A Note on Applicability of the Incompleteness Theorem to Human Mind

We shall present some relations between consistency and reflection principles which explain why is Godel's incompleteness theorem wrongly used to argue that thinking machines are impossible. 1 Introduction Since its publishing Godel's incompleteness theorem attracted a lot of attention among philosophers. In 1959 Lucas [8] presented an argument that this theorem implies that human thinking is essentially different from what any machine can do. This means that the ultimate goal of artificial intelligence cannot be achieved. The argument is roughly the following. A machine (nowadays we would rather say "a computer") behaves according to fixed rules (a program), hence we can view it as a formal system. Applying Godel's theorem to this system we get a true sentence which is unprovable in the system. Thus the machine does not know that the sentence is true while we can see that it is true. The spectrum of attitudes of various people to this argument was nicely characterized by Hofstadter [..