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Friedrich Ludwig Gottlob Frege

(8 Nov 1848-26 Jul1925)

Friedrich Ludwig Gottlob Frege (bornNovember 8,1848 inWismar, diedJuly 26,1925 inBad Kleinen), was aGermanmathematician,logician, andphilosopher who founded modern mathematical logic andanalytic philosophy.

Frege is arguably the greatest logician sinceAristotle. His revolutionaryBegriffsschrift (Concept Script) from1879 marked the beginning of a new epoch in the history of logic by displacing the oldTerm Logic that had held sway virtually unchanged since Aristotle.

Frege was the first to devise an axiomatization of propositional logic and of predicate logic, the latter of which was his own invention. The quantification so essential toBertrand Russell's theory of descriptions, and to Russell andAlfred North Whitehead'sPrincipia Mathematica, was also due to Frege. His work was largely unrecognized in his own day, and his ideas spread chiefly through those he influenced, particularlyGiuseppe Peano and Russell.Ludwig Wittgenstein andEdmund Husserl were among the other philosophical notables strongly influenced by Frege.

Frege was also an importantphilosopher of language. The distinction between thesense and reference of a proper name (Eigenname) was his discovery (seephilosophy of language), also the distinction betweenConcept and Object.

Frege was the first major proponent oflogicism -- the view that mathematics is reducible to logic. HisGrundgesetze der Arithmetik was an attempt to explicitly derive the laws of arithmetic from logic. After the first volume was published (at the author's expense), Russell discovered theparadox which bears his name, and that the axioms of theGrundgesetze led to this contradiction; he wrote to Frege, who acknowledged the contradiction in an appendix to volume two of theGrundgesetze, noting what he perceived to be the faulty axiom. Frege never did manage to amend his axioms to his satisfaction, however; and after Frege's death,Kurt Gödel'sincompleteness theorems showed that Frege's logicist program was impossible.

He started studying at theUniversity of Jena in1869 and moved toGöttingen after two years, where he received his Ph.D. in1873. After returning toJena two years later, he became lecturer of mathematics. In1879, he was made associate professor and in1896 became professor of mathematics.

His principal works are:

·     Begriffsschrift (Concept Script), eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle a. S.,1879

·     Die Grundlagen der Arithmetik (The Foundations of Arithmetic): eine logisch-mathematische Untersuchung über den Begriff der Zahl, Breslau,1884

·     "Funktion und Begriff" ("Function and Concept"): Talk given in a Meeting onJanuary 9,1891 of theJenaischen Gesellschaft für Medizin und Naturwissenschaft, Jena,1891

·     "Über Sinn und Bedeutung" ("On Sense and Denotation"), inZeitschrift für Philosophie und philosophische Kritik, C (1892): 25-50

·     "Über Begriff und Gegenstand" ("On Concept and Object"), in Vierteljahresschrift für wissenschaftliche Philosophie, XVI (1892): 192-205

·     Grundgesetze der Arithmetik ("Basic Laws of Arithmetic"), Jena: Verlag Hermann Pohle, Band I (1893), Band II (1903)

·     Was ist eine Funktion? ("What is a Function?"), inFestschrift Ludwig Boltzmann gewidmet zum sechzigsten Geburtstage,February 20,1904, S. Meyer (ed.), Leipzig,1904, pp. 656-666

·     "Der Gedanke" ("The Thought") Eine logische Untersuchung, inBeiträge zur Philosophie des Deutschen Idealismus I (1918-1919): 58-77

·     "Die Verneinung" ("Negation"), inBeiträge zur Philosophie des deutschen Idealismus I (1918-1919): 143-157

·     "Gedankengefüge" ("Compound Thought"), inBeiträge zur Philosophie des Deutschen Idealismus III (1923): 36-51

Frege intended these last three papers to be published in a book to be calledLogical Investigations; in1975 they were posthumously published (in English translation, at least) under this title.

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