In “Minds, Machines, and Gödel”, 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”. 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”. It seems to me that both of these claims are exaggerated. It is true that no minds can be explained as machines. 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. (shrink)

Current discussions of how words have meaning owe a great deal to the two ideas of family resemblances and paradigm cases. But the relations between these ideas have not been examined sufficiently. Some people regard the ideas as pretty much the same, or at least as complementary. Others regard them as distinct but compatible instruments for ordinary language analysis. I believe that both attitudes are probably wrong. Almost certainly, neither attitude is justified given the most common understandings of the two (...) ideas. (shrink)