The Gödel incompleteness theorem and intelligent machines

Abstract

There is a belief in some quarters that Gödel's incompleteness theorem expresses the existence of an intrinsic property of computing machinery which limits their use as creative robots and renders them unsuitable for the simulation of intelligent behavior. We do not subscribe to this view, and it will be the purpose of this paper to indicate why not. To do this, we shall develop in Part I, the concepts of recursive function theory necessary to state Gödel's theorem so that an intelligent argument as to its consequences may be inferred. The method we have chosen - programs - seems to us to be that with which the reader will be most familiar and which has the greatest intuitive appeal. The main result, the Gödel incompleteness theorem, will then appear as a statement to the effect that a certain set of integers can not be generated by a program. In Part II we show how in certain cases, sets of integers having similar properties may be generated by a modified program, and draw some conclusions vis-à-vis machine intelligence. We wish to emphasize that while our presentation is very informal, it is possible to give rigorous demonstrations of all theorems stated, and we shall henceforth regard this as implicit.