Classical logic

Most semantics of classical logic are bivalent, meaning all of the possible denotations of propositions can be categorized as either true or false.

William Stanley Jevons and John Venn, who also had the modern understanding of existential import, expanded Boole's system.

Classical logic reached fruition in Bertrand Russell and A. N. Whitehead's Principia Mathematica, and Ludwig Wittgenstein's Tractatus Logico Philosophicus.

Russell and Whitehead were influenced by Peano (it uses his notation) and Frege and sought to show mathematics was derived from logic.

Wittgenstein was influenced by Frege and Russell and initially considered the Tractatus to have solved all problems of philosophy.

Many mathematical theorems rely on classical rules of inference such as disjunctive syllogism and the double negation elimination.

With the advent of algebraic logic, it became apparent that classical propositional calculus admits other semantics.