The problem seems to be that we have free choice of internal formal systems and
A consistent system, extended by an unprovable axiom, is also consistent, (since if this property was false then we would be able to prove the axiom by taking the extension and searching for a contradiction).
Consequently accepting the unprovable as true or false only has consequences for other unprovable statements.
I don’t think this entire exercise says anything.
In short we expect for probablistic logics and decision theories to converge under self-reflection.
yes but these are all second-order-logic terms! They are incomplete… You are again trying to justify the mind with it’s own products. You are allowed to use ONLY first-order-logic terms!
Gödel effectively disrupted the foundations of Peano Arithmetic through his use of Gödel numbering. His groundbreaking proof—formulated within first-order logic—demonstrated something profound: that systems of symbols are inherently incomplete. They cannot fully encapsulate all truths within their own framework.
And why is that? Because symbols themselves are not real in the physical sense. You won’t find them “in nature”—they are abstract representations, not tangible entities.
Take a car, for instance. What is a car? It’s made of atoms. But what is an atom? Protons, neutrons, quarks… the layers of symbolic abstraction continue infinitely in every direction. Each concept is built upon others, none of which are the “ultimate” reality.
So what is real?
Even the word “real” is a property—a label we assign, another symbol in the chain.
What about sound? What is sound really? Vibrations? Perceptions? Again, more layers of abstraction.
And numbers—what are they? “One” of something, “two” of something… based on distinctions, on patterns, on logic. Conditional statements: if this, then that.
Come on—make the jump.
It is a very abstract idea… It does seem as gibberish if you are not acquainted… but it’s not. And I think that you might “get it”. It has a high burder. That’s why I am not really mad that people here do not get the logic behind it.
There is something in reality that is inscrutable for us humans. And that thing works in second order logic. It is not Exsiting or nonexisting, but sound. Evolution exploits that thing… to create something that converges towards something that would be… almost impossible, but not quite. Unknowable.
This line of argument seems to indicate that physical systems can only completely model smaller physical systems (or the trivial model of themselves), and so complete models of reality are intractable.
That’s a great observation — and I think you’re absolutely right to sense that this line of reasoning touches epistemic limits in physical systems generally.
But I’d caution against trying to immediately affirm new metaphysical claims based on those limits (e.g., “models of reality are intractable” or “systems can only model smaller systems”).
Why? Because that move risks falling back into the trap that EN is trying to illuminate:
That we use the very categories generated by a formally incomplete system (our mind) to make claims about what can or can’t be known.
Try to combine two things at once:
1. En would love to eliminate everything if it could.
The logic behind it: What stays can stay. (first order logic)
EN would also love to eliminate first-order logic — but it can’t. Because first-order logic would eliminate EN first.
Why? Because EN is a second-order construct — it talks about how systems model themselves, which means it presupposes the formal structure of first-order logic just to get off the ground.
So EN doesn’t transcend logic. It’s embedded in it. Which is fitting — since EN is precisely about illusions that arise within an expressive system, not outside of it.
2. What EN is trying to show is that these categories — “consciousness,” “internal access,” even “modeling” — are not reliable ontologies, but functional illusions created by a system that must regulate itself despite its incompleteness.
So rather than taking EN as a reason to affirm new limits about “reality” or “systems,” the move is more like: “Let’s stop trusting the categories that feel self-evident — because their self-evidence is exactly what the illusion predicts.”
It’s not about building a new metaphysical map. It’s about realizing why any map we draw from the inside will always seem complete — even when it isn’t.
Now...
You might say that then we are fucked. But that is not the case:
- Turing and Gödel proved that it is possible to critique second order logic with first order logic. - Whole of Physics is in First-Order-Logic (Except that Poincaree synchronisation issue which okay) - Group Theory is insanely complex. First-Order-Logic
Now is second order logic bed? No it is insanely usefull in context of how humans evolved: To make general (fast) assumptions about many things! Sets and such. ZFC. Evolution.
