Take 3:
It is possible to as consistent internally, with completeness AND(logically consistent) in a strong sense(not tautological) to make a model, that matches the map?
That is testable.
Someone: There is for all of the observations from the map one model and only one as described above, which matches the map.
Me: No!
Someone: That is a contradiction.
Me: No! It is an over-reduction, which don't take into account the classical second law of thought as for the world and not just abstract logic. The non-contradiction law for the world is that something can't for the same time, place and property/sense have another property, which is different as opposite to the first property, but that doesn't rule out that something else at another time and place can have a different as opposite property.
That is it. It is that simple and that is the limit of logic and the world.
You can't make as consistent internally, with completeness AND(logically consistent) in a strong sense (not tautological) a model of all of the world, because I can in effect do it differently.
In philosophy, that is the limit of the coherence theory of truth in the strong sense. That is what you are doing.
You are not the only human, how have considered, what logic is.
So here it is for humans in general as common: There is a limit to human mobility apparently. E.g. no human on earth can fly solely by the use of their individual bodies. That doesn't mean that mobility is impossible. It means that it is limited, but not impossible.
It is the same for human behavior, when it comes to the use of reason, logic/proof, objectivity, evidence, knowledge and so on.
The joke with your natural model, is that we, naked apes, are so fond of our big brains, what we believe, we can make sense of all of the world. But that is not, how biology works. The replication of the fittest gene don't "test" for making sense of all of the world. For us as a sexual reproducing life form, it "tests" for the 4 Fs relative to our biological niche. It doesn't test for and it can't test for making sense of all the world.
Your idea is no different than the idea of God. You can believe in it, but you can't show, that it works for all of the world.
I don't believe in the truth for all of the world, so I am a non-believer, yet I am a believer in God, because that works of me as me. And, yes, I can't show that as for all of the world, but neither can you do that with the truth.
The difference is, that you believe, it works for an universal "we". It doesn't!!! I know that for both of our positions, yet you judge me by a standard, that you yourself can't achieve. That has a name. It is called inconsistent.
Welcome to the big league of the really big words.
I never win nor do I loose. I always make it a draw. We are both humans with warts and all. We just consider that differently, because you believe your warts are "better" than me. They are not nor are they worse. They are different and as long as you "play for a win", I play for a draw. I don't hold Objective Authority with the Truth over other humans. Nor do you and your "we", but as longs as you in effect claim that, I "fight" you to achieve a draw.
We are all equal as being different parts of the world and we share similarities, but we are not the same with logic as above, so as long as you in effect, claim you be able to do something, which you in effect do differently than you claim, I "fight" you.
We are both believers and non-believers. We just do it differently.
In effect, stop claiming logic for all of the world. I just answer "No!".