How did George Boole’s algebraic tradition treat logic as a calculus?

George Boole’s algebraic tradition treated logic as a calculus ratiocinator—a tool primarily designed for drawing inferences rather than serving as a universal medium of communication. By applying the methods of algebra to logical forms, Boole demonstrated that logical symbols could be manipulated similarly to numerical quantities, effectively separating the symbols of quantity from those of operation.12

In this framework, Boole argued that logic should be allied with mathematics rather than philosophy. His system, now known as Boolean algebra, allows for the systematic manipulation of propositions using logical connectives like AND and OR. Because this approach treats logic as a calculus, it is flexible; it can be discussed, theorized about, and modified as needed. Unlike the "logic as language" tradition, which views logical truths as universal, Boole’s algebraic logic was designed to operate across all possible universes of discourse, allowing for the selection of specific domains for particular applications. This symbolic method enables one to derive conclusions that are logically contained within any given set of premises.231