Penrose’s Philosophical Error

Abstract

Computer learning techniques, as embodied in neural networks, are modelled on the way we learn and make decisions. With the ever greater power of computers, one may wonder if a point might be reached when it could be said that the computer has become conscious, that it behaves in the way that a thinking human being behaves. In his book Shadows of the Mind, Roger Penrose argues that our conscious mentality cannot be fully understood in terms of computational models, using mathematical theorems due to Gödel and Turing. The mathematics of computation and formal systems is developed in some detail, and it is shown that Penrose’s argument does not work.