His work in particular had a heavy influence on philosophy, science and religion through the Middle Ages. But Aristotle's logic was logic expressed in ordinary language, so was still subject to the ambiguities of natural languages. It was with the publication in 1847 of G. Boole's The Mathematical Analysis of Logic and A. DeMorgan's Formal Logic that symbolic logic came into being, and logic became recognized as part of mathematics. It is symbolic logic that we shall study in this chapter. Since Boole and DeMorgan, logic and mathematics have been inextricably intertwined.
Logic is part of mathematics, but at the same time it is the language of mathematics.
In the late 19th and early 20th century it was believed that all of mathematics could be reduced to symbolic logic and made purely formal. We'll mention more about this as we go along. The study of symbolic logic is usually broken into several parts. The first and most fundamental is the propositional calculus , and this is the subject of most of this web text. Built on top of this is the predicate calculus , which is the language of mathematics, but goes beyond the scope of this web text.