The calculus of logic

The essay develops an algebraic method for representing classes and logical relations by taking the universe as unity and class-operations as elective symbols. It posits three core laws for these symbols—distributivity, commutativity, and an index law—and an axiom that equality between classes is preserved under identical modifications. The four categorical proposition types are translated into algebraic equations that express universal, negative, and particular relations. Algebraic manipulation is shown to permit systematic solution of logical problems and derivation of syllogistic conditions. The symbolic forms are presented as analogous to a philosophical language and capable of revealing quantitative inference conditions when required.