This paper presents, from a historical and logical-philosophical perspective, the Gödelian arguments of two Oxford scholars, John Lucas and Roger Penrose. Both have been based on Gödel's Theorem to refute mechanism, computationalism and the possibility of creating an AI capable of simulating or duplicating the human mind. In the conclusions, the growing application of empirical methods in mathematics is mentioned and a possible path that would support Lucas and Penrose's arguments is speculated.

J. R. Lucas serves warning that he stands ready to refute any sufficiently specific accusation that he is a machine. let any mechanist say, to his face, that he is some particular machine M; Lucas will respond by producing forthwith a suitable Gödel sentence ϕM. Having produced ϕM, he will then argue that — given certain credible premises about himself — he could not have done so if the accusation that he was M had been true. let the mechanist try (...) again; Lucas will counter him again in the same way. It is not possible to accuse Lucas truly of being a machine. (shrink)