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    Self-Referential Statements 

   Here is a group of self-referential statements. They illustrate somewhat 
the relationship between meaning and the symbolism of meaning. 

   This sentence contradicts itself--or rather--well, no, actually it 
doesn't! 
   This sentence contains exactly threee erors. 
   In order to make sense of "this sentence", you will have to ignore the 
quotes in "it". 
   You can't have "your cake" and spell it "too". 
   This is a sentence with "onions", "lettuce", "tomato", and "a side of 
fries to go". 
   This is a hamburger with vowels, consonants, commas, and a period at the 
end. 
   Every last word in this sentence is a grotesque misspelling of 
"towmatow". 
   A ceux qui ne comprennent pas l'anglais, la phrase citée ci-dessous ne 
dit rien. "For those who know no French, the sentence above has no meaning." 
   The Spanish sentence "Esta frase en espańol es difícil a traducir en 
inglés." is difficult to translate into English. 
   When one this sentence into the German to translate wanted, would one the 
fact exploit, that the word order and the punctuation already with the 
German conventions agree? 
   If this sentence were in Chinese, it would say something else. 
   When you are not looking at it, this sentence is in Italian. 
   This sentence spent most of last year in Hungarian, and was only recently 
translated back into English. 
   .siht ekil ti gnidaer eb d'uoy ,werbeH ni erew ecnetnes siht fI 
   No language can express every thought unambiguously, least of all this 
one. 
   Anything is possible, right?   No. It's not possible for you to be wrong 
when you assert that anything is possible. 
   i should begin with a capital letter. 
   It feels sooo good to have your eyes run over my curves and serifs. 
   Please, oh please, publish me in your collection of self-referential 
sentences! 
   What would this sentence be like if it were not self-referential? 
   Is "NO" your answer to this question? 
   What does this question ask for? 
   Does this question make sense? 
   This sentence would be seven words long if it were six words shorter. 
   "Has eighteen letters" does. 
   This sentence has five (5) words. 
   This sentence has cabbage six words.
   In the time it takes you to read this sentence, eighty-six letters could 
have been processed by your brain. 
   This sentence was in the past tense. 
   This sentence are not grammatically correct. 
   This is not a complete. Sentence. This either. 
   a preposition. This sentence ends in 
   which actually is not a complete sentence, but merely a subordinate 
clause. 
   This is to be or actually not two sentences to be, that is the combined 
question. 
   This sentence is a !!!! premature punctuator 
   This sentence, though not interrogative, nevertheless ends in a question 
mark? 
   This sentence ends with a period 
   This sentence ends with two periods.  Or are there three? 
   This hear sentence do'nt know Inglush purty good. 
   This prophecy will come true. 
   This sentence will end before you can say "Jack Rob 
   What is a question that mentions the word "umbrella" for no apparent 
reason? 
   Does this sentence remind you of Agatha Christie? 
   I am the thought you are now thinking. 
   This inert sentence is my body, but my soul is alive, dancing in the 
currents of your brain. 
   The reader of this sentence exists only while reading me. 
   I used to think the brain was the most important organ in the body, until 
I realized who was telling me that. 
   I got a new Jewish Mother talking doll. You pull the string and she says: 
"What? Again with the string!?" 
   This sentence refers to every sentence that does not refer to itself. 
   There are two kinds of people: those who finish what they start, and so 
on. 
   The last words of Pancho Villa: "Tell them I said something."
   I've heard that this sentence is a rumor. 
   This sentence takes up one line which might otherwise be blank. 
   This sentence can serve as either the beginning of a paragraph or the 
end, depending on its placement. 
   The whole point of this sentence is to make clear what the whole point of 
this sentence is. 
   P is, for each individual, the number of minutes per month that that 
person spends thinking about the number P. 
   Deliver this message. 
   It is your duty to convince others that this sentence is true. 
   What question no verb? 
   This sentence no verb.    
   This sentence has contains two verbs. 
   This sentence verbs good, like a sentence should. 
   I have nothing to say, and I am saying it. 
   I have nothing to say, but I am not going to admit it. 
   The following sentence is true. 
   The preceeding sentence is false. 
   This statement is unprovable.
   Can you figure out what this statement means? 
   How can you tell if you have properly answered this question? 
   I tried hard to fail, but all my attempts were successful.
   Lots of things in life are uncertain, and I certainly don't require 
certainty everywhere outside this sentence! 
   This sentence is false only on Tuesdays; on other days it is true. 
   This sentence is true only on Tuesdays; on other days it is false. 
   (That the preceeding two sentences are exactly the same length may be 
significant. Or it may not be.) 
   This sentence does in fact not have the property it claims not to have. 
   This sentence contains only one nonstandard English flutzpah. 
   If you think this sentence is confusing, then change one pig. 
   You have, of course, just begun reading the sentence that you have just 
finished reading. 
   The delicate early Spring snow, tenderly caught by eddying breezes, 
swirled and spun into and out of bright, lustrous shapes that gleamed 
against the emerald-blazoned azure drape of sky and sparkled there for a 
moment, hanging briefly, before settling gently to the soft, green-tufted 
meadow with all the sticky, syrupy sweetness of a sickly over-written 
sentence. 
   If I were you, who would be reading this sentence? 
   If you were me, who would have written it? 
   It goes without saying that 
   If I had finished this sentence, 
   In this sentence the final three words 
   This sentence every third, but it still comprehensible. 
   This would easier understand fewer had omitted. 
   This impossible except context. 
   You have been sentenced to death. 
   I have been sentenced to death. 

