Gottlob Frege

Abstract

Gottlob Frege (b. 1848–d. 1925) was a German mathematician, logician, and philosopher who is generally regarded as one of the founders of the analytic tradition in philosophy—together with Bertrand Russell, G. E. Moore, and Ludwig Wittgenstein. Frege’s main project was to demonstrate the logicist thesis that arithmetic can be reduced to logic. In attempting to do so, he revolutionized logical theory, creating the first system of modern predicate logic in his first book, Begriffsschrift (1879; the term is often left untranslated: see Main Works). In The Foundations of Arithmetic (Die Grundlagen der Arithmetik, 1884), he offered an informal account of his logicist project, showing how the natural numbers could be defined as extensions of (logically definable) concepts—roughly, what we would now call sets or classes. In Basic Laws of Arithmetic (Grundgesetze der Arithmetik, Vol. 1 [1893], Vol. 2 [1903]), he then set out to demonstrate formally, using his logical system, that arithmetic could be reduced to logic. Between the Foundations and Basic Laws he thought through—and revised—his underlying philosophical ideas, explaining them in three of his most influential essays: “Function and Concept” (1891), “On Sense and Reference” (1892), and “On Concept and Object” (1892). In 1902, however, as the second volume of Basic Laws was in press, Russell wrote to Frege informing him of a contradiction that he had discovered in Frege’s system—now known as Russell’s paradox. Frege attempted to resolve the paradox in a hastily written appendix, but he soon realized that the attempt failed and he abandoned his logicist project. He continued to work on his philosophical and logical ideas, though, planning but never completing a textbook on logic; what survived was eventually published posthumously. In the last years of his life he wrote three essays in a series called “Logical Investigations,” the first of which—“Thought”—has also been much discussed and cited. Frege influenced Russell, Rudolf Carnap (who attended two of his lecture courses), and especially Wittgenstein; however, it was only after his death that the significance of his work began to be widely recognized, and it was not until after the Second World War that his writings began to be translated into English (the only exception being the opening thirty pages of Basic Laws, which had appeared in 1915–1917). Today Frege’s place in the history of philosophy is secure, and interest in his work is still blossoming, not just in Anglo-American analytic philosophy, but also right across the world. (Acknowledgments: I would like to thank Gottfried Gabriel, Robert May, and Kai Wehmeier for comments on the first draft of this article and suggestions for additions.)