A Non-Formulable Theorem: A Fundamental Limit of Finite Syntactic Systems and Its Consequences for Security and AI

Abstract: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.

Cryptography and Security (cs.CR); Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO)

arXiv:2609.04086 [cs.CR]

(or arXiv:2609.04086v1 [cs.CR] for this version)

https://doi.org/10.48550/arXiv.2609.04086 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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