   Not all self-referential statements are intended to be humorous--or even 
self-referential. Consider the following statement, by Daniel C. Dennett, 
Distinguished Arts and Sciences Professor at Tufts University: 
   "Our powerful subjective impression that we are conscious of sensory 
perceptions in real time is in truth an illusion. Philosophers realized long 
ago that things are not how they seem. Even our illusions are not what they 
seem, because they are built of still more illusions." 
   But Dennett himself, as well as his statements, are "sensory perceptions" 
to his audience. If our thoughts - which are formed from our sensory 
perceptions - are no more than "illusions" then Dennett cannot legitimately 
use the concept "truth." He has rendered it meaningless (indistinguishable 
from illusion) within his self-contradictory context.  
   Perhaps Professor Dennett is himself a figment of his own imagination? 
   As an Objectivist, I see this sort of thing as being not merely 
ridiculous philosophic nonsense, but as being plain and simple evil. It has 
as its effect the undermining of rational cognitive functioning. I really 
don't know whether or not that is Dennett's specific goal, but it IS the 
effect his teachings will have on young students. 

   Another famous philosopher remarked: 
   "There are no certainties in life; there are only probabilities." 
   Which, if true, would mean that the "certainty" expressed by his 
statement is itself merely a probability. 

   Karl Popper maintained that "however hard we try, we shall never discover 
a reliable way of singling out the best of a set of rival opinions." 
   But consider the following set of two rival opinions: 
   1. However hard we try, we shall never discover a reliable way of 
singling out the best of a set of rival opinions. 
   2. If we try hard enough, we can discover a reliable way of singling out 
the best of a set of rival opinions. 
   Observe that Popper has singled out rival opinion #1 as being the best of 
this set of two rival opinions. But in the act of singling out #1, he 
contradicts his thesis that there is no way to single out the best of the 
set. 
   David Deutsch, a British scientist and student of Popper, applies 
Popper's thesis by saying "whenever we have to choose between a set of 
controversial theories or options, there is no mechanically applicable 
criterion that can guarantee to, or even be likely to, pick the best 
contender.... Whatever method we use for making decisions, we will always be 
likely to make mistakes." 
   It is a clear implication of his statement that he is presenting part of 
a method for making decisions, and thus the statement must be applicable to 
itself. We can say: "Using the statement 'Whatever method we use for making 
decisions, we will always be likely to make mistakes' is likely to be a 
mistake." 
   And that ain't no mistake! 


   It is quite possible to have not just sentences that are self-
referential, but lists of sentences in which the sentences refer to the list 
that contains them: 
    
   #1 This list contains exactly one sentence. 
   #2 This list contains exactly two sentences. 
   #3 This list contains exactly three sentences. 
   #4 This list contains exactly four sentences. 
   #5 This list contains exactly five sentences. 
   #6 This list contains exactly six sentences. 
    
   #11 This list contains exactly one true sentence. 
   #12 This list contains exactly two true sentences. 
   #13 This list contains exactly three true sentences. 
   #14 This list contains exactly four true sentences. 
   #15 This list contains exactly five true sentences. 
   #16 This list contains exactly six true sentences. 
   #17 This list contains exactly seven true sentences. 

   #21 There is exactly one false statement in this list. 
   #22 There are exactly two false statements in this list. 
   #23 There are exactly three false statements in this list. 
   #24 There are exactly four false statements in this list. 
   #25 There are exactly five false statements in this list. 
   #26 There are exactly six false statements in this list. 
   #27 There are exactly seven false statements in this list. 
   #28 There are exactly eight false statements in this list. 

