"Everything that tends towards “truths without contradictions” in set theory leads to contradiction."
Perfect, because that is exactly what Gödel already showed 100 years ago.
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Also, in philosophy, folks tend to build and discuss their perspectives around concepts. The concepts are accepted as correct, and yet there is no requirement that concepts are based on an actual foundation.
The word Democracy is a good example, because some forget to delve in deeper and realize there are two fundamentally different versions of democracy: one version discriminates and as many as 49.9% of the voters can end up receiving nothing they desired, whereas the other version is pure and up to 99.9% of the voters are represented by their choice. Just as an example that when the details or not declared, then we are bicycling in the air.
Another word is Universe; this is not a scientific word, and yet hardly anyone realizes that this word is not found in science because so many scientists are using it. I will discuss it further below, but the point is that concepts can be accepted by humans without these concepts required to have aa declared foundation.
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The set of Everything is automatically two-fold. There is the set that excludes Nothing, and there is a the set that includes Nothing. So, the set of Everything exists in two versions, while on the face of it they would be identical (but they are not). More on this also below.
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Keep in mind that there are just two versions of overall truths (and therefore not the suspected three versions).
There is the negative and there is the neutral. And there is NO positive truth at the overall level.
Negative overall truths:
-There is no truth (which is presented as true);
-The only certainty is uncertainty.
Both are truths that exist at the overall level, and yet they exist only in the negative.
Neutral overall truths:
Words that capture entire settings without contradictions:
Everything
Universe
Life
Balance
Reality
Whole
Nature
Mankind
All
All these words are neither negative or positive. They are basically labels that point to all they encompass without going into any of the details.
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Lastly, mathematical building blocks.
1, 2, 3, 4, 5, 6, 7, 8, and 9 are the building blocks of the decimal system.
The entire set can be declared as 1, a complete set of the decimal building blocks.
Yet the 1 inside the set means 'unit', whereas the one that appoints the entire set as 1 means 'whole'.
If in your mind you make both 1s be one and the same, then you are not smart. There are two systems here, and both 1s belong to a different system.
In the binary system, we have 0s and 1s only, and these numbers do not behave like the numbers in the decimal system. Rather, they are like 'on' and 'off', to keep this quick and simple.
Lastly, the neutral truths from the overall level.
There is nothing there but a 1.
Everything, 1.
Universe, 1.
Life, 1.
Balance, 1.
Reality, 1.
Whole, 1.
Nature, 1.
Mankind, 1.
All, 1.
Now, if we add zero into the mix, then we stepped away from the words that represent 1 all by themselves.
If we add zero to everything, for instance, then we jumped from the one-word to the dual word, which is perhaps easier to understand with the examples male-female, and young-old.
Conclusion: The human mind is the essence in how we understand everything. The article you consider very pessimistic is actually quite accurate.
Lastly:
The universe is either unified or the universe is the result of the fundamental lack of unification.
Gödel and Usó-Doménech are correct, Alexander. We have to accept that there is no unification. If there was a God once, God got godself into some problems, and ended up undermining godself. We live in the result; we are (part of) the result.
