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Self-referential Paradoxes
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Self-referential Paradoxes |
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Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US 
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How many mistakes are there in the sentence: 'Ther are three misteaks in this sentence'? |
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Cpat Hair
since 2001-06-05
Posts 11793 |
none.... Mistakes does not appear in the sentence at all.  |
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Christopher
Moderator
Member Rara Avis
since 1999-08-02
Posts 8296Purgatorial Incarceration |
Three. I can even explain why, though i was stumped at first.  |
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Stephanos
since 2000-07-31
Posts 3618Statesboro, GA, USA |
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. |
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Essorant Member Elite
since 2002-08-10
Posts 4769Regina, Saskatchewan; Canada |
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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Crazy Eddie Member
since 2002-09-14
Posts 178 |
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.  |
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Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
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? |
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Cpat Hair
since 2001-06-05
Posts 11793 |
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).] |
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Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
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. |
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Cpat Hair
since 2001-06-05
Posts 11793 |
(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. |
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Cpat Hair
since 2001-06-05
Posts 11793 |
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).] |
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Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
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? |
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RSWells Member Elite
since 2001-06-17
Posts 2533 |
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? |
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Nan
Administrator
Member Seraphic
since 1999-05-20
Posts 21191Cape Cod Massachusetts USA |
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..  |
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Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
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? |
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Christopher
Moderator
Member Rara Avis
since 1999-08-02
Posts 8296Purgatorial Incarceration |
Yup - I'm sure.
quote: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).] |
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Essorant Member Elite
since 2002-08-10
Posts 4769Regina, Saskatchewan; Canada |
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).] |
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Essorant Member Elite
since 2002-08-10
Posts 4769Regina, Saskatchewan; Canada |
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).] |
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Christopher
Moderator
Member Rara Avis
since 1999-08-02
Posts 8296Purgatorial Incarceration |
damn. ok, fine. you win. grrrr. i typed it out even and still didn't see it. i dont like you anymore Ron.  |
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Stephanos
since 2000-07-31
Posts 3618Statesboro, GA, USA |
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).] |
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Elizabeth
Moderator
Member Ascendant
since 1999-06-07
Posts 6871Minnesota |
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. |
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Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
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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Stephanos
since 2000-07-31
Posts 3618Statesboro, GA, USA |
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).] |
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Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
"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. |
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Stephanos
since 2000-07-31
Posts 3618Statesboro, GA, USA |
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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Crazy Eddie Member
since 2002-09-14
Posts 178 |
Ron, Having trouble making them drink? Using an example of a Paradox that allowed reference to grammatical mistakes in a forum full of poets and writers could be classed as an unfortunate accident waiting to happen. This statement is true. And This statement is false. Would have been safer examples. I spent some time a couple of years ago trying to explain to my wife why the first was not a paradox and the second definitely was. That explanation may be of some use to clarify the term paradox and in particular the self-referencing aspect of the above examples. The paradox is based upon a fundamental rule - that every proposition has a truth-value that is either true or false. It isn’t important whether the truth-value is known, only that it exists and is either true or false. In fact the truth-value can be both at different times and in different places and situations: It is raining. Could have a truth-value of true or false depending on whether it is in fact raining. It must be one or the other and cannot be both at the same time If we were to apply the same truth-value test to the first example - “This statement is true” – . We can only reference the statement itself to decided whether it is true or false, the proposition itself demands that the truth-value is in fact true but we can test that. If we re-write the proposition to read: This statement has a truth-value of true. Then temporarily assign it a truth-value of true the logic of the proposition works – the truth-value of the statement is true and the proposition has a truth-value of true. Now let’s try assigning a truth-value of false – the truth-value of the statement is false and the proposition has a truth-value of false, the logic works again. However because the statement is