Goedel's Theorem and Mechanism

In Minds, machines, and Godel, (1) J. R. Lucas claims that Goedel’s incompleteness theorem constitutes a proof “that Mechanism is false, that is, that minds cannot be explained as machines”. (2) He claims further that “if the proof of the falsity of mechanism is valid, it is of the greatest consequence for the whole of philosophy”. (3) It seems to me that both of these claims are exaggerated. It is true that no mind can be explained as a machine. But it is not true that Goedel’s theorem proves this. At most, Goedel’s theorem proves that not all minds can be explained as machines. Since this is so, Goedel’s theorem cannot be expected to throw much light on why minds are different from machines. Lucas overestimates the importance of Goedel’s theorem for the topic of mechanism, I believe, because he presumes falsely that being unable to follow any but mechanical procedures in mathematics makes something a machine. Lucas explains Goedel’s theorem in this way: Goedel’s theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot be proved-in- the system, but which we can see to be true. (4)