Thread: The Liars Paradox

"This sentence is false" - a paradox indeed.

However, it doesn't matter for one simple reason: that sentence would never be used with meaning. It can be said, yes, just as you just wrote it here. But this is merely a demonstration. The actual sentence, "this sentence is false" would never be used in any context, nor for any meaningful reason.

Thus, it matters little of what paradox it creates as this paradox doesn't affect anything.

Where have I seen this... Oh yes.

http://www.dreamviews.com/forum/inde...howtopic=33912

Here is one.

Everything I tell you is a lie.

I suggest you don't listen to my suggestions. (My own)

It is really just sophomoric.. just like, "Well, if God can do anything; can he make a rock he can't pick up?"

But perhaps the problem lays in our conception of reality..

The sentence gives the answer.

Its false.

If it is true that it is false, its still false.

It makes no sense. It's just a play of words. That's it. Your guys are looking for the meaning in something that's absolutely not worth it.

I think the whole sentence is non-existent because they both cancel each other out. Also there is no way we can show proof of truth nor can we display any proof of falsehood. So therefore this sentence is incomprehensible to our way of thinking.

Put it this way, it doesn't belong in our reality.

it is not a proper statment.
WHAT dose it say is false?
Itself?
What is itself?
I rest my case

one of my teachers (a slightly egopathic one ) says that "truth" is an attribute to the speech, not simply a stand-alone concept.

so you can't say that "O'nus" or "posts" is "true" or "false".
i could maybe say that "O'nus posted" is "true", because this statement attributes to "o'nus" something that belongs, and that "O'nus didn't post" is false because it attributes him "not posting", that don't belongs. True is the connection

"this sentence is false" only simulates a "A is B" situation. (that would be: "A is B" is true, or "A is B" is false)
this is more like """A is False" is False" - so like" "A is B" is B" and desolate loop.
so it keeps on going around on the language plan, not only without referring to any actual pair of elements to connect (and which connection could be true or false), but witout even reaching the "sorf-of-a-truth" of a definition ("the word A" is B).

so
ok
i pointlessly burnt neurons to say:
Hei, it's a paradox!!! it's no surprise for it not to have solutions!!!

ok. i stop thinking because i'm getting confused.
AND i am supposed to be studying philosophy. That's nooooo good!

This is like saying: If you put a cat in a closed of box with no food, and you have no high tech equiptment and now way to open the box, can you ever truely know the cat is dead?

In other words, pointless

Originally Posted by fieldwhy

What do you think about this sentence:

This sentence is false

[/b]

I think it is an awesome concept. It is a true paradox, and I have pondered on it for a long time, still not coming up with a solid resolution. It is one of those principles that really makes me question reality.

I highly disagree with everybody who said that it is pointless or has no meaning or has no relevance, etc. It is a paradox that is every bit as baffling as Zeno's Paradox. It is also just as critical of reality as we think we know it and just as unresolved.

One of the basic principles of logic, one that you are likely to study early in the semester if you take a logic class, is "Either A or not A". It is also stated as "P or not P". That rule says that a very specific proposition is either the case or it is not. There is no third alternative. See "the law of the excluded middle"...

http://64.233.187.104/search?q=cache:X-iUG...t=clnk&cd=2

http://72.14.209.104/search?q=cacheqxHJq...t=clnk&cd=1

Ambiguous statements provide no exception, as some might try to argue. It is not statements, but propositions. The fact that a claim is undefined only means the the proposition has not been clearly stated. A specific situation, whether understood or not, is either the case or it is not. The paradox in this thread is something that throws a monkey wrench into that basic principle of logic. Either the statement is false or it is not. Period. Not being false does not inherently make a statement true, but something is either false or it is not. But the mentioned paradox is one of the few things that seems to be in the region between A and not A, although the discipline of logic is not ready to accept that such a thing is possible. Before we rewrite what are understood to be the laws of logic, let's think about the two possibilities...

Possibility 1: The statement is FALSE: In this case, the statement says exactly what it is, false. Thus, it makes a true statement, making it true, making it false, making it true, making it false (ad infinitum). This is a contradiction, so the statement cannot possibly be FALSE.