self-referencing, claiming that it is true, probability dictates that it is likely to have a truth-value of true but a truth-value of false is possible. This statement is false. This second example is more difficult (if not impossible) to assign a truth–value to, if we re-write the proposition we get this: This statement has a truth-value of false. Let’s temporarily assign a truth-value of false and check the logic – the truth-value of the statement is false and the proposition has a truth-value of false. This obviously doesn’t work, if the truth-value of the proposition is false the truth-value of the statement must be true. Ok, let’s try temporarily assigning a truth-value of true– the truth-value of the statement is true and the truth-value of the proposition is true. This doesn’t work either, if the truth-value of the statement is true the truth-value of the proposition must be false. The paradox is that it must be one or the other but it can’t be both or none, I think the common factor you’re looking for Ron could be classified as self-creating contradiction. [This message has been edited by Crazy Eddie (10-12-2002 04:16 PM).] |
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Brad Member Ascendant
since 1999-08-20
Posts 5705Jejudo, South Korea |
I'm not completely sure I'm applying this theory correctly but consider Russel's theory of types. It seems clear that it is a paradox in first order logic but you can abstract it and say, "'Ther are three misteaks in this sentence'is true' is a paradox' is true. By abstracting into what's called second order logic, the statement itself is no longer paradoxical. Paradoxical statements in second order logic can be abstracted into third order logics and so on and so forth. If this is unclear, I'll try to explain the reasoning on set theory later. Now, as it turns out, this nice little trick has had some real world practical application. Still, I intuitively feel that were trading one logical problem, the paradox, for another, the infinite regression. Or perhaps we should call it the infinite progression. Brad |
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Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
Self-creating contradiction has some promise, Eddie. But I'm not sure it's a great deal more helpful than simply looking for the paradox. Let's look at a less obvious example. Every rule has an exception. If we define the statement as a rule, which isn't a stretch I think, then this is certainly a self-referencing statement. Is it true, false, or a paradox? If it's true, then there must be an exception to this rule, too, meaning it can't be true. It's a paradox, or as you say, a self-creating contradiction. But, if the statement is false? Then there's no contradiction and no paradox. Unfortunately, this falls in the class of "exhaustive" sets where it's impossible to prove it false. The best we can probably hope to do is find a rule with no "known" exception, and that's not good enough to prove that this maybe-a-paradox rule is false. In short, I don't really know if it's a paradox. Any self-referencing statement, I think, is automatically suspect. But how suspect? Brad, you pretty much got it, at least to my understanding. Russell's treatment was to allow anything within a given set to only reference things within lower order sets. With this method, he disallowed direct self-referencing (within the same set) and also prevented indirect self-referencing ("The following sentence is true. The preceding sentence is false."). Of course, it had this nasty little side-effect - I could no longer talk about me. Gödel showed that the elimination of paradoxes necessarily introduced inconsistency. We "might" be able to get rid of paradoxes, but we really don't want to. That's cool. But I'd still like to understand a bit more about their nature. |
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Toerag Member Ascendant
since 1999-07-29
Posts 5622Ala bam a |
It all comes down to whether you are looking thru a windshield that is in fact a windshield as in (shielding one from the wind), or...if it's a window, a clear object intended for seeing through....I am quite sure the real mistake was in your spelling checker however [This message has been edited by Toerag (10-15-2002 08:04 AM).] |
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Stephanos
since 2000-07-31
Posts 3618Statesboro, GA, USA |
Maybe some of you could help me, as I am not familiar with the philosophical terminology related to this phenomenon under discussion... Is there not among all the great minds who have written about self referential paradoxes, the notion or suggestion that in order for a sentence to be true or false, (logically) there is required some external standard or reference by which to judge it true or false. For when I read the sentence, "This sentence is false". this is what happens in my brain ... (help me if I am hopelessly or philosophically or linguistically naive) ... I think to myself, "It is impossible to say meaningfully that this sentence is either false or true, because it refers to nothing distinct from itself which can be judged as true or false. Any assignment of true or false would be completely arbitrary (for the sake of seeing where the sentence goes) which in my mind does not comport with the determination of any truth. When I inquire why I should believe the sentence to be false, the only answer that can come from the sentence itself is "because it is false", begging the question. I am stuck in a position of wondering why the game should be played at all, because the whole structure of the sentence lends to an absurdity. Paradoxes are often just truths in seeming juxtaposition, but paradoxes which cannot be explained may be absurdities, not real paradox at all. The bar of logic seems to deny such a sentence a hearing at all, that's why it flounders outside of court in and endless regression or progression of stalemate. Am I the only one who has seen something fundamentally wrong with the question itself? Who would write such a sentence in real life, for the purpose of making a statement? Is there nothing required of the intent of the stater? Doesn't a statement necessitate a certain intrinsic integrity of purpose in order to be genuine? ie that it was really trying to state something, and not merely pose an intellectual or linguistic dilemma? [This message has been edited by Stephanos (10-15-2002 11:11 PM).] |
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