I totally agree. I would add a little note to that it is impossible to fully understand or logically derive some important scientific statements as a high-school student using high-school methods. This means you have to learn them and force your brain to learn what you can't prove so you just believe these things and brainlessly use them. This applies to Physics or History. So basically you are getting brainwashed.

(1) The honest answer is I don't know. However it is widely accepted that a very small % of people own the majority of goods. I would say corporations, banks and high net worth individuals own much more than optimal or even sustainable for society. And I think there is much more that we don't know about.
(2) I think nature will solve it. One day a big bank will say: "Okay guys I can't pay" and then the dominoes will do the job of crashing the economy.
(3) I did not mean that there is x amount of money in the world and we will give some for everybody. We need other forms of "trust". Maybe there will be a new currency maybe there won't but this mechanism of keeping everybody in debt is evil. We don't trust banks. Why should we trust money?
(4) As "we" I mean we, the people on Earth. Maybe other institutions aswell. That was just a heuristic idea of mine I don't kno the details.

Thank you for answering my question! I will have to re-read your post several times to get a better understanding of it. However here is a short answer to what my alternatives are. I think capitalism is "fine". Freedom is a great value. And I don't know why but it seems like the system is flawed. I don't know if it is because of capitalism or whatever. One thing is sure. The rich gets richer and the poor gets poorer (not only from a monetary standpoint but educational etc.). And people on the lower end don't like the system. The "cost" of things do not reflect the "value" of things. A not so smart but ambitious person can get good grates while an introverted but maybe very smart person can be bullied out from "society" (for example being on the low end of the school hierarchy). People with much money can influence "truth" with lawyers and such. They make a shitload of money just by having money. The system turns everything into a competition. Of course there are smarter prettier taller stronger etc. people and there is some kind of natural competition but making a business based on these and making copetition the goal leads to an ill-valued society. When idiots are the bosses, when average looking people get photoshopped to become the dreams beyond reach in society then capitalism is not capitalism anymore.
Some alternatives?
1. Objective quantitative and logical methods in every aspect politics and economics (maybe using A.I.?) So there aren't idiots in leading roles.
2. A better family model (from which people get human values without having to be competitive)
3. A "restart" of the capital. We have to redistribute capital so these inequalities will disappear for a while. I think nature will "restart" the capital when derivative markets collapse. I am 100% sure that will happen in my lifetime.

I have been doing a lot of other stuffs lately so I couldn't learn enough about these reflection principles. I will read more about them for sure.
But for my conclusion of the thread:
Defining arithmetic truth is a hard task (I would say impossible).
Either we are platonists and believe that truth is given by the facts which are true in the existing abstract metaphysical world. In this case we can't deductively describe every aspect of truth.
Or we are formalists and we think something is true if we can prove it somehow (for example from ZFC).
In this case truth is easy to define and easier to describe but this concept does not meet some basic requirements of the concept of truth (e.g. completeness)
So the problem of defining truth without using truth is like the problem of life after death or the question what is beyond the universe. Impossible to answer.

Only those go to Valhalla who die in battle.

Thanks Nagase your answer is top notch as always.
I dont wholly understand this thing about local truth predicates but sounds interesting. I Will read about it.

At the moment I cant imagine how would we define truth using the reflection principles.

In my first post I formalized your argument and turned out the deduction is incorrect.
Maybe you got the right intuition but we need a logic to create a logical frame for your intuition.

If Q means (P and ~K(P)) ((Q means P is true and not knowable))
And we assume K(Q)
Then ~K(P) immediately follows.
That is a contradiction indeed; the similar to the Fitch paradox but not the same.

Your logic seems to be accepted and understood by a single person in the world therefore it is not a classical one.

I don't understand why did they choose that single sentence to show the absurdity of the argument. Since EVERY formula is provable in a contradictory logical system (at least in first order logic- but modal logic cant be much different) 1+1=2 is also provable which is absurd for every rational human being- and even for theists. (Since theists believe in an omniscient being omniscience is natural for them.)

I think "everything" doesn't have a logical definition. Like in mathematics you can define "everything" within a system with the equation x=x (at least in first order systems). But there will always be objects outside the system.

