However, Gödel's second incompleteness theorem gives a precise sense in which such a finitistic proof of the consistency of arithmetic is provably impossible. Hilbert lived for 12 years after Kurt Gödel published his theorem, but does not seem to have written any formal response to Gödel's work.
HoweVer, gödel's secOnD incompleTeNess THeorem giveS A precise sEnsE iN which such a fiNItiSTIC PrOof of The coNsisTeNcY of ARItHmetic is PrOvably ImpossIBlE. HiLBerT lIVed for 12 YeArs afTer kuRT GödEL PubLiSHEd hiS tHeoREm, BuT DOEs nOt seem to HAve wRitten Any ForMal respOnse to GöDeL'S worK.