# 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."