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This statement is false
Is it true or false

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This statement is false

gesler0811
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Posted 05/05/08 - 11:11 AM: Subject: This statement is false	#1
This is something I kind of pondered a while back to the point that I was about to have a fit. I have modified it here for your reading and thinking pleasure: This statement is false. Is the above statement true or false?

pluke
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Posted 05/05/08 - 03:30 PM:	#2
If I recall correctly, a Greek Philosopher died of lack of sleep whilst trying to solve that statement.

ugx2000
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Posted 05/05/08 - 09:39 PM:	#3
Context!
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Death Monkey
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Posted 05/06/08 - 12:27 AM:	#4
It is not a statement at all. It is a string of words that do not form a coherent statement. Attempting to assign a truth value to it is therefore a mistake to begin with. To illustrate, is the following statement true or false? "My round triangle enjoys eating blue ideas" Again, the above is simply not a statement. It is meaningless gibberish. Your example is just less obviously gibberish, because it is easy to forget that not every syntactically well-formed sentence is actually a statement to which a truth value can be assigned. My example just makes this fact more obvious. DM
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gesler0811
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Posted 05/06/08 - 07:36 AM:	#5
I thought I had a solution that was similar to what you said, DM, but I am not sure I completely agree with you. It is a complete sentence that makes a claim that is not inherently contradictory. It seems it should be verifiable then by a true/false claim. Of course I am open to the possibility that I am wrong. I would be interested to hear what others have to say on the matter. I think the biggest difference is that this 'statement' as I call it, or 'string of words' as you call it is at least verifiable, unlike 'My round triangle enjoys eating blue ideas.' A similar statement might be 'I can't think.' It is making a different claim, but the implications are similar. Would that qualify as gibberish as well? I don't know.

will11
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Posted 05/06/08 - 12:45 PM:	#6
The statement is TRUE... Because 'this statement is false' is a statement, so technically a statement has to be true, HENCE THIS STATEMENT IS TRUE THAT THIS STATEMENT IS FALSE.

WW_III_ANGRY
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1 of 1 people found this post helpful Posted 05/06/08 - 07:46 PM:	#7
Its irrational and or inconclusive, there is nothing really stated that needs to be determined if the statement is true or false. More often than not when this sentence is used, it would be referring to another, seperate statement.

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Posted 05/06/08 - 07:58 PM:	#8
The answer to your question relies upon which system of logic you are using to evaluate it. Of course, if you use Aristotle's classical logic, you'll die not knowing the answer. But luckily, some brilliant logicians in the past couple hundred of years have developed new ways of thinking about this. So essentially, spend four years in a university philosophy department, learning logic and come back to the question.
_____________________ "Whenever you think you are facing a contradiction, check your premises. You will find that one of them is wrong." ~Ayn Rand

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Posted 05/06/08 - 08:06 PM:	#9
You don't need 4 years in a university to learn the inherent thought process in all mentally healthy humans.

