I wasn't sure where to put these, so I decided to put this in the Philosophy and Religion section, because this statement that I am about to post was first used by an Atheist as an attempt to disprove the existence of God. I can't remember his name, but he said that if he was ever to be judged in front of God, and was allowed to ask a question, he would use this one:
| Quote: |
Is the following statement true or false? You will never say that this statement is true.
|
I thought this was clever, so I decided to post it here. It is similar to that question asking if God can create a stone too large to lift. There are several ways to analyse that sentence.
First, you can point out that it is incomplete. When you say, "this sentence is..." you are talking nonsense. "This sentence" does not yet exist at that point, so "this sentence" can't be anything. Only once the sentence is complete is there a "this sentence"... but by that point it's too late.
Second, you can point out that it creates an infinite regress, like an infinite loop in a programming language (yes, i will say it is true; no, that makes it false; but then it's true; but then it's false...), which means it can neither be true nor false. It's like an irrational number, like π, which is neither even nor odd because it never has a last digit to make it even or odd.
And finally you can just take the Indi method. If it was God, i'd just say: "This statement is true." and smite the smartass while shrugging, "i could be wrong, though."
Reminds me of Douglass Adam's "and then God disappeared in a puff of logic."
Eh, if God is half as great as He's said to be, then he could probably unravel the paradox. After all, He can do anything, and is supposed to be on a much higher level of thinking than us.
Either that, or He might just say some of the same things Indi just said. Or He might just say "No, it is not true or false."
Just remember that question in case you ever need to incapacitate a robot.
This statement is true. I win 
| Indi wrote: |
There are several ways to analyse that sentence.
First, you can point out that it is incomplete. When you say, "this sentence is..." you are talking nonsense. "This sentence" does not yet exist at that point, so "this sentence" can't be anything. Only once the sentence is complete is there a "this sentence"... but by that point it's too late.
|
I don't understand what you are trying the say. The statement is existing as I am saying it. I guess if it could be changed to, "You will never say that the statement I am currently saying is true."
| Quote: |
Second, you can point out that it creates an infinite regress, like an infinite loop in a programming language (yes, i will say it is true; no, that makes it false; but then it's true; but then it's false...), which means it can neither be true nor false. It's like an irrational number, like π, which is neither even nor odd because it never has a last digit to make it even or odd.
|
That's the point. This is sort of like the logic that some people try and use to prove that God can't exist. If God is all powerful and can do anything, then can he create a stone too heavy for him to lift? Well God is supposed to be able to do anything so of course he can create a stone too heavy for him to lift! But if he can't life it, then he can't do everything and he isn't all powerful. The only difference is that this logic just shows that if God exists, he can't be all powerful. The first one actually creates a loop if tried to answer.
| Quote: |
And finally you can just take the Indi method. If it was God, i'd just say: "This statement is true." and smite the smartass while shrugging, "i could be wrong, though."
|
That's probably the most effective way to handle the situation. | liljp617 wrote: |
| This statement is true. I win :) |
But if it's true, you will never say that it's true, which you just did! | Afaceinthematrix wrote: |
| liljp617 wrote: | | This statement is true. I win |
But if it's true, you will never say that it's true, which you just did! |
But that would just make you incorrect for assuming we won't say true. 
| Afaceinthematrix wrote: |
| I don't understand what you are trying the say. The statement is existing as I am saying it. I guess if it could be changed to, "You will never say that the statement I am currently saying is true." |
Let me give you an analogy. If i took you out to an empty plot of land, handed you a shovel, and started digging, then turned to you and said, "This is a nice house, isn't it?", wouldn't you think i was crazy? The house obviously doesn't exist. The fact that we are in the process of building it does not make it exist. It won't exist until it is finished.
The same is true for a sentence. It doesn't exist before you say it, and it doesn't exist while you are saying it. It only exists once it is complete. i'll show you:
The dog ran up t
What is the last sentence i wrote? The correct answer is "i'll show you", because "The dog ran up t" is not a sentence, it is merely a fragment of a sentence.
So "this sentence is false" makes no sense, because while the sentence is in construction, it - like the house - does not yet exist. It can't "be" anything if it does not exist, which makes the resulting sentence nonsense (literally nonsense, like "tree dog from defenestrates" - it means nothing, it's just gibberish).
