Many people are fond of saying, ‘They will never make a machine to replace the human mind – it does many things which no machine could ever do.’ A beautiful answer to this was given by J. von Neumann in a talk on computers given in Princeton in 1948, which the writer was privileged to attend. In reply to the canonical question from the audience (‘But of course, a mere machine can’t really think, can it?’), he said:
You insist that there is something a machine cannot do. If you will tell me precisely what it is that a machine cannot do, then I can always make a machine which will do just that!
In principle, the only operations which a machine cannot perform for us are those which we cannot describe in detail, or which could not be completed in a finite number of steps. E.T.Jaynes, Probability Theory, The Logic of Science