Frege, Gottlob

Frege, Gottlob (gôt`lōp frā`gə), 1848–1925, German philosopher and mathematician. He was professor of mathematics (1879–1918) at the Univ. of Jena. Frege was one of the founders of modern symbolic logic, and his work profoundly influenced Bertrand Russell. He claimed that all mathematics could be derived from purely logical principles and definitions. He considered verbal concepts to be expressible as symbolic functions with one or more variables. His books include Begriffsschrift (1879); Die Grundlagen der Arithmetik (1884; tr. The Foundations of Arithmetic, 1950); Grundgesetze der Arithmetik (2 vol., 1893–1903).

Bibliography

See P. T. Geach and M. Black, ed., Philosophical Writings of Gottlob Frege (1952); M. Resnik, Frege and the Philosophy of Mathematics (1980); M. Dummett, The Interpretation of Frege's Philosophy (repr. 1981).

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Frege, (Friedrich Ludwig) Gottlob

(born Nov. 8, 1848, Wismar, Mecklenburg-Schwerin—died July 26, 1925, Bad Kleinen, Ger.) German mathematician and logician, inventor of modern mathematical logic and one of the founders of the analytic tradition in philosophy. He taught at the University of Jena from 1871 to 1917. His Begriffsschrift (1879, “Conceptscript”), was the first presentation of a system of mathematical logic in the modern sense. Using an original notation of quantifiers and variables, he was able to give formal expression to sentences containing multiple quantification, such as “Everybody loves someone”; this is impossible in the syllogistic derived from Aristotle, which had been considered complete until the time of Immanuel Kant (see predicate calculus). In the Die Grundlagen der Arithmetik he attempted to establish the doctrine later known as logicism. He also made significant contributions to the philosophy of language, including a highly influential theory of the distinction between sense and reference. Though Frege's work was admired by Bertrand Russell and the early Ludwig Wittgenstein, it was unknown to or ignored by most other philosophers and mathematicians during Frege's lifetime; its significance was not generally appreciated until the mid-20th century.

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Frege, Gottlob - Gottlob Frege

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Frege, Gottlob 

Born Nov. 8, 1848, in Wismar; died July 26, 1925, in Bad Kleinen. German logician.

Frege received his Ph.D. from the University of Göttingen in 1873. He was a professor at the University of Jena from 1879 to 1918. Frege’s principal work was The Fundamental Laws of Arithmetic (vols. 1–2, 1893–1903), in which he proposed a system of formalized arithmetic based on a second-order predicate calculus that he developed. His intention was to provide a substantiation of the notion of the reducibility of mathematics to logic (seeLOGICISM).

REFERENCES

Biriukov, B. V. “O rabotakh Frege po filosofskim voprosam matematiki.” In the collection Filosofskie voprosy estestvoznaniia, fasc. 2. Moscow, 1959.
Stiazhkin, N. I. Formirovanie matematicheskoi logiki. Moscow, 1967. (Contains bibliography.)