The changed form doesn't fix matters either, it just makes it more verbose (assuming it works, which it doesn't, as i'll explain in a bit). "The statement you are currently saying" does not exist until it is complete, and you can't make any statements about that statement "being" or "having" anything while it doesn't exist. Of course, your "fixed" statement is really not what you think it is. It is no longer a logical conundrum, it is now a prediction. i could easily say "the statement you just said is true... well, looks like you were mistaken", and no logic is violated.
| Afaceinthematrix wrote: |
| Quote: |
Second, you can point out that it creates an infinite regress, like an infinite loop in a programming language (yes, i will say it is true; no, that makes it false; but then it's true; but then it's false...), which means it can neither be true nor false. It's like an irrational number, like π, which is neither even nor odd because it never has a last digit to make it even or odd.
|
That's the point. This is sort of like the logic that some people try and use to prove that God can't exist. If God is all powerful and can do anything, then can he create a stone too heavy for him to lift? Well God is supposed to be able to do anything so of course he can create a stone too heavy for him to lift! But if he can't life it, then he can't do everything and he isn't all powerful. The only difference is that this logic just shows that if God exists, he can't be all powerful. The first one actually creates a loop if tried to answer. |
Close enough. ^_^;
As far as i know, no one with any sense is stupid enough to use the omnipotence paradox (the "rock you can't lift" thing) to prove that God doesn't exist. That's just plain idiotic - it's like doing something like this: "Joe says boats exist and are more dense than water. Well, anything that is more dense than water sinks, and boats are supposed to float. Therefore Joe is wrong - boats don't exist." If anyone tries to pass that off on you as a good argument, just shake your head sadly.
Rather, what people use the omnipotence paradox in the context of religion for is to prove the idea of a divine being - omnipotent or not - is absurd. The omnipotence paradox is just one part of the argument, which is quite sophisticated, actually. i'll give a really short version: Let's say that there is a "thing" that is greater than everything else in the universe - a supreme "thing". If so, then that "thing" either can't create a rock he can't lift, or he can create a rock he can't lift. If he can't, then he is not the greatest thing in existence - something greater prevents him from doing something (creating a rock he can't lift, which even a lesser being like myself can do easily). If he can, then he is not the greatest thing in the universe (because the rock will be greater). Therefore, the idea of a "greatest thing in the universe" - a "supreme thing" is illogical. And since most religions claim that their pet god is a "supreme thing", "greater than anything else", this argument shows that they're full of crap. That's the really short version. ^_^; | Afaceinthematrix wrote: |
| liljp617 wrote: | | This statement is true. I win |
But if it's true, you will never say that it's true, which you just did! |
He didn't say it! He just typed it on his keyboard! | catscratches wrote: |
| Afaceinthematrix wrote: | | liljp617 wrote: | | This statement is true. I win |
But if it's true, you will never say that it's true, which you just did! |
He didn't say it! He just typed it on his keyboard! |
BAM! Truly the knockout punch. | catscratches wrote: |
| Afaceinthematrix wrote: | | liljp617 wrote: | | This statement is true. I win :) |
But if it's true, you will never say that it's true, which you just did! |
He didn't say it! He just typed it on his keyboard! |
But if you read the original post, it says the scenario....
| Quote: |
if he was ever to be judged in front of God, and was allowed to ask a question, he would use this one:
|
This whole topic is assuming that you are standing in front of God thinking of a question to ask him.
[quote="HalfBloodPrince"][quote="catscratches"][quote="Afaceinthematrix"] | liljp617 wrote: |
| This statement is true. I win :) |
| Quote: |
BAM! Truly the knockout punch. :) |
Not quite... because like I said, the original post states that the scenario... and so when he said that, I was assuming that he knew the stipulations, which state that you are asking this question to God as you are being judged.
Oh yeah, and I forgot to add something... You can say something without speaking it. There's a difference. Are you saying that someone who's tongue got cut out never has anything to say? Sure he never has anything to speak, but he can still say something. So by typing it, you are saying it.
