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I am lying!

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jknilinux:
Moonfisher-

If you disallow self-referential statements, you just disallowed a whole bunch of perfectly fine statements- "This sentence has five words." is an example. Are you saying this is wrong/not a proposition (which we'll assume for the sake of argument isn't a truth value)? Because I can safely say that that makes sense, and is a valid statement, and is true. Do you disagree?

Anyway, "the green cloud tastes sad" makes sense, but if you taste a green cloud, I think you'll find they don't taste sad. Sadness is not a known taste, so it's a self-contradictory statement (assume it's true- the cloud will therefore taste sad, but you cannot taste sadness. So it also does not taste sad. It tastes sad and doesn't taste sad, so the statement must be false, in which case it just doesn't taste sad. Same with "colorless green ideas sleep furiously", or whatever else you try.) So, it's just false.

"fbjidklgbhfil", on the other hand, is different. It has no known meaning, and so cannot be translated into logic.

"This sentence is false" has meaning, and can be translated into logic, unfortunately. The problem is that is can't be false, since you'll still get a contradiction in that case, meaning it's true.

Peter-

I know you can express false things- that's not the problem. The reason why things are false is that if they were true, there would be a true contradiction, which means everything, including all previously false things, must become true. "This is not a sentence" is false because if it were true, then it would be true that it is not a sentence. It is by definition a sentence. So, it must be both a sentence and not a sentence- a true contradiction.

If it's a true contradiction, you can represent it in logic as P and not P. "This is not a sentence" AND NOT "This is not a sentence"

If something AND something else are true, then both something is true and something else is true. So I'll just say "This is not a sentence" for right now, since it's true.

When something is true, you can add anything to it with an or- if it's raining, then you can also say "it's raining or it's not raining"- one is obviously false, but that's OK since one is still true, so the or statement is still true. For this proof, I'll use "This is not a sentence" OR "I'm a purple tomato"

When you have an OR, if one thing on one side is false, then the other thing on the other side must be true. If it's raining OR it's not raining, and it's false that it's raining, then the other one must be true, so it's true that it's not raining. So, since it's false that this is not a sentence, because it is a sentence, then the other one must be correct, which says "I'm a purple tomato", must be true.

Therefore, I'm a purple tomato.

So, "This is not a sentence" must be false, right? What happens if it's false? Well, then it's false that it's not a sentence, so it's true that it is a sentence, which is true. So, it is false.

I feel I might have missed something else you said- let me know if I did.


Anyway, the problem with the liar paradox is that if it is false, then it must be true. Hence, it is both, so it is false, so it is true, so it is neither, etc...

Moonfisher:
Well 0 divided by any amount will give you 0, so "in theory" you could divide 0 by 0 and get zero. You could also argue that dividing by 0 would equal infinity, but this wouldn't work well with all the other rules that we apply in math. No matter how we look at it math is just a set of rules that we determine, and so is logic.
So there's no right or wrong answer... but you asked for a rule that would prevent the "paradox" that you mentioned, and not allowing a proposition to refer to itself would solve this paradox. The 3 line liar is not an exception to the rule that you yourself proposed...
You're right that it will disallow statements that are "valid" or rather statements that don't pose a paradox, since nothing is actualy valid or invalid... so it comes down to wether you feel it's more important to have access to form such a proposition or to eliminate propositions that are in theory infinate.
It's true that :
1: "1 is true"
woudl give :
1: "(1 is true) is true) is ture) asf asf..."
And an infinity of "true" statements will obviously let you know what the answer to the proposition is... but the proposition is still infinate... in theory.
I'm not saying it's wrong to have an infinate proposition... but the paradox you mention could sugest that it may help logic to disallow "infinate" propositions. In the end the rules are made by us, there's no wrong or right, just attempts to create a "world" where we can explain and justify everything.
It's sounds like you're looking for an absolute truth... but I'm not sure that can actualy be found through logic... or anywhere for that matter.

As fot the sentence I mentioned... this has nothing to do with logic, it's not a proposition, it's not logic... it's a sentence, and gramaticaly it makes sence, but from our point of view it's just nonsence.
Writing random letters does not follow the rules of gramar or spelling that we use, but the other sentence does, it just makes no sence because you can't taste a feeling. Basicaly it's applying the rules of gramar to construct a "correct" sentence that makes no sence. I'm not looking for an answer or confirmation on wether the sentence is true or false, my point is that the sentence makes no sence dispite having followed the rules of gramar... you would need a million rules to make sure you can only create meaningfull sentences (a problem when trying to create an AI capable of faking comunication). But this has nothing to do with logic or true/false statements, it was just an example from outside the world of logic. (Just because you can express logic as a sentence it does not mean that sentenses are bound by the rules of logic, the actual sentence "This sentence is false" actualy makes sence... not from a logical point of view, but the sentence itself makes sence, people can understand it)

abyaly:
Moonfisher, you seem to be caught up in the idea that propositions that refer to each other can only be evaluated if you reduce them. This is not the case. While some propositions sets are equivalent to a single proposition, this is not always the case and is NOT a requirement.

The three line liar is not a single self-referential statement. It would be equivalent to a single self-referential statement if you allowed it, but since you don't, it isn't.

Moonfisher:
You're right, it's not a requirement... never said it was, just saying, in THEORY you would enter the value of the proposition you're refering to in that position, just like you would with math.
The statement X = X+1 in math would in theory create an infinate loop... but it all depends on the rules you want to apply.
In the end, you have an artifitial world wich obeys the rules that we define ourselves... so it may not be a requirement, but it could be, and if it was it would make some sence in some ways...

abyaly:
It might make sense to you to create such a requirement, but it would cut away a lot of good stuff. You would pretty much disallow all recursion, which is a really useful way to describe things.
The programming language Haskell is a good example of the benefit. Self-referential objects that can be expanded indefinitely are core to the language. You would have a hard time getting anything done without them. The language itself includes very powerful abstraction methods, so destroying the entire language just to get an easy restriction on logic would create a lot of extra work for some people.

When coming up rules of logic, you need to realize that your scope includes a lot.

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