   The true statements are #6, #11, and #27. 


   "This sentence contains exactly threee erors." 
   This statement is a clever example of Kurt Gödel's Undecidability (or 
Incompleteness) Theorem, which asserts: "Within any system of axioms, it is 
possible to express a statement whose truth value is undecidable according 
to the axioms of that system." 
   Let us put the sentence into the family of its close relatives, and see 
if, by examining it in this context, we can determine where truth lies, 
where falsehood lies, and where, on the border between truth and falsity, we 
encounter undecidability. 
   #1. This sentence contains exactly onee eror. 
   #2. This sentence contains exactly twoo erors. 
   #3. This sentence contains exactly threee erors. 
   #4. This sentence contains exactly fourr erors. 
   #5. This sentence contains exactly fivee erors. 
   etc. 

   Consider #1, and observe that it has three errors: 
   1. the extra "e".    2. the absent "r".     3. the word "one". 
   Thus there are in fact three errors in #1, and therefore #1 is false. 

   Consider #2, and observe that it has just two errors: 
   1. the extra "o".    2. the absent "r". 
   Since the word "two" accurately enumerates the number of errors in the 
sentence, #2 is a true statement. 

   Let us skip #3 for a moment and go on to consider #4. 
   Observe that it has three errors: 
   1. the extra "r".    2. the absent "r".    3. the word "four". 
   Thus there are in fact three errors in #4, and therefore #4 is false. 

   Observe the similarity in #5: 
   1. the extra "e".    2. the absent "r".    3. the word "five". 
   There are in fact three errors in #5, and therefore #5 is false. 

   A moment's contemplation will reveal that all the statements whose 
numbers are greater than 3 are false, in just the same way that #4 and #5 
are false. 
   We can now see that it is quite easy to decide the truth value of every 
statement in this potentially unlimited list. Every statement, that is, 
except for #3. This sneaky little fellow is going to be difficult! But let's 
take a look at it and see what it reveals. 
   To enumerate its errors: 
   1. the extra "e".    2. the absent "r". 
   These are unequivocal errors--there is no doubt about them--so it is safe 
to say that #3 does indeed contain two errors. But does it contain EXACTLY 
two errors? Is not the word "three" also an error? If so, then statement #3 
would contain three errors and thus would have to be true. But if the 
statement WERE true, then the word "three" would NOT be an error. This would 
leave only two errors in statement #3. But then the word "three" would have 
to be...... 
   And so we find ourselves bouncing back and forth forever, oscillating 
between the two typo errors on the one hand, and the word "three" on the 
other hand. In short, we are STUCK in this quandary. We cannot ever decide 
whether #3 is true or false. But this is precisely the situation that Mr. 
Gödel warned us about! 

   The philosophy of Objectivism provides an explanatory underpinning for 
Gödel's theorem, in its ranking of the axiomatic concepts: Existence, 
Identity and Consciousness. Existence being the most fundamental of these, 
it follows that Consciousness is subsumed by Existence (contained within 
Existence) and therefore that the totality of Existence cannot be 
encompassed by Consciousness. The Undecidability Theorem demonstrates this 
in the symbolic realm, and the Quantum Physics manifests it in the physical 
(existential) realm. 
   This quandary is also indirect proof that any subjectivist epistemology 
must be wrong. It must indeed be true that our symbolic representations 
genuinely do correspond to Reality. If they did not, they would not have the 
power to demonstrate the dominance of Existence over Consciousness. 


   Driven to despair by his fruitless attempts to understand the universe, 
the sage, Devadasa, finally announced in exasperation: 
   "All statements that contain the word God are false." 
   Instantly, his least-favorite disciple, Somasiri, replied: 
   "The sentence I am now speaking contains the word God. I fail to see, oh 
Noble Master, how my simple statement can be false." 
   Devadasa considered the matter for a moment. Then he answered, this time 
with apparent satisfaction: 
   "Only statments that do NOT contain the word God can be true." 
   After a brief pause, Somasiri replied: 
   "If that statement applies to itself, oh Venerable One, it cannot be 
true, because it contains the word God. But if it is NOT true...." 
   In exasperation, Devadasa interrupted by asserting: 
   "Any statement that contains the word God is meaningless." 
   "But then, oh Wisest of the Wise, your very statement must be 
meaningless, because it does itself contain the word God." 
   At this point, Devadasa broke his begging bowl upon Somasiri's head, and 
should therefore be honored as the true founder of Zen. 



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