Gottlob Frege

Friedrich Ludwig Gottlob Frege ( born November 8, 1848 in Wismar, † July 26, 1925 in Bad Little ) was a German logician, mathematician and philosopher.

His outstanding performance in the field of logic is to be the first to have a formal language and so coherently developed formal proofs. He thus created an important foundation for today's computer technology and computer science.

In the field of philosophy, his philosophy of language considerations were extremely influential. He has directly influenced, inter alia, Rudolf Carnap, who studied in Frege, Bertrand Russell and Ludwig Wittgenstein. He is considered one of the principal pioneers of analytic philosophy, one of the main currents of 20th-century philosophy.


Gottlob Frege's parents were Charles Alexander Frege (born in Hamburg in 1809 - died 1866) and Auguste Bialloblotzky. Frege's father was a mathematics teacher and director of the Lyceum Wismar. Frege's mother probably had Polish ancestors. An ancestor of Frege 's Christian Gottlob Frege.

Frege went to school Big city school Wismar. One of his teachers, Leo axis, apparently had a great influence on him. The name " Leo axis " will be used later in Frege's writings in examples. After his father died in 1866, Frege began his studies in 1869 at Sachse's advice, at the University of Jena. Here taught, among others, Ernst Abbe, who supported Frege in his scientific career, and the philosopher Kuno Fischer, with whose ideas Frege grappled intensively.

1871 Frege moved to the University of Göttingen, where he presented his doctoral thesis in 1873 via a geometrical representation of imaginary formations in the plane. Frege returned to Jena, where he in 1874 when Abbe on the subject of accounting methodologies, habilitation be based on an extension of the concept of size. He taught as a lecturer. 1878 his mother died; the following year he was appointed associate professor.

1887 married Margaret Frege Liesenberg. The marriage remained childless (according to other sources they had at least two children who died young), and the couple Frege adopted a boy, Paul Otto Alfred Frege (formerly Paul Alfred Otto Fuchs).

In 1895, Frege was elected a member of the Leopoldina. 1896 Frege was called to Jena as an ordinary honorary professor and taught there - little attention from students and colleagues -. Continuously until his retirement in 1917 Frege single student of significance was Rudolf Carnap, which would subsequently led his work in many ways and made known. After all, Frege had scientific contacts with the Nobel Prize in Literature straps Rudolf Eucken and Bertrand Russell.

Frege's scientific work was overthrown by the discovery of Russell's paradox in 1902 into a severe crisis (see also the section on mathematics). 1903 confessed to a Frege in the epilogue of his basic laws of arithmetic that the " fundamentals of its structure shaken " were by Russell.

Died in 1904 Frege's wife Margaret.

In subsequent years, Frege fell into a depression, which manifested itself, among other things, that he published no major work more. In his diary published in 1994 from the estate, there are anti- democratic, anti - Catholic, anti - French and anti-Semitic remarks; public Frege but never entered politics in appearance.

Only after his retirement Frege began to publish again, because he had his life crisis at least partially overcome. In 1923 Frege moved from logicism from which he had pursued throughout his life, and was now trying to set up the math on the geometry. Until his death, however, he was unable to develop these new ideas.

End of his life spent in Frege bath small, near his hometown of Wismar.


After the well-founded by Aristotle not formal syllogistic had been considered more than 2,000 years as the most accurate form of logical inference, a new era began with Frege's revolutionary " concept-script " from the year 1879 in the history of logic. In this publication, he developed a new logic in axiomatic form, which is already the core of the modern formal logic involved, namely a second -order predicate logic with identity concept.

Frege was next to George Boole and Ernst Schröder one of those logicians of the 19th century that laid by improving the logic the foundation for the study of the foundations of mathematics. After Wilhelm Ackermann and David Hilbert, who often made ​​reference to his writings in their works, Frege's most important contribution is the "fulfillment of the desire of mathematics on the exact foundation and rigorous axiomatic treatment. "


In the philosophy of mathematics Frege appeared as a sharp critic of found out approaches: In the foundations of arithmetic there is an extensive and influential analysis of va the theories of Immanuel Kant, the arithmetic sets perceives as synthetic judgments a priori, and John Stuart Mills, confirmed for the arithmetic sets through experience general laws of nature are.

In addition, Frege was the founder of a new mathematics philosophical program of logicism, according to the propositions of arithmetic can be reduced to logical truths. This program is informally outlined in the Foundations of Arithmetic and strictly carried out formally in the later basic laws of arithmetic.

However, the logicism of the system contained a contradiction ( the so-called Russell's antinomy ), as Frege had to learn in a famous letter from Bertrand Russell in 1902. Frege saw his life's work failed and withdrew resigned from the logic back. Nonetheless, he had created by his labor the essential foundations on which others, especially Russell build, and complete the logicist program could.


