Beliefs, Models, Analogies

A Game Like Chess and a Formalized Mathematical Calculus

"...general meta-chess' theorems can be established whose proof involves only a finite number of permissable configurations on the board. The metachess' theorem about the number of possible opening moves for white can be established in this way; and so can the meta-chess' theorem that if white has only two Knights and the King, and black only his King, it is impossible for white to force black into a mate.

"We have quoted this analogy at lenth because it illustrates the concept of calculus not only in metamathematics but also in metacommunication. For if we expand the analogy to include the two players we are no longer studying an abstract game but, rather, sequences of human interaction that are strictly governed by a complex body of rules."