"Gödel, Nagel, Minds and Machines"

Just fifty years ago, Ernest Nagel and Kurt Gödel became involved in a serious imbroglio about the possible inclusion of Gödel's original work on incompleteness in the book, Gödel's Proof, then being written by Nagel with James R. Newman. What led to the conflict were some unprecedented demands that Gödel made over the use of his material and his involvement in the contents of the book--demands that resulted in an explosive reaction on Nagel's part. In the end the proposal came to naught. But the story is of interest because of what was basically at issue, namely their provocative related but contrasting views on the possible significance of Gödel's theorems for minds vs. machines in the development of mathematics. That is our point of departure for the attempts by Gödel, and later Lucas and Penrose, to establish definitive consequences of those theorems, attempts which--as we shall see--depend on highly idealized and problematic assumptions about minds, machines and mathematics. In particular, I shall argue that there is a fundamental equivocation involved in those assumptions that needs to be reexamined. In conclusion, that will lead us to a new way of looking at how the mind works in deriving mathematics that straddles the mechanist and anti-mechanist viewpoints.