Modern logic began with the publication in 1879 of the Begriffsschrift of Gottlob Frege (1848–1925). In the Begriffsschrift we find for the first time a comprehensive treatment of the ideas of generality and existence, because sentence forms which were hitherto accommodated only by complicated ad hoc theories are here provided with an adequate symbolization by the device of quantification, rules for which are adjoined to the first complete formalization of the classical propositional calculus. The result closely approximates a modern formal axiomatic theory. It meets Frege's aim of a codification of the logical principles used in mathematical reasoning, although the rules of inference (substitution and modus ponens) and the definition of other logical constants in terms of the primitives (negation, implication, the universal quantifier, and identity) are not explicitly formalized but are mentioned as obviously justified by reference to the intended interpretation. A proof of completeness was not to be...