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Posted 05/06/08 - 09:20 PM:	#10
It is not the kind of sentence about which it makes any sense to say it's true or false. Only sentences in which some predicate is ascribed to a subject can meaningfully be said to be true or false. What we mean by true or false is whether or not the predicate in a sentence is or is not ascribable to the subject. No predicate is being ascribed to a subject in that sentence, so there's nothing to be true or false. Cheers. jd
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Posted 05/07/08 - 06:29 AM:	#11
gesler0811, I thought I had a solution that was similar to what you said, DM, but I am not sure I completely agree with you. It is a complete sentence that makes a claim that is not inherently contradictory. But that's just it. It is inherently contradictory. In fact, this is exactly how I arrived at the conclusion that it is not an actual statement. Please note that when I say "statement", I specifically mean a proposition that is meaningful and can have a truth value assigned to it. Some people use the word "statement" to just refer to any sentence that is not a question. That is not what I am talking about. That said, I used an indirect proof. Start with the premise that if we parse the sentence according to the rules of the English language, that we will end up with a statement. If we do so, we end up with a contradiction. The resulting "statement" can be neither true nor false. The only possible conclusion, then, is that our premise was wrong. The sentence cannot be parsed according to the rules of the English language into a statement. It seems it should be verifiable then by a true/false claim. Of course I am open to the possibility that I am wrong. I would be interested to hear what others have to say on the matter. One cannot even address the issue of verifiability until one knows what the statement is asserting. In this case it is not asserting anything. It cannot be asserting that it is a true statement, because if it is then it is also asserting that it is a false statement, and vice-versa. I think the biggest difference is that this 'statement' as I call it, or 'string of words' as you call it is at least verifiable, unlike 'My round triangle enjoys eating blue ideas.' The problem with these two sentences is quite the same. In both cases we are unable to parse the string of words into a meaningful statement. There is no way to verify either of them, because neither of them specifies anything that could potentially be verified. They are both meaningless. A similar statement might be 'I can't think.' It is making a different claim, but the implications are similar. Would that qualify as gibberish as well? This is completely different. That statement is not inherently self-contradictory. On the contrary, it is simply false. With the example from the opening post, the sentence, if regarded as a statement, can be neither true nor false. Your example is simply false. You can think. I suspect that you are mixing up the notion of a sentence being inherently self-contradictory, and the notion of a statement contradicting that which we know or believe to be false. As an example: "My brother is a married bachelor" is self-contradictory. It is nonsensical. "My brother is not human, but I am", is meaningful. It may seem contradictory, because if I am human than my brother must be too, but this is not a logical contradiction. It just contradicts a set of facts we believe to be true. Namely that Human parents can only give birth to human children. Likewise with your example, we believe that all people can think, so for a person to say he can't think would seem to be contradictory, but as with the example of my brother, this just means that we can be confident that the statement is false. In the original example of this thread, we cannot conclude that the statement is false, because that also leads to a logical contradiction. DM
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will11
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0 of 1 people found this post helpful Posted 05/07/08 - 09:11 AM:	#12
Its very simple sentence. 'This statement is false' The above sentence is a statement, and a statement has to be true..so lets say that the above statement is true. So if it is true, the things said in it should also be true.... So this statement says that it is false, so if we agree that a statement should be true, then statement is saying the truth that it is false....So THIS STATEMENT IS FALSE.

WW_III_ANGRY
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Posted 05/07/08 - 10:18 AM:	#13
will11 wrote: Its very simple sentence. 'This statement is false' The above sentence is a statement, and a statement has to be true..so lets say that the above statement is true. So if it is true, the things said in it should also be true.... So this statement says that it is false, so if we agree that a statement should be true, then statement is saying the truth that it is false....So THIS STATEMENT IS FALSE. Your lgoic is flawed from your first premise. .."and a statement has to be true" No. Then there would be no such thing as a lie if that were true.

WW_III_ANGRY
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Posted 05/07/08 - 10:18 AM:	#14
will11 wrote: Its very simple sentence. 'This statement is false' The above sentence is a statement, and a statement has to be true..so lets say that the above statement is true. So if it is true, the things said in it should also be true.... So this statement says that it is false, so if we agree that a statement should be true, then statement is saying the truth that it is false....So THIS STATEMENT IS FALSE. Your logic is flawed from your first premise. .."and a statement has to be true" No. Then there would be no such thing as a lie if that were true.

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Posted 05/07/08 - 10:26 AM:	#15
I think Death Monkey has made a number of very good points in this thread. The way I often look at it, is that many paradoxes perplex people because of a certain Boolean prejudice. We reason that if a statement is not true then it must be false, and if a statement is not false then it must be true. But there's a difference between logical-NOT and the English word 'not'. In the latter case, we may be saying something is not true because it is not evaluatable as meaningful statement at all. Or, another way of putting it, is that there is an implicit third value, even in Boolean logic, of nil, NULL, error, not-a-truth-value, whatever you want to call it. Not every statement can be evaluated.

will11
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Posted 05/07/08 - 10:29 AM:	#16
Yes, generally a statement is believed to be true, or considered truth. So if it is true, then the statement is false.

Mijin
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Posted 05/08/08 - 05:55 AM:	#17
will11 wrote: So if it is true, then the statement is false. In the above sentence "the statement" and "it" actually refer to the same noun. Do you see the problem with your reasoning if we use the same noun in both parts of the sentence? "So if it is true, then it is false" "So if the statement is true, then the statement is false" will11 wrote: Yes, generally a statement is believed to be true, or considered truth. ...until proven guilty? A statement may be true or false (or, indeed, it may not be possible to assign it a truth value at all). I don't get what you mean by a statement generally being believed to be true.

