Gottlob Frege

Frege's Begriffsschrift appeared in 1879 and introduced a formal system for quantifiers and predicates. It is often treated as a foundation of modern logic.

Frege's 1892 essay On Sense and Reference separates a term's reference from the way that reference is presented. His classic example contrasts names such as the morning star and the evening star, both referring to Venus.

Russell studied Frege's logic and found a contradiction in Frege's system, now called Russell's paradox. Frege acknowledged the problem in the second volume of Basic Laws of Arithmetic.

Frege tried to show that arithmetic could be derived from logic alone, a project later called logicism. His Foundations of Arithmetic was published in 1884.