# Truth vs Provability **Domain:** Mathematical Logic / Epistemology **Doc Type:** Conceptual Distinction **Maturity:** Foundational **Related:** [[Gödel's Incompleteness Theorems]], [[Formal Systems]], [[Mathematical Foundations]], [[Epistemic Humility]] ## Definition **Truth and provability are different relations.** Truth concerns satisfaction in an interpretation or model; provability concerns derivability from axioms by formal rules inside a specified system. ## Gödel Context The incompleteness results reveal sentences that are not decided by a sufficiently strong formal theory. Calling a Gödel sentence “true” requires attention to the intended model and the assumptions under which the metatheoretic reasoning is conducted. ## Machine-Intelligence Context A model's inability to certify an output does not establish that the output is true, and fluent assertion does not constitute proof. This distinction connects formal logic to provenance, external grounding and [[Model Contestability]]. ## Backlinks - [[Gödel's Incompleteness Theorems]] - [[wiki/Bauhaus Architects of AI|Bauhaus Architects of AI]]