Boole thought of his system as a mathematics without numbers. “It is simply a fact,” he wrote, “that the ultimate laws of logic—those alone on which it is possible to construct a science of logic—are mathematical in their form and expression, although not belonging to the mathematics of quantity.” The only numbers allowed, he proposed, were zero and one. It was all or nothing: “The respective interpretation of the symbols 0 and 1 in the system of logic are Nothing and Universe.” Until now logic had belonged to philosophy. Boole was claiming possession on behalf of mathematics.