Possibility 2: The statement is NOT FALSE: In this case, the statement makes a claim that IS false, making it false, making it true, making it false, making it true (ad infinitum). This is a contradiction, so the statement cannot possibly be NOT FALSE.

According to the laws of logic, there is no third alternative. So what is the deal? I have no idea.

According to the laws of logic, there is no third alternative. So what is the deal? I have no idea[/b]

the deal is with the nature of truth and logic in both cases these are defeated. with out truth and logic what are you let with nothing in a higher train of thought it says that their is no such thing as logic or meaning we just are like the statement just exsist.

Originally Posted by becomingagodo

the deal is with the nature of truth and logic in both cases these are defeated. with out truth and logic what are you let with nothing in a higher train of thought it says that their is no such thing as logic or meaning we just are like the statement just exsist.
[/b]

I'm not quite sure what you mean. The sentence is one of three things.

1. false (impossible)
2. not false (impossible)
3. third alternative, which the laws of logic say is impossible

Which is it? You seem to be saying that there is a third alternative where truth and logic are defeated, so it is neither 1 or 2. Is that what you are saying? You are probably right, but that turns reality as we know it on its head. There is a Nobel Prize waiting for somebody on this.

Perhaps it is both true and false? That too defies the law of the excluded middle, but I think that law may have been disproven.

Originally Posted by Universal

I'm not quite sure what you mean. The sentence is one of three things.

1. false (impossible)
2. not false (impossible)
3. third alternative, which the laws of logic say is impossible

[/b]

A sentence of this form- 'a is b' (is being the key word), there are only two truth values that can be assigned to the sentence. These being, logically true and logically false. But it is impossible to determine which one fits the particular sentence because it is a simple declaritive sentence which has no logical properties that can determine the truth of itself. 'The sky is blue' is a sentence in the same form. But you cannot say that this is logically true, likewise, you cannot say that this is logically false (don't try to argue that, you will lose). These sentences cannot be defined in virtue of their logical form; their truths rely on empirical oberservations. The truth property of a sentence, 'P', in the form 'a is b' cannot be recovered using logic.

'This sentence is false' is an interesting idea because it cannot be defined by logic in light of its improper form but rather it can only be defined by its content (which relies on empirical evidence). The interesting part is that this particular sentence itself calls upon logic to determine its truth property but logic has no authority to determine its truth property.

Originally Posted by evolo

A sentence of this form- 'a is b' (is being the key word), there are only two truth values that can be assigned to the sentence. These being, logically true and logically false. But it is impossible to determine which one fits the particular sentence because it is a simple declaritive sentence which has no logical properties that can determine the truth of itself. 'The sky is blue' is a sentence in the same form. But you cannot say that this is logically true, likewise, you cannot say that this is logically false (don't try to argue that, you will lose). These sentences cannot be defined in virtue of their logical form; their truths rely on empirical oberservations. The truth property of a sentence, 'P', in the form 'a is b' cannot be recovered using logic.

'This sentence is false' is an interesting idea because it cannot be defined by logic in light of its improper form but rather it can only be defined by its content (which relies on empirical evidence). The interesting part is that this particular sentence itself calls upon logic to determine its truth property but logic has no authority to determine its truth property.
[/b]

"a is b" is a proposition. I am not sure why you think it is not. Why would such a sentence not be recoverable using logic? Why would the law of the excluded middle not apply to "a is b" propositions? That is not a stated exception in any logic text book. The law of the excluded middle says that a proposition is either correct or not correct. It does not have to be false because it is not correct, but it is either correct or not correct. The sky is blue" is either correct or it is not. However, that is at the point of actually being a defined proposition. Operational definitions have to be involved. "Blue" has to be defined in accordance with a range of light wave frequencies, and the specific sky at the specific moment has to be defined, or at least involved. Whatever the sentence very specifically means is either correct or not correct. That is what the law of the excluded middle says. So "This sentence is false", according to the law of the excluded middle, is either correct or not correct. However, the law of the excluded middle has been challenged.

