.)
quote:
I just don't get your logic on this one. If someone says "look at this painting," why would you think they expected you to provide your own painting to look at?
But someone is not saying, "Look at this painting." With the logic question, the word "this" is being used with a degree of ambiguity. Let's look at it another way:
quote:
In the answer to this question, how many letters are there?
quote:
There are seven words in this statement.
For the answer in the original question to make sense, one would have be able substitute the answer as a statement using the context of the question. Thus:
quote:
How many letters are there in the answer to this question?
quote:
There are four letters in the answer to how many letters are there in the answer to this question.
However, there is no means of obtaining an answer of "four" without introducing a new question. Even if the answer was simplified as:
quote:
There are four letters in the answer to this question.
If the words following "How many letters are there..." were manipulated as part of the question then "this question" does become self-referential, but the answer would not be "four".
quote:
- How many letters are there [in the answer to this question]? - (twenty-six/8-9)
- How many "letters" are there [in the answer to this question]? - (1)
- How many letters are there in "the answer to this question"? - (12 or 23)
quote:
Overthinking. How are any of those answers the amount of letters in themselves?
1 - "How many letters are there?" is the only actual question. "The answer to this question" is twenty-six, which is composed of 9 letters (including two t's)
2 - This is derived the same way, but focus is placed on the word "letters", of which there is only one.
3 - "...in the answer to this question" are the only words in which we are asked to determine the number of letters. These words are composed of 23 letters (12 of which are repeating).
[This message has been edited by philocinemas (edited May 31, 2010).]
First of all, I don't believe there is any ambiguity in "this" at all. I find it quite specific. "This" = "How many letters are there in the answer to this question?" (If we think about it too long we fall into recursion, which is the only way we can beat the computer overlords.) If it were "some question" or "a question" then there would be ambiguity. "This" is a specifier. It is only ambiguous when used poorly. And if I'm going to participate in a riddle I'm going to hope it actually works.
Second of all words are not lightly placed in a riddle and they aren't lightly removed. The only way your story works is if you discount half the words. The real question isn't "How many letters are there?" The real question is, as stated, "How many letters are there in the answer to this question?" X = X. X ≠ x-3. (Of course you are seeing it a x = y-3, which I don't see any justification for.) You have to satisfy all parts of the riddle to get the right answer, not just the ones that aren't prepositional phrases.
Just because the question is self-referential does not mean its original intent is invalidated, especially if it is referring to itself only to specify that it is asking for the answer to itself. (Which is only necessary to clear up the ambiguity of "the answer".)
quote:
There are four letters in the answer to how many letters are there in the answer to this question.
quote:
There are four letters in the answer to: "How many letters are there in the answer to this question?".
I hold no illusions that I will convince you, I just wanted to get my argument out and I think I've got it right where I want it. I want to live in a world where words mean what they mean, even if my novels tell a different story.
I suppose one (or many) could create a new language where each word has one meaning, and one meaning only...but to express what could express already in fuzzy English would expand the base of words you would need by, oh, maybe twentyfold at a bare minimum.
(I've been reading this book I picked up while I was on vacation...In the Land of Invented Languages: Adventures in Lingusitic Creativity, Madness, and Genius, by Arika Okrent, which details the invention of and problems with many invented languages, some at length...a good read and I'll recommend it to anyone who wants to invent a language for an SF or fantasy story...)
Here is what you are stating:
How many- x
letters- L
are there- y
in the answer to this question- [xL=y]=y (or) y=z
-Self Referential- [xL=y]=y
There is no way to represent [xL=y]=4, y=(four). y cannot be both (4) and (four).
-Second Question- y=z
This requires a third variable (L is not one of the variables), thus it is not self referential.
z=(four), y=4, xL=4=(four)
quote:
"This" = "How many letters are there in the answer to this question?"
- "this" only refers to "question"
If it reads as you suggest then this would be the result:
How many letters are there in the answer to: How many letters are there in the answer to: How many letters are there in the answer to: How many letters are there in the answer to, etc.
We never get to "this question" because it is constantly referring back to itself. Only until you separate the question from the prepositional phrases or the words "the answer to this question" do you ever reach an actual question.
The exception is if this were prompting another question that provided its own answer, which is what "four"=4 does.
Just wondering.
However, if one isn't familiar with the language then it just looks like complete gibberish.
Personally I'd put it as F(a) = La where a = F(a)
The function of answer{F(a)* is the amount of letters{L* in the answer{a* with the answer{a* being the result of the function of answer{F(a)*. Which, yes, is an infinite loop, but here's the rub. This is the reason we are smarter than computers, we can see an infinite loop without trying to calculate it. We can get past the cover of The Monster at the End of This Book, even though we could turn it into "the monster at the end of: the monster at the end of: the monster at the end of: . . ." if we really wanted to. Then we'd never learn that it was [Spoiler Alert]Grover[/Spoiler Alert]. You don't have to calculate "this question" you just know that it means the question you're looking at. Then you can concentrate on figuring out the answer. "How many," means the answer is a number. "Letters are there," means that that number signifies the amount of letters in something. "In the answer," tells us what that something is. "To this question," tells us that the answer we need to determine the amount of letters of is also the answer to the question we are considering. Thus the self-referential question demands a self referential answer. (Which is four, or cinqo, or 0 if you want to go the numbers aren't letters route.)
And by the way, four does equal 4, because they mean the same thing. In the same way that 1/2 = 50/100, and (m - 1)(2m + 3) = 2Mē + m - 3 mean the same thing.
(Or we could do it like this F = "How many letters" O = "are there" U = "in the answer" R = "to this question?" thus it becomes F x O x U x R = FOUR .)
quote:
In the answer to this question, how many letters are there?
I quite liked philocinemas' different answering of different questions in the above question. However, English is sufficiently vague that there are a whole lot of equally correct answers, even to the mathematical pure interpretations. For example
There are twenty five letters
Prime number
Twelve of them
I would say sixteen
Two more than sixteen
There are many sentences that can be spoken with correct grammar (with actual words found in the standard-English dictionary), but can not be correctly written. Try to come up with one (or two).
There are three ways to spell there.
Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo.
Anytime we make a statement that "there is more than one way to spell (a specific word)", we make it an impossible sentence to write unless we us phonetic spelling, which is not usually an actual word.
I suppose I'll have to come up with something more challenging (here's another old riddle)I bet this will get a quick answer too -
Can anyone tell me why Bob and Mary are dead, lying in a puddle of water and surrounded by broken glass?
Okay here is my favorite.
Bill is lying dead in the middle of the desert with half a toothpick in his hand. There are no tracks of any kind around him. How did he die?
[This message has been edited by Pyre Dynasty (edited June 06, 2010).]