My purpose in this brief paper is to consider the implications of a radically different computer architecure to some fundamental problems in the foundations of Cognitive Science. More exactly, I wish to consider the ramifications of the 'Gödel-Minds-Machines' controversy of the late 1960s on a dynamically changing computer architecture which, I venture to suggest, is going to revolutionize which 'functions' of the human mind can and cannot be modelled by (non-human) computational automata. I will proceed on the presupposition that the (...) reader is familiar with some of the fundamentals of computational theory and mathematical logic. (shrink)

In this paper we interpret a characterization of the Gödel 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 Gödel'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. (shrink)