"a is b" is a proposition. I am not sure why you think it is not. Why would such a sentence not be recoverable using logic? Why would the law of the excluded middle not apply to "a is b" propositions? That is not a stated exception in any logic text book. The law of the excluded middle says that a proposition is either correct or not correct. It does not have to be false because it is not correct, but it is either correct or not correct. The sky is blue" is either correct or it is not. However, that is at the point of actually being a defined proposition. Operational definitions have to be involved. "Blue" has to be defined in accordance with a range of light wave frequencies, and the specific sky at the specific moment has to be defined, or at least involved. Whatever the sentence very specifically means is either correct or not correct. That is what the law of the excluded middle says. So "This sentence is false", according to the law of the excluded middle, is either correct or not correct. However, the law of the excluded middle has been challenged.[/b]

your assuming that their only one truth or that truth exsist the paradox dismantle logic to show that you cant assume anything about truth. the sky is blue is define by not what it is but it opposite i.e. every other colour if they didnt exsist whould blue exsist. by assuming opposite their is a correct and wrong anwser then you dont know anything about truth you just know opposite. their can be thing between truth and false their is a middle ground where they both transform into each other see Heraclitus flux http://en.wikipedia.org/wiki/Heraclitus that were your logic is flawed universal mind.

Originally Posted by becomingagodo

your assuming that their only one truth or that truth exsist the paradox dismantle logic to show that you cant assume anything about truth. the sky is blue is define by not what it is but it opposite i.e. every other colour if they didnt exsist whould blue exsist. by assuming opposite their is a correct and wrong anwser then you dont know anything about truth you just know opposite. their can be thing between truth and false their is a middle ground where they both transform into each other see Heraclitus flux http://en.wikipedia.org/wiki/Heraclitus that were your logic is flawed universal mind.
[/b]

Where is my logic flawed? I listed three possibilities. One of them involves the falsity of the law of the excluded middle. Is that the one you agree with? It seems to be. If so, then I laid that down as an option. So what's the flaw?

Originally Posted by becomingagodo

The sentence is one of three things.

1. false (impossible)
2. not false (impossible)
3. third alternative, which the laws of logic say is impossible

Which is it? You seem to be saying that there is a third alternative where truth and logic are defeated, so it is neither 1 or 2. Is that what you are saying? You are probably right, but that turns reality as we know it on its head. There is a Nobel Prize waiting for somebody on this.

Perhaps it is both true and false? That too defies the law of the excluded middle, but I think that law may have been disproven.
[/b]

You agree with #3, right? Strangely, it seems to be the only one that has any possibility of being true. But maybe... Perhaps there is an option #4 in which #1 and #2 are both right. Maybe this all proves that contradictions can exist in reality. What?

I can't believe I'm saying that crazy stuff. I am going to get to the bottom of this!

Where is my logic flawed?[/b]

it depend on what you call logic i trying to say that you can say this is true and this is false theirfore if you combined them they will equal a paradox. see this relies on someone thing called syllogism which using two statement to deduce another if you believe in this then YOUR own logic is flawed not logic itself. logic can only be flawed if you make assumption. ironincally if your saying logic is flawed then this logic must be flawed or are you trying to say in some circumstances it is flawed. a postmodern anwser would be that logic is not flawed it can incorrect it just based on assumption or that assumption shape the way you see thing. it you believe in hypothesis, syllogism, sythesis and any absolute truth then your logic is flawed again iroincally i dont agree with what i just said or believe in it or believe in what i just writen. i can describe where you wrong in more detail universal mind your assuming thing or absolute truth are not chaotic or rational having both characteristic it only would be a contrediction if it was true which you can only assume which lead back into chaos. the point is their no such thing as reasons it just based on assumption their is only chaos and order infinitly.

I haven't read all the responses, but in semantics, it would be said (according to some people - there are many ways of analyzing it) that the original sentence "This sentence is false" has no truth value - that is, it is neither true nor false. (I always hated semantics)

http://en.wikipedia.org/wiki/Liar_Paradox