Gödel, Lucas, and mechanical models of the mind
Robert F. Hadley · Computational Intelligence · 1987
In Minds, Machines, and Gödel, Lucas offers an argument, based upon Godel's incompleteness theorems, that his mind cannot be modelled by a machine. This argument has generated a variety of alleged refutations, some of which are incompatible with others. It is argued here that the incompatibility of these refutations points to a puzzle or paradox which has not yet been resolved. A solution to this puzzle is presented in which it is argued that the existence of an algorithm, capable of generating a godel sentence for an axiomatic model of that same algorithm, is not incompatible with Godels well‐known results. It is further argued that, contrary to received opinion, Gödel's results do not provide grounds for believing that cognitive agents are incapable of proving the consistency of correct formal models of their own cognitive mechanisms. This is shown to be so, even on the assumption that these formal models are known by those agents (on empirical grounds) to be formal models of themselves. Finally, the implications of the above issues for theoretical questions in AI are explored.