# Undecidability **Domain:** Logic / Computability Theory **Doc Type:** Concept **Maturity:** Foundational **Related:** [[Gödel's Incompleteness Theorems]], [[Halting Problem]], [[Decision Problem]], [[Formal Systems]], [[Alan Turing]] ## Definition **Undecidability** is the property of a decision problem for which no algorithm can correctly return an answer for every permitted input, or of a sentence that a specified formal theory can neither prove nor refute. ## Distinctions Proof-theoretic incompleteness, Turing undecidability, semantic indeterminacy and practical uncertainty are related but not interchangeable. The relevant system, question and decision procedure must always be named. ## Corpus Context This node keeps the ontology from converting every unresolved question about consciousness or machine behavior into a Gödel result. An empirical question may remain unsettled without being formally undecidable. ## Sources / Provenance - [[Gödel's Incompleteness Theorems]] - [[Halting Problem]] - [Stanford Encyclopedia of Philosophy — Computability and Complexity](https://plato.stanford.edu/entries/computability/)