Last edited by Afaceinthematrix on Wed Apr 09, 2008 7:12 am; edited 1 time in totalEach phrase presuming, of course, that "God" is incapable of lying.
| Afaceinthematrix wrote: |
I wasn't sure where to put these, so I decided to put this in the Philosophy and Religion section, because this statement that I am about to post was first used by an Atheist as an attempt to disprove the existence of God. I can't remember his name, but he said that if he was ever to be judged in front of God, and was allowed to ask a question, he would use this one:
| Quote: |
Is the following statement true or false? You will never say that this statement is true.
|
I thought this was clever, so I decided to post it here. It is similar to that question asking if God can create a stone too large to lift. |
No one ever said that God can't lie.
but it does remind me of a story I heard once:
A traveler was approached by the Devil at a crossroads. He told the traveler that he would give him his weight in gold if the traveler could think of something that the devil was incapable of doing. So the traveler asked, "You know where every place in existence is, right?"
The Devil, with a smug smile, replied, "Of course. I have been around since the beginning, Since God first started shaping the universe. I know everywhere that has ever been."
So the traveler said, "OK. Get lost."
I'm sure I've left out some details, it's been a long time since I heard this one. | Quote: |
No one ever said that God can't lie.
|
I'm not big into religion, but isn't God supposed to be perfect because you can't sin in Heaven? And isn't lying against the ten commandments? | Indi wrote: |
| Afaceinthematrix wrote: | | I don't understand what you are trying the say. The statement is existing as I am saying it. I guess if it could be changed to, "You will never say that the statement I am currently saying is true." |
Let me give you an analogy. If i took you out to an empty plot of land, handed you a shovel, and started digging, then turned to you and said, "This is a nice house, isn't it?", wouldn't you think i was crazy? The house obviously doesn't exist. The fact that we are in the process of building it does not make it exist. It won't exist until it is finished.
The same is true for a sentence. It doesn't exist before you say it, and it doesn't exist while you are saying it. It only exists once it is complete. i'll show you:
The dog ran up t
What is the last sentence i wrote? The correct answer is "i'll show you", because "The dog ran up t" is not a sentence, it is merely a fragment of a sentence.
So "this sentence is false" makes no sense, because while the sentence is in construction, it - like the house - does not yet exist. It can't "be" anything if it does not exist, which makes the resulting sentence nonsense (literally nonsense, like "tree dog from defenestrates" - it means nothing, it's just gibberish).
The changed form doesn't fix matters either, it just makes it more verbose (assuming it works, which it doesn't, as i'll explain in a bit). "The statement you are currently saying" does not exist until it is complete, and you can't make any statements about that statement "being" or "having" anything while it doesn't exist. Of course, your "fixed" statement is really not what you think it is. It is no longer a logical conundrum, it is now a prediction. i could easily say "the statement you just said is true... well, looks like you were mistaken", and no logic is violated.
| Afaceinthematrix wrote: | | Quote: |
Second, you can point out that it creates an infinite regress, like an infinite loop in a programming language (yes, i will say it is true; no, that makes it false; but then it's true; but then it's false...), which means it can neither be true nor false. It's like an irrational number, like π, which is neither even nor odd because it never has a last digit to make it even or odd.
|
That's the point. This is sort of like the logic that some people try and use to prove that God can't exist. If God is all powerful and can do anything, then can he create a stone too heavy for him to lift? Well God is supposed to be able to do anything so of course he can create a stone too heavy for him to lift! But if he can't life it, then he can't do everything and he isn't all powerful. The only difference is that this logic just shows that if God exists, he can't be all powerful. The first one actually creates a loop if tried to answer. |
Close enough. ^_^;
As far as i know, no one with any sense is stupid enough to use the omnipotence paradox (the "rock you can't lift" thing) to prove that God doesn't exist. That's just plain idiotic - it's like doing something like this: "Joe says boats exist and are more dense than water. Well, anything that is more dense than water sinks, and boats are supposed to float. Therefore Joe is wrong - boats don't exist." If anyone tries to pass that off on you as a good argument, just shake your head sadly.
