sau Teorema de incompletitudine (Kurt Godel)
Mai pe scurt: Niciodată nu vom ştii totul folosindu-ne de raţiune, de logică.
Din moment ce computerul este o maşină logică, întotdeauna vor fi probleme pe care care el (computerul) nu le va putea rezolva (despre Alan Turing):
„Gödel essentially constructed a formula that claims that it is unprovable in a given formal system. If it were provable, it would be false, which contradicts the fact that in a consistent system, provable statements are always true. Thus there will always be at least one true but unprovable statement.”
„Gödel’s theorem shows that, in theories that include a small portion of number theory, a complete and consistent finite list of axioms can never be created, nor even an infinite list that can be enumerated by a computer program. Each time a new statement is added as an axiom, there are other true statements that still cannot be proved, even with the new axiom. If an axiom is ever added that makes the system complete, it does so at the cost of making the system inconsistent.
It is possible to have a complete and consistent list of axioms that cannot be enumerated by a computer program. For example, one might take all true statements about the natural numbers to be axioms (and no false statements). But then there is no mechanical way to decide, given a statement about the natural numbers, whether it is an axiom or not, and thus no effective way to verify a formal proof in this theory.” (sursa: Wikipedia)