[ivan.moony]

About defining truthfulness

While designing a logic language, I encountered this problem in defining how true formulas should look like. The problem was in that when we define a general formula `GF` such that `True <-> GF`, the whole system always collapses to `True`, and then back to the whole `GF` when we instantiate either of `GF` elements. Because hard-coding any constants was not a desired option, a compromise solution had to be found. Such a compromise would let us use the notion of truth without violating Tarski's results. It happens that such a compromise exist. We may define an analogue to a general truth at the root of the whole system by a plain consequence like `Top -> U`, where `U` is a growing Universe of expressions that are true, while the same Universe is considered as an underlying theory we want to express in our logic language. Specific fragments of this Universe still have a chance to recursively loop back to `Top` symbol without making the system collapse. In a free interpretation, `Top` symbol represents only a given subset of all possible true formulas, which is why its name is distinct from `True`. Of course, the `Top` symbol is not globally restricted, yet it is as extensible as the universe `U` is.

[AgentSmith]

There is no sufficiently complex theory that can be consistent and complete at the same time.

Gödel's incompleteness theorems also have an important meaning for artificial intelligence. In fact they imply that each artificial intelligence always has limitations. With other words: There are things the AI does not know or cannot do, or the AI does not exist.

[LOCKSUIT]

"There are sentences in this theory that can't be proved nor disproved."

But there are sentences in this theory that can be acknowledged, feared, hated, loved, bought, and so on!

[LOCKSUIT]

"There are sentences in this theory that can't be proved nor disproved." No, I as a human myself can prove/disprove this and understand it. This is a sentence that says the sentences in it (the theory) can't be proven nor disproven, so let's take this sentence, prove/disprove it, and, we disprove it, because there is not sentences in this sentence that can't be proven nor disproven, otherwise if there was then we would prove this sentence. Also, there is sentences in this theory that may be disproven by certain readers, or proven, and I realized this after thinking "There are sentences in this theory that you can't be mad at.". But there are sentences in this theory that can be acknowledged, feared, hated, loved, bought, and so on! Ok so it basically says you can't disproven nor prove this sentence, and I think: what is there to prove/disprove?, this i guess > "you can't prove nor disprove this sentence", I'm sure we can reach an agreement. Ok I did it, the sentence is proven true if I CAN'T prove it nnoorr disprove it, else false disprove. Clearly there is nothing that can be proven, nor that can be disproven. So there are sentences in this theory, that can't be proven? True. Nor disproven? True. So True. But now wait it just said itself cannot be proven and I just agreed with the line that itself cannot be proven yet I just proved itself true that it is true.....yes i did, I proven this line. Then again I might reframe to FALSE because it said itself cannot be proven.....but then it said itself couldn't be disproven false either and if i do say so now then it is false......so false?.....................it true if can't be true or false.........if i can say true or false which i did then it is false OMG DID IT

"There are sentences in this theory that can't be proved nor disproved."
FALSE AFAIK

The main concept of my discovery here is that there is no object in it that can be proven or disproven, so it, is, true..........yet it says itself cant be true nor false so because i have indeed said one of them (true), then the sentence is, false.

To go further, i guess it, is an object, and it says itself as an object can't be proven nor disproven (unless we focus on the "sentences IN this theory"), well, i can mark it true or false, hence it'd be false.

SO: If i can mark it true positive or false negative then it is false. And I can. So false. Also, in a sense yes true there is sentences in itself/itself can't be really proven or disproven so yes True but then being true makes it false anyhow.

However if you look at your grading/marking of it as a separate thing, then True, it can't be proven nor disoroven, so it's True and positive. Then you could make a clone of this and make this one False for being that you say it true yet it say it cannot be true hence it false no good, that way you get the both of best worlds.

Now you end up with in ur brain:
"False i can mark it +/-."
"True it is right."
"False cus it said it couldn't be right nor wrong."
"And same for if you mean it or the sentences in it."
"Or whatever the hell your brain thinks."

Who wants cake!?