The problem seems to be that we have free choice of internal formal systems and
A consistent system, extended by an unprovable axiom, is also consistent, (since if this property was false then we would be able to prove the axiom by taking the extension and searching for a contradiction).
Consequently accepting the unprovable as true or false only has consequences for other unprovable statements.
I don’t think this entire exercise says anything.
In short we expect for probablistic logics and decision theories to converge under self-reflection.
yes but these are all second-order-logic terms! They are incomplete… You are again trying to justify the mind with it’s own products. You are allowed to use ONLY first-order-logic terms!
Gödel effectively disrupted the foundations of Peano Arithmetic through his use of Gödel numbering. His groundbreaking proof—formulated within first-order logic—demonstrated something profound: that systems of symbols are inherently incomplete. They cannot fully encapsulate all truths within their own framework.
And why is that? Because symbols themselves are not real in the physical sense. You won’t find them “in nature”—they are abstract representations, not tangible entities.
Take a car, for instance. What is a car? It’s made of atoms. But what is an atom? Protons, neutrons, quarks… the layers of symbolic abstraction continue infinitely in every direction. Each concept is built upon others, none of which are the “ultimate” reality.
So what is real?
Even the word “real” is a property—a label we assign, another symbol in the chain.
What about sound? What is sound really? Vibrations? Perceptions? Again, more layers of abstraction.
And numbers—what are they? “One” of something, “two” of something… based on distinctions, on patterns, on logic. Conditional statements: if this, then that.
Come on—make the jump.
It is a very abstract idea… It does seem as gibberish if you are not acquainted… but it’s not. And I think that you might “get it”. It has a high burder. That’s why I am not really mad that people here do not get the logic behind it.
There is something in reality that is inscrutable for us humans. And that thing works in second order logic. It is not Exsiting or nonexisting, but sound. Evolution exploits that thing… to create something that converges towards something that would be… almost impossible, but not quite. Unknowable.
Thought before I need to log off for the day,
This line of argument seems to indicate that physical systems can only completely model smaller physical systems (or the trivial model of themselves), and so complete models of reality are intractable.
I am not sure what else you are trying to get at.
That’s a great observation — and I think you’re absolutely right to sense that this line of reasoning touches epistemic limits in physical systems generally.
But I’d caution against trying to immediately affirm new metaphysical claims based on those limits (e.g., “models of reality are intractable” or “systems can only model smaller systems”).
Why? Because that move risks falling back into the trap that EN is trying to illuminate:
That we use the very categories generated by a formally incomplete system (our mind) to make claims about what can or can’t be known.
Try to combine two things at once:
1. En would love to eliminate everything if it could.
The logic behind it: What stays can stay. (first order logic)
EN would also love to eliminate first-order logic — but it can’t.
Because first-order logic would eliminate EN first.
Why? Because EN is a second-order construct — it talks about how systems model themselves, which means it presupposes the formal structure of first-order logic just to get off the ground.
So EN doesn’t transcend logic. It’s embedded in it.
Which is fitting — since EN is precisely about illusions that arise within an expressive system, not outside of it.
2. What EN is trying to show is that these categories — “consciousness,” “internal access,” even “modeling” — are not reliable ontologies, but functional illusions created by a system that must regulate itself despite its incompleteness.
So rather than taking EN as a reason to affirm new limits about “reality” or “systems,” the move is more like:
“Let’s stop trusting the categories that feel self-evident — because their self-evidence is exactly what the illusion predicts.”
It’s not about building a new metaphysical map. It’s about realizing why any map we draw from the inside will always seem complete — even when it isn’t.
Now...
You might say that then we are fucked. But that is not the case:
- Turing and Gödel proved that it is possible to critique second order logic with first order logic.
- Whole of Physics is in First-Order-Logic (Except that Poincaree synchronisation issue which okay)
- Group Theory is insanely complex. First-Order-Logic
Now is second order logic bed? No it is insanely usefull in context of how humans evolved: To make general (fast) assumptions about many things! Sets and such. ZFC. Evolution.