GÖDEL’S INCOMPLETENESS IN THE HISTORY OF AI: Proof, Performance, and Change of Epistemic Norms

Gödel’s incompleteness theorems are often invoked in artificial intelligence as if they settled sweeping questions about mind, machine, and the limits of reason. This paper argues that such invocations are best understood not as straightforward applications of logic but as indicators of changing epistemic norms in AI. Incompleteness functions as a boundary object: a stable theorem whose authority is repeatedly recruited to articulate “closure anxieties”—worries about whether intelligence, explanation, or safety can be fully captured within a fixed formal, representational, or evaluative scheme. After delimiting what incompleteness does and does not entail, the paper reconstructs the canonical Gödel-in- AI controversy (Turing → Lucas → standard replies), showing that the anti-mechanist argument depends on controversial auxiliary premises about consistency, meta-level knowledge, and the unit of comparison. It then traces a post-symbolic shift in which “Gödel” becomes a limit-marker in performance-driven machine learning, where disputes center on representational closure and evaluation practices rather than provability. Finally, it examines the return of proof as a design ideal in self-modifying agents: “Gödel” names the aspiration to provably beneficial self-improvement, while practical research replaces proof with benchmark-based validation. The result is a historically grounded diagnosis of contemporary AI: proof remains a regulative ideal, but warrant is increasingly produced through empirical proxies, and “Gödel” persists as a name for that gap.