Abstract
The emergence of formal or mathematical logic in the 19th and the early 20th century was the outcome of two parallel and partly independent lines of development, whose key figures were Charles S. Peirce and Gottlob Frege. Most of Peirce's work in logic—for example, his early work on Boolean algebra and the logic of relations—falls clearly in the calculus tradition. The same holds for his later work—for example, the logic of existential graphs. Peirce himself observed that the system of existential graphs was not intended to serve as a universal language for mathematicians or other reasoners, like that of Peano. He also denied that it was intended as calculus or apparatus by which conclusions can be reached and problems solved with greater facility than by more familiar systems of expression. According to Peirce, a logical universe is, no doubt, a collection of logical subjects, but not necessarily of meta-physical subjects, or substances.