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Posted 05/08/08 - 06:24 AM:	#18
will11 wrote: Yes, generally a statement is believed to be true, or considered truth. So if it is true, then the statement is false. Thats crazy talk.

will11
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Posted 05/08/08 - 07:52 AM:	#19
What I mean is...if a statement is considered to be true, then what it is saying should also be true, hence the statement says that it is false...so the statement is false. As simple as that! It may sound to you a bit crazy, but dude the concept and the argument is such that it may seem confusing...but just try to ponder over what i am saying

gesler0811
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Posted 05/08/08 - 08:17 AM:	#20
Thanks Death Monkey, for the insight. I had a similar thought that went along the lines of "a statement cannot be considered true or false until the statement is complete and makes a claim. The statement cannot call itself true or false in mid sentence because there is not yet a complete statement to be evaluated. Therefore "This statement is false" does not compute logically. But then I started wondering if it would change anything if I reworded the whole thing as follows: By the time I finish typing this sentence, everything I would have said in this sentence will be completely false.

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Posted 05/08/08 - 10:01 AM:	#21
will11 wrote: What I mean is...if a statement is considered to be true, then what it is saying should also be true, hence the statement says that it is false...so the statement is false. As simple as that! If the statement is true, then what it 'says' is true (i.e., that it is false). Therefore, if it is true, then it is false. That is the paradox (half of it). It is not a solution to the paradox. This paradox has been around since the beginning of philosophy and philosophers have continued to argue about it right up until the present. There was a great deal of discussion of it during the last century. If it had an obvious resolution, one of the philosophers/logicians who considered it it would have noticed and that would be the end of it.

will11
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Posted 05/08/08 - 01:23 PM:	#22
Well there may be another explanation to it. The reason why no person has ever been able to solve it is because of the obvious reason that the statement is false, and the statement itself says that 'this statement is false.So therefore if the statement claims itself to be false, then the statement is wrong, illogical, senseless thing written, which need not be explained.

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Posted 05/08/08 - 01:32 PM:	#23
gesler, I had a similar thought that went along the lines of "a statement cannot be considered true or false until the statement is complete and makes a claim. The statement cannot call itself true or false in mid sentence because there is not yet a complete statement to be evaluated. Therefore "This statement is false" does not compute logically. I think you are hitting on the problem, which is one of self-reference. You can think about it this way. What does would it mean to say that the statement is true? In this case, that cannot be specified. The part of the statement that would normally establish what it means for the statement to be true, just refers back to the truth value of the statement. You would actually have the same problem with "This statement is true". On the surface, this seems to be OK, because there is no contradiction. But there is really no statement there to be true. The sentence conveys absolutely nothing. It would be like in mathematics saying: X is defined to be equivelent to Y Y is defined to be equivelent to X Neither X nor Y are well-defined. Saying that one variable equals another is fine, as long as at least one of them is defined in some way other than just saying that it is equal to the other one. Similarly, the original sentence "This statement is false", is analogous to saying: X is defined to be equivelent to Y Y is defined to be equivelemt to NOT X This is more obviously nonsensical than the previous example, because of its contradictory nature. But neither of them are actually meaningful. But then I started wondering if it would change anything if I reworded the whole thing as follows: By the time I finish typing this sentence, everything I would have said in this sentence will be completely false. In consideration of what I have said above, I don't think this really addresses the problem. The meaning of the sentence is still not well-defined. DM
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Posted 05/09/08 - 12:00 AM:	#24
will11 wrote: Well there may be another explanation to it. The reason why no person has ever been able to solve it is because of the obvious reason that the statement is false, and the statement itself says that 'this statement is false.So therefore if the statement claims itself to be false, then the statement is wrong, illogical, senseless thing written, which need not be explained. I don't think that you understand the paradox. The statement 'says' that it is false. Therefore, if it is false (as it 'says'), then it is true. If it is true, then what it 'says' is true (that it is false), so it is false. If you want to say that it is ill-formed, that is one thing, but you can't say that it's false because if it's false, then it's true.

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Posted 05/09/08 - 06:07 AM:	#25
will11 wrote: Well there may be another explanation to it. The reason why no person has ever been able to solve it is because of the obvious reason that the statement is false, and the statement itself says that 'this statement is false.So therefore if the statement claims itself to be false, then the statement is wrong, illogical, senseless thing written, which need not be explained. I think you're looking too deeply to a matter that has only a shallow answer. If you think the statement is claiming its own statement is false, then that means claim that "this statement is false" is false which means is not true, so it means its true, but it says its false, but it can't be because its not true so its false but its true so its false but its true so its false but its true. You cannot answer an illogical statement in a logical manner, the claim is irrational and incomplete. Its an insane statement.

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