Gottlob Frege


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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 logicsymbolic logic
or mathematical logic,
formalized system of deductive logic, employing abstract symbols for the various aspects of natural language. Symbolic logic draws on the concepts and techniques of mathematics, notably set theory, and in turn has contributed to
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, 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).

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.)

Gottlob Frege

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Gottlob Frege

(person, history, philosophy, mathematics, logic, theory)
(1848-1925) A mathematician who put mathematics on a new and more solid foundation. He purged mathematics of mistaken, sloppy reasoning and the influence of Pythagoras. Mathematics was shown to be a subdivision of formal logic.

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41) Gottlob Frege, Begriffsschrift, (Halle, 1879), xi-xii.
Next year Russell wrote to Gottlob Frege of his paradox which showed that the axioms Frege was using to formalize his logic were inconsistent (cf.
10) The two expressions share their reference in the same way Gottlob Frege offers his example of the "morning star" and "evening star" as two distinct expressions of the same reference (Bedeutung).
Calculus Ratiocinator, is esoteric--a working knowledge of Latin alone would not suffice to make clear the opposition intended by it, since lingua universalis and calculus ratiocinator are technical terms invented by Gottfried Wilhelm Leibniz during the seventeenth century and revived by Gottlob Frege in the nineteenth.
Moore and, in a separate paper, with Gottlob Frege, Russell's logicism, his theory of descriptions and his substitutional theory, 'the theory of types', his method of analysis, his neutral monism and his metaphysics of logical atomism, his structuralism and the absolute description of the world, his influence on knowledge by acquaintance to knowledge by causation, an essay on 'Russell, Experience, and the Roots of Science' and finally an essay on 'Bertrand Russell: Moral Philosopher or Unphilosophical Moralist'.
However, contemporary semantic theory does make much use of another distinction, similar in important respects, namely the distinction between the sense and the reference of words, a distinction first propounded by the German philosopher Gottlob Frege in 1892 in his paper Uber Sinn und Bedeutung (usually translated into English as On Sense and Reference).
The German logician Gottlob Frege had come up with an answer: "three" is merely the set of all threesomes, the set of all those sets whose members can be exhaustively paired off with Larry, Curly, and Moe.
The general notion of "propositional function" was first broached by Gottlob Frege in the year of Korzybski's birth, 1879, and further developed by Bertrand Russell (with Alfred North Whitehead) in their Principia Mathematica of 1910-1913.
Poland) points out an unbridgeable gap between the notion of quantificational truth expressed by German mathematician and philosopher Gottlob Frege (1848-1925), and the notion of reference.