Rather, what people use the omnipotence paradox in the context of religion for is to prove the idea of a divine being - omnipotent or not - is absurd. The omnipotence paradox is just one part of the argument, which is quite sophisticated, actually. i'll give a really short version: Let's say that there is a "thing" that is greater than everything else in the universe - a supreme "thing". If so, then that "thing" either can't create a rock he can't lift, or he can create a rock he can't lift. If he can't, then he is not the greatest thing in existence - something greater prevents him from doing something (creating a rock he can't lift, which even a lesser being like myself can do easily). If he can, then he is not the greatest thing in the universe (because the rock will be greater). Therefore, the idea of a "greatest thing in the universe" - a "supreme thing" is illogical. And since most religions claim that their pet god is a "supreme thing", "greater than anything else", this argument shows that they're full of crap. That's the really short version. ^_^; |
But doesn't there come a point where you can understand what someone is saying, even if it isn't complete? For instance, if you were building a house and you've built the foundation, put up the beams, and half of the walls, you still wouldn't be done. You'd need to put the rest of the walls, the roof, and maybe wiring, plumbing, carpet, or those other luxuries. Even though you haven't finished, I can still say, "Wow! That's a big house." without you thinking that I'm crazy, right? I can tell that it's big because you've built enough of it for me to be able to conclude that. All you needed to build was the foundation and a few walls and I was already able to see the size. | Afaceinthematrix wrote: |
| Quote: |
No one ever said that God can't lie.
|
I'm not big into religion, but isn't God supposed to be perfect because you can't sin in Heaven? And isn't lying against the ten commandments? |
This is true about Christian God, but the point is that this at worst could not prove that no god exists, it could only disprove the Christian/ Jewish/ Muslim God. | Afaceinthematrix wrote: |
| But doesn't there come a point where you can understand what someone is saying, even if it isn't complete? For instance, if you were building a house and you've built the foundation, put up the beams, and half of the walls, you still wouldn't be done. You'd need to put the rest of the walls, the roof, and maybe wiring, plumbing, carpet, or those other luxuries. Even though you haven't finished, I can still say, "Wow! That's a big house." without you thinking that I'm crazy, right? I can tell that it's big because you've built enough of it for me to be able to conclude that. All you needed to build was the foundation and a few walls and I was already able to see the size. |
Language is very structured, so it is usually not too hard to guess the meaning of garbled or incomplete sentences. But just because you can guess the punch line doesn't mean the joke has been told.
If you looked at the shell of a house (or even at the blueprints!) and said, "Wow! That's a big house," you would be wrong. The correct thing to say is: "Wow! That will be a big house." Most people are smart enough to make that substitution almost unconsciously, so you don't even realize that you're doing it. (And we do this often, actually. There are many cases where we speak of things as fait accompli before they have been done - because they are so obviously inevitable.)
In real life, the precise point where a house is "finished" - the instant where it stops being a potential house or a house under construction and becomes a house - is rather arbitrary. Is the house done when the structure is complete? When the doors and windows are added? When it's painted? When it's decorated? *shrug* Depends. But wherever you draw that line, a house is not a house (in your view) until that line is crossed.
But for a sentence, things aren't so grey. The sentence is complete when all the words have been completely uttered/written (or, in the case of writing, when the final punctuation mark is down). Simple.
But even though you may be able to guess what the next sentence will be when it is complete, the fact remains that it won't "be" anything until that happens. You can even say, "The next sentence will be 'This sentence is false'," so you don't even need to guess what the next sentence will be. But the problem remains: when you go to say, "this sentence is...", "this sentence", even though you know what it will look like, does not exist. Yet.
You should tell your friend that if he wants to stump the Almighty, he should probably do his homework better. ^_^; This "paradox" is not unsolvable, and in fact there are many different ways of framing a solution. i only mentioned a couple. The only thing philosophers debate these days is which is the best way of framing the solution. | Indi wrote: |
| Afaceinthematrix wrote: | | But doesn't there come a point where you can understand what someone is saying, even if it isn't complete? For instance, if you were building a house and you've built the foundation, put up the beams, and half of the walls, you still wouldn't be done. You'd need to put the rest of the walls, the roof, and maybe wiring, plumbing, carpet, or those other luxuries. Even though you haven't finished, I can still say, "Wow! That's a big house." without you thinking that I'm crazy, right? I can tell that it's big because you've built enough of it for me to be able to conclude that. All you needed to build was the foundation and a few walls and I was already able to see the size. |
Language is very structured, so it is usually not too hard to guess the meaning of garbled or incomplete sentences. But just because you can guess the punch line doesn't mean the joke has been told.
