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I am lying!
bacillus:
--- Quote ---cond
x x !=
start
stop
--- End quote ---
The problem with this, or any paradox for that matter, is that it has no useful applications.
jknilinux:
Moonfisher- If by meaningless or invalid you mean something that cannot be true or false, then meaninglessness or invalidity is a new truth-value, by definition, since that means that "if a sentence is meaningless, then it's not true or false. If a sentence is not true or false, then it's meaningless."
So, something must be true, false, or meaningless- what about "This statement is not true"? If it's true, then it must not be true, so it's true and not true, so it's false or meaningless. If it's false, then what it's saying is false, so it's false that it's not true, so it's true or meaningless. So, it can't be true, it can't be false, so it's just meaningless... yay! And everything works, right?
Well, no. As it turns out, if it's meaningless, then what it's saying is true- it says it's not true, so it says "I'm false or meaningless". Since it's right, it's true. So, if it's meaningless, it's true, and we get a paradox all over again.
Jez- Just like I showed above, you can have 3 truth values, or 4 truth values, or infinitely many truth values, and you'll solve the original paradox, but you can't solve what's known as the strenghtened liar- "This sentence is not true." Because, if it's truth value Q, or whatever else you make up, then it's true, so it's false, etc...
Also, although the 1-2-3 statement is weirder, it's important because many solutions to the original liar or the strengthened liar fail in front of paradox 1-2-3 - aka what I call the "ultimate liar". For example, we could say a statement cannot refer to itself. That solves the original AND the strengthened liar, but the ultimate liar is not self-referential, so that doesn't work. It's just an acid test for any solution that people come up with.
Peterb- Actually, no. A contradiction is something of the form "x and ~x", while a paradox is a proof of a contradiction from acceptable premises. Just writing down "X and ~X" AKA "X = ~X" is not a paradox, since it must be false according to the rules of logic. Think about it- can x ever possibly equal ~x? Of course not, so it's just false.
However, this isn't the case with the liar- if it's false, then it must be true. It is not saying it isn't itself. It's a paradox because I can prove a contradiction based off of it, but it itself isn't a contradiction. To see the proof, you'll need to look at the "tarski's proof" document I included.
Bacillus-
I'm glad no logicians heard you. Zeno's paradoxes are helping guide current quantum physics, and have even helped spawn a new area of physics- digital physics. Russel's paradox showed that the original set theory was wrong, and Godel's incompleteness theorem, which is basically a version of the liar paradox that's been proven in math, showed that math must be incomplete or inconsistent. Once (if ever) the liar paradox is solved, it will reveal new fundamental truths about truth itself. So far, it seems that logic itself must simply be incomplete or inconsistent to solve the liar, which itself would be earth-shattering in all fields dealing with logic (aka all fields) if proved.
Peter:
--- Quote from: jknilinux ---Moonfisher- If by meaningless or invalid you mean something that cannot be true or false, then meaninglessness or invalidity is a new truth-value, by definition, since that means that "if a sentence is meaningless, then it's not true or false. If a sentence is not true or false, then it's meaningless."
So, something must be true, false, or meaningless- what about "This statement is not true"? If it's true, then it must not be true, so it's true and not true, so it's false or meaningless. If it's false, then what it's saying is false, so it's false that it's not true, so it's true or meaningless. So, it can't be true, it can't be false, so it's just meaningless... yay! And everything works, right?
Well, no. As it turns out, if it's meaningless, then what it's saying is true- it says it's not true, so it says "I'm false or meaningless". Since it's right, it's true. So, if it's meaningless, it's true, and we get a paradox all over again.
--- End quote ---
I think if something is meaningless, then it is. Then it doesn't say anything at all. And the paradox stops.
This statement is not true. Meaningless, the statement isn't true or false, it could be both, maybe neather.
--- Quote ---Also, although the 1-2-3 statement is weirder, it's important because many solutions to the original liar or the strengthened liar fail in front of paradox 1-2-3 - aka what I call the "ultimate liar". For example, we could say a statement cannot refer to itself. That solves the original AND the strengthened liar, but the ultimate liar is not self-referential, so that doesn't work. It's just an acid test for any solution that people come up with.
