Did Gödel prove that we are not machines? (On philosophical consequences of Gödel's theorem)

Abstract

Gödel's incompleteness theorem has been the most famous example of a mathematical theorem from which deep philosophical consequences follow. They are said to give an insight, first, into the nature of mathematics, and more generally of human knowledge, and second, into the nature of the mind. The limitations of logicist or formalist programmes of mathematics have had a clear significance against the background of the foundational schools of the early decades of this century. The limitations of mechanism, or of the vision underlying research in the field of Artificial Inteligence, gain significance only now. Yet, while the limitations imposed by Gödel's theorem upon the extent of formal methods seem unquestionable they seem to have very little to say about the restrictions concerning mathematical or computer practice. And the alleged consequences concerning the non-mechanical character of human mind are questionable. The standard reasoning, known as Lucas' argument, begs the question, and actually implies that Lucas is inconsistent!