If you looked at the shell of a house (or even at the blueprints!) and said, "Wow! That's a big house," you would be wrong. The correct thing to say is: "Wow! That will be a big house." Most people are smart enough to make that substitution almost unconsciously, so you don't even realize that you're doing it. (And we do this often, actually. There are many cases where we speak of things as fait accompli before they have been done - because they are so obviously inevitable.)
In real life, the precise point where a house is "finished" - the instant where it stops being a potential house or a house under construction and becomes a house - is rather arbitrary. Is the house done when the structure is complete? When the doors and windows are added? When it's painted? When it's decorated? *shrug* Depends. But wherever you draw that line, a house is not a house (in your view) until that line is crossed.
But for a sentence, things aren't so grey. The sentence is complete when all the words have been completely uttered/written (or, in the case of writing, when the final punctuation mark is down). Simple.
But even though you may be able to guess what the next sentence will be when it is complete, the fact remains that it won't "be" anything until that happens. You can even say, "The next sentence will be 'This sentence is false'," so you don't even need to guess what the next sentence will be. But the problem remains: when you go to say, "this sentence is...", "this sentence", even though you know what it will look like, does not exist. Yet.
You should tell your friend that if he wants to stump the Almighty, he should probably do his homework better. ^_^; This "paradox" is not unsolvable, and in fact there are many different ways of framing a solution. i only mentioned a couple. The only thing philosophers debate these days is which is the best way of framing the solution. |
All right, you're right. But I can easily change that to, "You will never say that the statement I am currently saying is true." Maybe I was misquoting the author of this logic question anyways. I am going to try and google the phrase, because I can't remember who said it (I think it may have been Kurt Godel, because he's known for his logic, but I'm not sure if it was him ), but supposedly this guy is supposed to be "The King of Logic" (from what I've heard). I've heard this quote several times before, because it's extremely popular among mathematicians and people majoring in math, because mathematicians (and scientists for that matter) tend to be highly non-religious. Of course this sentence doesn't really prove anything except that fact that English is an imperfect language. | Jinx wrote: |
| Afaceinthematrix wrote: |
| Quote: |
Is the following statement true or false? You will never say that this statement is true.
|
. |
No one ever said that God can't lie.
|
The question is only impossible to answer truthfully. God can say the statement is true or false or what-ever he likes, he just won't be right/telling the truth.
Just as I can say the sky is green.
And good story, btw.
=> JessOR:
"Is the following statement true or false? You will never say that this statement is true."
REPLY:
"The statement is true. You are wrong."
END. OF. STORY.
God can write the answer down, or use telepathy.
| Afaceinthematrix wrote: |
You will never say that this statement is true.
|
Ha ha that was very tricky! It is true!
Ok, now it is false! | HalfBloodPrince wrote: |
OR:
"Is the following statement true or false? You will never say that this statement is true."
REPLY:
"The statement is true. You are wrong."
END. OF. STORY. |
No. You're actually wrong. This is a true or false question and you are simply failing to answer the question correct. I am not telling you that you will never say that this sentence is true, I am simply asking you if that's true. So you're actually the one who is wrong. | Afaceinthematrix wrote: |
| All right, you're right. But I can easily change that to, "You will never say that the statement I am currently saying is true." |
Isn't that going back to the beginning?
| Afaceinthematrix wrote: |
| Maybe I was misquoting the author of this logic question anyways. I am going to try and google the phrase, because I can't remember who said it (I think it may have been Kurt Godel, because he's known for his logic, but I'm not sure if it was him ), but supposedly this guy is supposed to be "The King of Logic" (from what I've heard). I've heard this quote several times before, because it's extremely popular among mathematicians and people majoring in math, because mathematicians (and scientists for that matter) tend to be highly non-religious. |
Gödel (with the diaeresis), yes, you're on the right track. Gödel's incompleteness theorems are yet another way to solve the paradox. They're just rather complicated, and unless you want to go into set theory, you have to take a lot on faith to get the explanation, so i usually avoid them. But let's give it a whirl.
Gödel's incompleteness theorems tell us that for every set of statements with clearly defined rules, there is always a statement that breaks those rules (that is, one that can't be explained by the rules). Take arithmetic, for example - Gödel's theorem tells us that there are some statements in arithmetic that cannot be defined or proven by arithmetic alone.
Applied in this case, linguistics (or semantics, if you prefer), Gödel's theorems tell us that there are some semantic statements that cannot be defined or proven by semantics alone. This paradox happens to be one of them. You can try to explain it semantically until you turn blue in the face... but you can't, because you're outside of the limits of the field.
