The Universal Computer

Boole Turns Logic i nto Algebra

Using these ideas, Joe and Susan’s premises can be expressed by the

equations

L(1 − F )=0,

F =0,

WP =1,

WPH(1 − S)=0,

H =1.

Substituting the second equation in the first, we get L = 0, the first desired

conclusion. Substituting the third and fifth equations in the fourth, we get

1 − S =0thatisS = 1, the other desired conclusion.

Now of course, Joe and Susan had no need for this algebra. But the

fact that the kind of reasoning that ordinarily takes place informally and

implicitly in ordinary human interactions could be captured by Boole’s

algebra encouraged the hope that more complicated reasoning could be

captured as well. Mathematics may be thought of as systematically en-

capsulating highly complex logical inferences. This