Thesis: AGI, defined as an algorithmic system with universal cognitive competence, is structurally impossible.

I want to present a formal impossibility proof for Artificial General Intelligence, showing that any algorithmic system operating over finite symbolic structures must fail on a structurally essential class of decision problems.

This isn't about current technical limitations or computational resources. It's about mathematical constraints that no amount of engineering can overcome.

1.What AGI would need to be

Let me start with the "industry-standard definition" used by OpenAI, DeepMind, Bostrom, Goertzel, and most research communities:

AGI = an algorithmic system capable of performing all cognitive tasks at or above human-level performance.

This implies:
- Domain-general reasoning across arbitrary contexts
- Self-adaptive problem solving in unfamiliar environments
- Symbolic or sub-symbolic computability
- Autonomy without human guidance

I'll demonstrate that AGI defined this way isn't merely difficult - it's formally impossible due to structural limitations.

2. The core theorem: Infinite Choice Barrier

Let π be a total computable policy over a decision space X. Let Φ(x) be the ground-truth optimal answer to problem x ∈ X. Let Loss(π(x), Φ(x)) measure the deviation from optimality.

Theorem (Infinite Choice Barrier):
For any ε > 0, there exists x ∈ X such that:

Loss(π(x), Φ(x)) ≥ ε

Assumptions:
- X is irreducibly infinite (not recursively enumerable)
- π is total and computable (algorithmic)
- The loss function is semantically non-trivial

Proof sketch: The claim 'π is ε-optimal over all x ∈ X' defines a non-trivial semantic property over computable functions, which is undecidable by Rice's Theorem. Therefore, no computable policy can be uniformly optimal over all inputs in such spaces.

This gives us our fundamental impossibility result.

3. Three structural limitations (Corollaries)

This abstract barrier manifests in three concrete ways:

A. Semantic Closure

An algorithmic system operates over a finite symbol set Σ. It cannot generate or represent symbols outside Σ. Therefore, it cannot invent new conceptual primitives.

Formal constraint: If the system's vocabulary is Σ = {s₁, s₂, ..., sₙ}, then any concept requiring symbols outside Σ is unreachable.

Example: A Newtonian AI cannot produce the concept of "relative time" if that con...

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