It wasn't so much to make proofs rigorous, as to determine whether or not there would always exist "true" statements which could not be proved. Hilbert had alre

It wasn't so much to make proofs rigorous, as to determine whether or not there would always exist "true" statements which could not be proved. Hilbert had already proposed a set axioms for second-order arithmetic - he just didn't know whether they were both complete and consistent.