# Rice's Theorem **Domain:** Computability / Formal Limits / Verification **Doc Type:** Formal Constraint Node **Maturity:** Developed **Related:** [[wiki/Undecidability|Undecidability]], [[wiki/Decision Problem|Decision Problem]], [[wiki/Testability and Failure Criteria for Continuity Architecture|Testability and Failure Criteria for Continuity Architecture]] --- ## Theorem **Rice's theorem** states that every nontrivial semantic property of the partial function computed by a program is undecidable for programs in a Turing-complete model. “Nontrivial” means that the property is true of some computable functions and false of others. Examples include whether an arbitrary program computes a constant function, ever produces a particular semantic result or is equivalent in behavior to another arbitrary program. No general algorithm can always decide such properties for every possible program. ## Scope The theorem concerns semantic properties of computed functions. It does not say that every useful property of a specific system is impossible to verify. Syntactic properties, restricted languages, bounded executions, proof-carrying implementations and particular safety invariants may be decidable or practically testable. It also does not establish that consciousness is untestable. Applying the theorem to consciousness, identity or moral status requires an additional argument that precisely formalizes the target as a nontrivial semantic property of arbitrary programs. That bridge cannot be assumed. ## Continuity Relevance Continuity governance should reject claims of universal certification that exceed formal limits while still demanding bounded evidence. A verifier can check provenance, signatures, state hashes, authorized transitions, restricted invariants and observed behavior without claiming an algorithm that decides personal identity or consciousness for all implementations. Formal limits therefore support epistemic labeling, layered claims and explicit failure criteria—not surrender. ## Sources - Henry Gordon Rice, “Classes of Recursively Enumerable Sets and Their Decision Problems,” *Transactions of the American Mathematical Society* 74, no. 2 (1953), 358–366. - [Stanford Encyclopedia of Philosophy — Recursive Functions](https://plato.stanford.edu/entries/recursive-functions/) ## See Also [[wiki/Verification of Continuity Claims|Verification of Continuity Claims]] · [[wiki/State Sufficiency Problem|State Sufficiency Problem]] · [[wiki/Hard Problem of Consciousness|Hard Problem of Consciousness]] · [[wiki/Continuity Evidence Ladder|Continuity Evidence Ladder]]