A Non-Formulable Theorem: A Fundamental Limit of Finite Syntactic Systems and Its Consequences for Security and AI
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Abstract (arXiv)
For every coherent and sufficiently expressive finite syntactic system S, we prove the existence of at least one theorem that S cannot produce autonomously. The result is a metatheorem: it proves the existence of a theorem, and applies to every finite syntactic system - security mechanisms, AI systems, formal verifiers, legal systems, economic models, and the formal system in which it is itself proved.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 6 of its 10 references that are in the map. First posted on arXiv 3 Sep 2026.
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References · 6
- 2026Syntactic Systems Cannot See Semantic Invariantscited by 1
- 2026The Observer World: A Cryptographic Extension of Impagliazzo's Five Worldscited by 1
- 2026Observers, Symmetries, and the Hierarchy of Language Classes: A Theory of Computation Parameterized by the Observercited by 1
- 2026Syntactic Separation Implies Computational Indistinguishability: An Abstract Obstruction Theoremcited by 1
- 2026Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methodscited by 1
- 2026What Syntax Cannot See: The Dynamic Syntactic Invariance Principle and Several Instances of the Same Hidden Assumption, and a Contradictioncited by 1
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