Begriffsschrift

Begriffsschrift, published in 1879 by Gottlob Frege, is a landmark in the history of logic. The work presents a formal notation and a deductive system intended to express and derive logical laws with the aim of grounding mathematics in logic. It is widely regarded as one of the first systematic formalizations of predicate logic, introducing ideas that would shape the development of modern logic and the philosophy of language.

The central contribution of Begriffsschrift is its distinctive two‑dimensional notation, sometimes described as concept-script. Frege replaces natural-language expressions with a formal apparatus that treats predicates, functions, and arguments as essential components of logical reasoning. A main formula expresses a function and the place for its argument, while a bound variable and a binding stroke indicate scope. This notation allows complex propositions, including quantified statements, to be represented unambiguously and manipulated according to a small set of inference rules. Although not identical to modern first‑order notation, Frege’s system anticipates key features of predicate calculus, such as function application, argument roles, and the use of variables bound by scope.

The book contains a compact set of axioms and theorems for both propositional logic and what would later be recognized as predicate logic. Frege demonstrates how logical laws can be derived mechanically from these primitives, arguing that mathematics can be reduced to logic. The Begriffsschrift laid the groundwork for Frege’s subsequent works, notably the Grundgesetze der Arithmetik, and it exerted a lasting influence on the development of formal logic, influencing later logicians and the eventual rise of symbolic logic in the 20th century.