Gödel, Penrose and the possibility of AI

摘要

It is argued that Penrose's use of Gödel's theorem to show that no machine can reproduce the achievements of a human mathematician depends on extra assumptions that would also show that no machine could ever check the validity of mathematical proofs; and it is claimed that the latter result contradicts views about the possibility of communicating mathematical proofs that are widely held and that are endorsed by Penrose.