Gottlob Frege

Gottlob Frege was a German logician, mathematician and philosopher at the University of Jena, regarded as the founder of modern mathematical logic and one of the most important logicians since Aristotle. In his 1879 book Begriffsschrift, Frege introduced a wholly new logical notation capable of expressing quantification and multiple generality, a system that became the basis for all subsequent formal predicate logic. Frege pursued the logicist project of deriving the truths of arithmetic from purely logical axioms, setting out the program in his 1884 Foundations of Arithmetic and attempting a full formal execution in the two-volume Basic Laws of Arithmetic, published in 1893 and 1903, only for Bertrand Russell to show in 1901 that one of its axioms produced a contradiction, a result now known as Russell's paradox. In his 1892 essay On Sense and Reference, Frege distinguished between a linguistic expression's sense, the mode by which it presents its referent, and its reference, the object it denotes, a distinction that became foundational to modern philosophy of language.