> Gödel's Incompleteness Theorem: any sufficiently rich formal system, together with an interpretation, has strings which are true but unprovable.
This is only half of it!
Gödel's Incompleteness Theorem states that any sufficiently rich formal system, together with an interpretation, either has strings which are true but unprovable or has strings which are provable but untrue. Either is possible! In practice people prefer to have true things that can't be proven rather than provable things that are untrue. But either is possible.
This is only half of it!
Gödel's Incompleteness Theorem states that any sufficiently rich formal system, together with an interpretation, either has strings which are true but unprovable or has strings which are provable but untrue. Either is possible! In practice people prefer to have true things that can't be proven rather than provable things that are untrue. But either is possible.