christopher   Email Christopher   Edit/Delete Message      Find Poems  View IP for Christopher

damn.

ok, fine.

you win.

grrrr. i typed it out even and still didn't see it. i dont like you anymore Ron.
Stephanos
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19 posted 10-11-2002 11:08 PM       View Profile for Stephanos   Email Stephanos   Edit/Delete Message      Find Poems   Click to visit Stephanos's Home Page   View IP for Stephanos

Doesn't the whole mystique of the dilemma rest upon an intentional misleading here?

"ther" and "misteaks" are what are commonly thought of as mistakes "in the sentence", ie grammatical or spelling mistakes.  But the validity of what the sentence is saying isn't commonly thought of as a syntax error.  

For example,  "Ellifants are green." contains one syntax error ... the mispelling of elephant.  But the statement that elephants are green is an inaccurate statement or thought of the speaker/ writer.  If the spelling were corrected, there would be nothing wrong with the sentence itself, no matter how inaccurate the statement is.  This whole paradox rests on blurring this distinction by lumping everything together in the one category, "mistakes".

An illusion of ambiguity.


Stephen


[This message has been edited by Stephanos (10-11-2002 11:11 PM).]

Elizabeth
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20 posted 10-11-2002 11:34 PM       View Profile for Elizabeth   Email Elizabeth   Edit/Delete Message      Find Poems   Click to visit Elizabeth's Home Page   View IP for Elizabeth

1. Misspelling of "there."
2. Misspelling of "mistakes."
3. The fact that there are only two mistakes while the sentence states there are three. This is the third mistake!

God bless America, my home sweet home.

Ron
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21 posted 10-12-2002 12:02 AM       View Profile for Ron   Email Ron   Edit/Delete Message      Find Poems   Click to visit Ron's Home Page   View IP for Ron

Essorant, see the web page I referenced earlier. Also, at the same site, on their page about quotation marks, look at the section that deals specifically with Double Punctuation.

Stephen, your point has merit, but doesn't really change anything. Even if I chose a bad example (and I'm starting to feel I should have posted this in the English Workshop), there are tons of good ones. "This sentence is false" isn't in the least bit ambiguous. But it is a paradox, and it's the self-referencing characteristic that makes it one. Bertrand Russell and Alfred North Whitehead published four very big volumes trying to devise a system that eliminated these paradoxes by eliminating the possibility of self-references. I'm not that ambitious. I'd just like to know if there's a common factor that characterizes these paradoxes and would make them easier to identify?
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22 posted 10-12-2002 12:54 AM       View Profile for Stephanos   Email Stephanos   Edit/Delete Message      Find Poems   Click to visit Stephanos's Home Page   View IP for Stephanos

Ron,

Just off the top of my head ... the sentence "This sentence is false" seems to be empty of any meaning.  It refers to absolutely nothing outside of itself rendering it irrational.  It lacks any criteria from which to judge if it is indeed true or false.  So the seeming paradox here is a sentence that can be both true and false at the same time.  But it is not true that anything can in actuality be true and false at the same time ... unless by sleight of hand (or pen) it is emptied of all meaningful points of reference and bent in on itself.  It is the irony of a dog chasing his tail.  The sentence simply says nothing of substance.  Nonentities aren't really true or false, they're just "not".  So perhaps a common factor that identifies these is a lack of any reference to anything real and verifiable.  A prerequisite of a sentence being "false" is that it actually refers to something that can be proven true or false.  You could actually reword the sentence to say, "This statement is false".  Then consider separating the two parts of the sentence.  "This statement" .... is false.  How can "This statement" standing alone be judged true or false, since it is not really a statement and doesn't refer to one?  "is false" is a judging clause.  It judges "This statement".  But "this statement" is not really a statement.  The sentence is nonsensical.


I would say this is a more rational statement ...

The sentence, "'This sentence is false' isn't in the least bit ambiguous" is false.  


[This message has been edited by Stephanos (10-12-2002 01:15 AM).]

Ron
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23 posted 10-12-2002 01:27 AM       View Profile for Ron   Email Ron   Edit/Delete Message      Find Poems   Click to visit Ron's Home Page   View IP for Ron

"My hair is blonde." With the exception of not being self-referencing, this statement follows the same structure and is certainly not nonsensical. More, "This statement is true" not only follows the same structure, is self-referencing, is not nonsensical, but is also not a paradox.

You're essentially trying to twist the language to make a paradox not a paradox. Trust me, some pretty bright guys have been trying to do that for over two thousand years without any real success. Go back and re-read our Liar's Paradox threads. They exist, and are even vital if our logical systems are to remain consistent.

I think self-referencing paradoxes are more than just a curiosity. The examples of aphorisms I listed earlier aren't trivial, not in philosophy, and certainly not for writers.
Stephanos
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24 posted 10-12-2002 02:03 AM       View Profile for Stephanos   Email Stephanos   Edit/Delete Message      Find Poems   Click to visit Stephanos's Home Page   View IP for Stephanos

Ron,

you said ""This statement is true" not only follows the same structure, is self-referencing, is not nonsensical, but is also not a paradox."


In what sense is it "true", since it doesn't really say anything?  I still protest that "This statement" is not a statement that says anything to be true about.  I would alter your analysis a bit and say that it is self referencing, non sensical but not paradoxical... no different really in essence than the "This statement is false" sentence . . .  The paradox in both instances is a farce.  A statement that doesn't really say anything at all cannot be true or false, much less true and false.

"My hair is blonde" is not self referencing.  That's a pretty big exception and makes all the difference.  It is a statement that says something meaningful.


I could easily reverse your statement and say that anyone who makes a "self referencing paradox" is essentially trying to twist the language to make a nonparadox (more accurately an absurdity) a paradox.  And it is obvious that these kinds of sentences are a twisting of language.  They are making an irrational self reference.  It reminds me of someone plugging an extension cord into itself and then trying to elicit amazement by pointing out that it is its own source of electricity.

Can the twisting of language rob a sentence of vital content and retain the cold mechanics of reference?  I still challenge you to tell me what the sentence "This statement is false" is really saying.  What is it stating which may be judged as true or false?

Unless you are able to answer this, I still maintain that the sentence is illogical.

[This message has been edited by Stephanos (10-12-2002 02:11 AM).]

 
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