Analytic & pragmatist · 1848–1925
Gottlob Frege
Jena mathematician who invented modern logic
Arithmetic can be derived from logic, and expressions have both a sense (a way of presenting something) and a reference (the thing itself): “the morning star” and “the evening star” differ in sense but both refer to Venus.
Life and thought
Gottlob Frege (1848–1925) spent his whole career teaching mathematics at the University of Jena and was little noticed in his lifetime. In the Begriffsschrift (1879), a short book in an unusual two-dimensional notation, he created the first modern logic of quantifiers and variables, the system every logic student now learns in other symbols. His aim was to show that arithmetic is nothing but logic. In 1902, as the second volume of his Basic Laws of Arithmetic went to press, Russell wrote to him that one of his axioms led to a contradiction; Frege added an appendix admitting that his foundations had been shaken.
In “On Sense and Reference” (1892) he asked how “the morning star is the evening star” can tell us something, when both names refer to the same planet, Venus. His answer: an expression has a reference, the object it picks out, and a sense, the way it presents that object. The two names share a reference but differ in sense, so the sentence is informative. Philosophy of language, and much of analytic philosophy, starts from this distinction.