Frege

Gottlob Frege (1848–1925) was a German logician, mathematician, and philosopher. He is widely regarded as the founder of modern logic and a central influence on analytic philosophy.

Frege developed a formal approach to logic that culminated in the Begriffsschrift (1879), a notation for rigorous deductive reasoning and for expressing quantified statements. He then argued that the laws of arithmetic could be derived from purely logical principles, a program known as logicism. In his later work, the Grundgesetze der Arithmetik (1893–1903), he attempted to ground arithmetic in logic, but the system relied on Basic Law V, whose inconsistency produced Russell's paradox and undermined the project.

In 1892 he published Über Sinn und Bedeutung (On Sense and Reference), introducing the distinction between Sinn (sense) and Bedeutung (reference). This framework distinguished the way terms present information from the objects they denote, influencing philosophy of language and mind. Frege also played a central role in developing a formal language capable of expressing mathematical proofs and the structure of mathematical truth.

Frege's ideas profoundly influenced Bertrand Russell, Alfred North Whitehead, and the broader analytic tradition. Although the foundational program faced a crisis due to the paradoxes arising within his system, Frege's logic and his theory of meaning and reference shaped subsequent work in logic, mathematics, and the philosophy of language for many decades.