The Completion of the Emergence of Modern Logic from Boole’s The Mathematical Analysis of Logic to Frege’s Begriffsschrift

Abstract

Modern logic begins with Boole’s The Mathematical Analysis of Logic when the algebra of logic was developed so that classical logic syllogisms were proven as algebraic equations and the turn from the logic of classes to propositional logic was suggested. The emergence was incomplete as Boole algebraised classical logic. Frege in Begriffsschrift replaced Aristotelian subject–predicate propositions by function and argument and displaced syllogisms with an axiomatic propositional calculus using conditionals, modus ponens and the law of substitution. Further Frege provided the breakthrough to lay down the groundwork for the development of quantified logic as well as the logic of relations. He achieved all of this through his innovative formal notations which have remained underrated. Frege hence completed the emergence of modern logic. Both Boole and Frege mathematised logic, but Frege’s goal was to logicise mathematics. However the emergence of modern logic in Frege should be detached from his logicism.