(Incidentally, most proofs of Gödel's incompleteness theorem use recursive (self-referential) statements to prove the theorem. Unsurprisingly, the paradox here is self-referential in nature - it is a sentence that refers (semantically) to itself.)
To put it another way, you have implied that you have a set of all statements S (which doesn't include interjections, commands or questions - these are not statements), and this set has a clearly defined rule that states that all statements are either true or false (as opposed to interjections, commands or questions, which are neither true nor false). Then you made up a statement "this statement is false", and found that the rules of S are not sufficient to determine whether that statement belongs in S or not (that is, whether it is true or false, or neither). Well, there's no surprise there: Gödel says there must be such statements.
| Afaceinthematrix wrote: |
| Of course this sentence doesn't really prove anything except that fact that English is an imperfect language. |
Well... ^_^;
Yes, the English language is far from perfect.
BUT!
The cause of this paradox is not that the language is not good enough, but (paradoxically) that it is too good. Language is so well defined it is (almost) mathematically precise in nature (when properly applied, of course). The problem here is not that there's a lack of precision in the language. It is that no matter how precise the language becomes it can never be complete. (That's a back-of-the envelope summation of Gödel.) Once it becomes precise enough, it is possible to spot the "cracks" where it breaks down - and there must be cracks. English is not perfect, but it is precise enough to spot that particular crack in the system.
(Theoretically, we could engineer a language that does not suffer from that particular problem (many computer languages do not, for example)... but by Gödel's theorems, it will suffer from some other problem, of a similar nature.)What is the right answer?
There is no right answer. If the questioner says that you will never say the statement is true, that makes the questioner a liar, that does make the answerer incorrect.
Are questioner and answerer even words? =P
| HalfBloodPrince wrote: |
There is no right answer. If the questioner says that you will never say the statement is true, that makes the questioner a liar, that does make the answerer incorrect.
Are questioner and answerer even words? =P |
Correct. If you ignore the possibility of lying (which is normal - when you ask if something is true or false, you don't normally assume deception anywhere unless it's part of the question, like "is so-and-so lying?") then the example given is neither true nor false.
This is not absurd, and it is not paradoxical. It is not hard - in fact, it is very easy - to construct sentences in English that are grammatically correct but semantic nonsense. "Quadruplicity drinks procrastination" is one from Bertrand Russell. "Colourless green ideas sleep furiously" is a famous example from Noam Chomsky. Both of these sentence look like legitimate English sentences, and they are quite legal. But they are meaningless.
Where you go from there is where things get fuzzy. It is common to say there are four kinds of legal sentences in English:
- Statements: Sentences that are either true or false. ("The ball is red." "i like cheese.")
- Questions: Sentences that request information. ("What colour is the ball?" "Where's the cheese?")
- Imperatives: Commands to urge agents to do things. ("Go get the ball" "Cheese me, baby.")
- Interjections: Expressions that communicate emotion or demand attention. ("Hey!" "Yay, cheese!")
But where does "this sentence is false" fit in? It's not a question, and it's not a command. If it's neither true nor false then it can't be a statement. But it doesn't express any emotion either. So... what is it?
Depends on who you ask. Some people will say that it is false... just by virtue of the fact that it isn't true. Others will extend the idea of statements to allow for indeterminate statements. Others will just say it's not a legitimate sentence. See, Afaceinthematrix's atheist friend is pretty screwed, because despite what he seems to think this problem is not unsolvable. We just don't yet have a perfect, universal framework for understanding linguistics that we can use to get a single, definitive explanation of the solution (really, work in linguistics is only fifty or so years old... it's a pretty young science). In plain English, we know how to solve it, and we can solve it with any of a dozen different competing theoretical frameworks. In a hundred years, maybe we will have narrowed down the field to the one "perfect" framework, but for now, we're still working on which one is the best. God, being God, would certainly have figured out the best theoretical framework for linguistics. Afaceinthematrix's atheist friend would therefore have his ass handed to him.What in the world does this have to do with the existence of God? Or did he want to place God as a liar? That is not atheist, that is theist. 
I agree with TBSC
it's rather a question regarding the supposed omniscience of GOD God can just say that the statement is false!
What stops him?