--- End quote ---
Try to put something like it in excel if excel says there is a loop coming back to itself, it refers to itself in the end. Excel is a clear number program, try it.
A=B+1
B=C+1
C=A+1
(with numbers and letters you can do everything, what is the point anyway?)
--- Quote ---Peterb- Actually, no. A contradiction is something of the form "x and ~x", while a paradox is a proof of a contradiction from acceptable premises. Just writing down "X and ~X" AKA "X = ~X" is not a paradox, since it must be false according to the rules of logic. Think about it- can x ever possibly equal ~x? Of course not, so it's just false.
However, this isn't the case with the liar- if it's false, then it must be true. It is not saying it isn't itself.
--- End quote ---
That apple is the same as that apple. It says is it the same to itself. Not something like the apple is the same to a apple.
If I look at it,
maybe you try the condition ''X X != '' in other ''strangely'' chosen symbols. But then how is ''~'' false?
--- Quote ---Bacillus-
I'm glad no logicians heard you. Zeno's paradoxes are helping guide current quantum physics, and have even helped spawn a new area of physics- digital physics. Russel's paradox showed that the original set theory was wrong, and Godel's incompleteness theorem, which is basically a version of the liar paradox that's been proven in math, showed that math must be incomplete or inconsistent. Once (if ever) the liar paradox is solved, it will reveal new fundamental truths about truth itself. So far, it seems that logic itself must simply be incomplete or inconsistent to solve the liar, which itself would be earth-shattering in all fields dealing with logic (aka all fields) if proved.
--- End quote ---
Well now is the time to show me the use for this. It sounds a little like a made-up kind op phycics.(not that you made it up)
But more on the stage of, what is the use for this?
What do true and false have to do with math?
jknilinux:
Peter-
Math is based on ZFC set theory, which is based on logic. You don't know it, but you use formal logic every day.
~x is the same as not x, and !x, and "x is false". In logic, we use ~ most.
By the way, are you saying that even though it cannot be meaningless if it is meaningless, that it should still be meaningless? "This is a sentence" leads to a contradiction if you try to make it meaningless, and "this is not true" also leads to a contradiction if you try to make it meaningless. Why does one remain meaningless while the other remains true?
A statement can never be both true and false. It is impossible by definition, and if even if it was, then I could prove p*~p (p and not p) from it. So, it must be false that something is both true and false.
And what does excel have to do with this? How does excel solve the paradox?
Peter:
--- Quote from: jknilinux ---Peter-
Math is based on ZFC set theory, which is based on logic. You don't know it, but you use formal logic every day.
~x is the same as not x, and !x, and "x is false". In logic, we use ~ most.
--- End quote ---
~X sounds to like is close to X. Not ''not X''. Doesn´t sound logic.
--- Quote ---By the way, are you saying that even though it cannot be meaningless if it is meaningless, that it should still be meaningless? "This is a sentence" leads to a contradiction if you try to make it meaningless, and "this is not true" also leads to a contradiction if you try to make it meaningless. Why does one remain meaningless while the other remains true?
--- End quote ---
How, what contradiction. Explain further. I´m not that fast.
--- Quote ---A statement can never be both true and false. It is impossible by definition, and if even if it was, then I could prove p*~p (p and not p) from it. So, it must be false that something is both true and false.
--- End quote ---
It is inpossible by definition and just you said the definition could be wrong becouse the statement are wrong.
You can express things that aren't true. That doesn't make the paper it is written on wrong. It is like saying the paper is wrong becouse you can write something wrong on it.
AB=AB2
1+1=3
I'm smart and I rule the world and 1+1=2, and you gimme now a cup of coffee.
Most of the sentense is rambling, but 1+1=2, it is,is it?
Anyway does this make the sentance wrong or right
Again, give a link. How did you come at this, anyway.
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