Textbook of AI

1848–1925, Mathematician, logician, philosopher

Also known as: Friedrich Ludwig Gottlob Frege

Gottlob Frege was a German mathematician and philosopher who, almost single-handedly, created modern formal logic. His 1879 Begriffsschrift ("concept-script") introduced quantifiers (universal and existential), bound variables, function-argument analysis of propositions, and a fully formal axiomatic deductive system, the framework of every subsequent first-order and higher-order logic, and the foundation of all symbolic AI, automated theorem proving and modern programming language semantics.

Frege's later Grundgesetze der Arithmetik (Volume I 1893, Volume II 1903) attempted to derive arithmetic from pure logic. The project, known as the logicist programme, was famously undermined when Bertrand Russell, in a 1902 letter, identified the contradiction now called Russell's paradox in Frege's Basic Law V. Frege acknowledged the problem in an appendix to Volume II and never published the planned third volume. Russell and Whitehead's Principia Mathematica (1910–13) attempted to repair the logicist programme using a theory of types.

Frege's analyses of sense and reference (Sinn und Bedeutung), of definite descriptions, and of the distinction between concept and object founded analytic philosophy of language. He spent his career at the University of Jena in relative obscurity; his work was popularised by Russell, Wittgenstein and Carnap. Frege held repugnant antisemitic views, recorded in late diaries, a fact that does not diminish the mathematical revolution he initiated but stands as part of the historical record.