ABSTRACT
The ultimate goal o f mathematics is to eliminate any need fo r intelligent thought.
—Alfred N. Whitehead
1.1 Evolution of the province of human thought One of the m ajor themes of the past century has been the growing replacement of human thought by computer programs. Whole areas of business, scientific, med ical, and governmental activities are now computerized, including sectors th a t we humans had thought belonged exclusively to us. The interpretation of electrocar diogram readings, for instance, can be carried out with very high reliability by software, without the intervention of physicians-not perfectly, to be sure, but very well indeed. Computers can fly airplanes; they can supervise and execute manufacturing processes, diagnose illnesses, play music, publish journals, etc.
