ABSTRACT COMPLEXITY THEORY AND THE MIND-MACHINE PROBLEM

In this paper we interpret a characterization of the Godel speed-up phenomenon as providing support for the 'Nagel-Newman thesis' that human theorem recognizers differ from mechanical theorem recognizers in that the former do not seem to be limited by Godel's incompleteness theorems whereas the latter do seem to be thus limited. However, we also maintain that (currently non-existent) programs which are open systems in that they continuously interact with, and are thus inseparable from, their environment, are not covered by the above (or probably any other recursion-theoretic) argument.