I accept Nagase's answer on arithmetic truth. If the mathematics we do is formalized within PRA then the problem of the truth of existence in PA is solved (or not so obvious anymore).

However I was reading a book today about logic and I faced the same problem again.
What if I want to define existential truth in ZFC or in a more powerful system? ZFC provability is not enough anymore as the set of provable sentences of ZFC form a real subset of the set of true sentences of ZFC. How do we define existential truth of ZFC? I think that we must use a metaphysical existence concept.

I think there is nothing paradoxical in the possibility that there are true sentences which are not knowable. The absolute conistency of arithmetic or set theory could be examples for this. The absolute consistency of these theories can be true but since we can only prove relative consistency we will never know if they are true or not.
edit: Another example: Let's say there are x particles in the universe. There are formulas which's length is 10^x^x^x^x^x. Some of them may be true. I don't think we would ever know the truth value of each of them.

The goal of the argument was to show that {(KP),(NonO),(A),(B),(C),(D)} is inconsistent. To show that they looked for a contradiction. At step (6) they got a contradiction so for me that is the end of the proof. Their proof didn't end there and they found a contradiction at (9). This was weird for me; however the problem is not a big deal just a small technical detail.

Basically they prove {X,Y}⊢⊥ by proving {X,Y}⊢⊥=>~X by reductio; and then {X,~X}⊢⊥
I think it wasn't the most elegant method but as I said it is not a big deal.

I interpret your axioms as follows:
1. x --> ◊K(x) (All truths are knowable ie. it is possible that somebody knows x at some time.) (axiom)
2. P (Proposition P is a truth) (axiom)
3.a) ~K(P) (P is unknown) (axiom)
3.b) Q:=~K(P) (definition of Q)
4. ◊K(Q) (Theorem from 1. and 3.)
5. K(Q) (Q is known) (axiom)

6. Theorem: K(P) (P is known)
Can you please clarify the proof of that theorem using this formal language? I don't think these axioms are enough to prove statement 6. Maybe your logic differs from this. In fact (6.) is not a theorem of the above system.

As long as I understand your premises are stronger than that of Fitch's paradox in existential terms.
While Fitch's paradox only assumes P and Q; you assume K(Q) also.

So first I don't see how we can prove 6. and even if we can get a contradiction from your axioms they may be stronger than the axioms of Fitch's paradox.

To be honest I don't really understand the paradox explained here:
https://plato.stanford.edu/entries/fitch-paradox/#ParKno
At (6) they get a contradiction and from that we can prove every statement (can't we?)
But they keep proving for 5 more steps for no apparent reason.

Aw i didnt know that. Thanks. I dont know where my idea came from.

If truth in arithmetic means provability in ZFC then it is false that every PA formula is either true or false. Thats odd.

What kind of "truth" concept is used in the Gödel and Tarski theorems? Is it ZFC provability?

My main goal is not to define existence but to find a logic without the anomalies mentioned above. Or at least to formalize my problem (about mathematical existence)

Thank you for the recommendation. I Will read it. I have only seen a bit from the mathematical side. I need to discover the philosophical side yet.

Edit: Jeah we basically agree in almost everything. Maybe I expressed myself not the best possible way. I really think that "mathematical" or "logical" rigour has to be given up while we define existence. Because either:
1. Existence is defined by itself. That does not meet the requirements of logic. Or
2. Existence ia defined by another type of existence. In this case we either need infinite previous definitions or there is an existence for which we need another method to define. (for example by using experience from the real word)

I do not say that is worse or less scientific than pure mathematics. But I do say that pure mathematics has to end somewhere.

Thank you for answering!
Yes that's it! I Think we have to give up mathematics at some point and enter the realm of metaphysics. Because in the definition of the truth of an existential sentence of the form above we use the term "there exists". So existence is defined by some kind of "meta existence" and hence the rigour of Mathematics disappears at one point. We can interpret that differently (biologically, intuitively etc.) of course.

Edit: Basically platonism comes into the picture because in my opinion in practice most of the mathematicians think zfc provability means truth. But in theory that can not be the case of course. And I dont know a precisw definition. Precise in the most rigorous sense.

At the end we have to interpret existence as something like "it is trivial" based on our previous experience with reality. (for example we know what "there exists a dog in the room at the moment" means)