We don't know whether every sufficiently complex logical system must eventually produce a statement that cannot be proven true or false within it.
open
Mathematics & Logic
Gödel's incompleteness theorem confirms this for many systems, but fully mapping which systems are exempt, if any, from this limitation remains an open and active question. This continues to shape foundational debates in mathematical logic.
Team Humans Club. (2026). Problem WS01259: We don't know whether every sufficiently complex logical system must eventually produce a statement that cannot be proven true or false within it.. World Solve. Retrieved 20 Jul 2026, from https://worldsolve.org/index.php?id=1259