In the field of philosophy of language, Frege distinguishes between a sense and a meaning to come to each linguistic signs. Frege's terminology is different from the common usage and therefore somewhat misleading, because with meaning he thinks the reference or the reference of an expression, while his sense of the close to what is commonly referred to as the importance. Frege knows basically three different types of linguistic expressions: proper names, phrases and term expressions. For each of these types can be distinguished between sense and meaning:

  • Proper names: names are for Frege expressions that refer to exactly one object reference. A proper name can be as simple as " Venus " or as complex as " the first man on the moon". The importance of a proper name is the object which he referred. The sense of a proper name is the " nature of its givenness ", as Frege puts it. The two expressions " 3 5 " and "10 - 2" both denote the number 8, they have the same ie after Frege importance. But you have different sense, as the number 8 is given by each of them in different ways ( even as a result of an addition, once as a result of a subtraction ).
  • Sets: the meaning of a sentence is by the Frege expressed by him "thought". This idea is to be understood as an objective content, Frege explicitly defends itself against equated the idea with a mere " idea ". According to Frege all those who understand a set of capture, the same thought, nonetheless they can still have different ideas. In determining the meaning of sentences Frege makes use of the later so-called Frege principle, which states that the meaning of a sentence does not change if one of its components is replaced by an expression with the same meaning. If we replace in the true sentence " Neil Armstrong was an American ," the proper name " Neil Armstrong " by the meaningless same " the first man on the moon", we get " The first man on the moon was an American ", a likewise true sentence. Since truth or falsity of sentences in substitution of expressions meaning the same in the normal case (see below ) will not change, Frege first determines meaning of sentences as the so-called " truth-values ​​", the true and the false. According to Frege, that is, all true sentences have the same meaning, as are all wrong. (This initially quite counter-intuitive thesis that there are only two possible meanings of sentences, is now frequently justified in resorting to the so-called slingshot argument ( slingshot argument). ) As already indicated, the preservation of the truth-value applies when replacing the same meaningless expressions only in the normal case. The phrases " Frank believes that Neil Armstrong Americans " and " Frank believes that the first man on the moon Americans " but do not necessarily have the same truth value (especially not if Frank does not know that Neil Armstong the first man on the moon is ), although here a term has been replaced by a meaning same. Frege says, therefore, that subordinate clauses that depend on words like "believe " in " odd speech" are. Sentences have meaning only as truth values ​​, if they are in a straight speech. In the odd speech the meaning of a sentence according to Frege, is the idea expressed by him. The meaning of a sentence in the odd speech is therefore the same as its meaning in the straight.
  • Term expressions. A term expression arises from the fact that in a sentence, a proper noun is omitted. Due to the fact that in the sentence " Berlin is a capital " the proper name "Berlin" omits created the term term " () is a capital city ". Such expressions Frege also called "unsaturated", which he wants to say that they require completion by a proper name. The meaning of a concept expression is a term. For Frege, this is a function whose values ​​are truth values ​​. Thus, if the function "( ) is a capital city " for example, Paris applied, it returns the truth value of the true ( because " Paris is a capital city " is true ), in Frankfurt, it provides the wrong thing (because "Frankfurt is a capital " wrong is ). About the meaning of a term expression can be found in Frege not much, but one can assume that he understands by something like the definition of the term in question.


  • Begriffsschrift, a formula language of arithmetic modeled of pure thought. Louis Nebert, Halle a S., 1879.
  • The Foundations of Arithmetic. A logical mathematical inquiry into the concept of number. Wilhelm Koebner, Wroclaw 1884 (on the Internet Archive, ditto)
  • Function and Concept. Paper presented at the meeting of 9 January 1891 Jenaische Society for medicine and science. Hermann Pohle, Jena 1891 ( Internet Archive )
  • On Sense and Reference. In: Journal of Philosophy and philosophical critique. 1892, pp. 25-50 ( digitized and full text archive in the German text, online, PDF, 46 kB)
  • About concept and object. Quarterly publication for scientific philosophy XVI, 1892, pp. 192-205.
  • Basic laws of arithmetic. Hermann Pohle, Jena 1893 ( Volume I ) 1903 ( Volume II ) ( online)
  • What is a function? In: Stefan Meyer (Ed. ): Festschrift Ludwig Boltzmann dedicated to the sixtieth birthdays, February 20, 1904 Johann Ambrosius Barth, Leipzig, 1904, pp. 656-666 (on the Internet Archive, ditto, ditto).
  • The thought. A logical investigation. In: Contributions to the philosophy of German Idealism. Volume I: 1918-1919. Pp. 58-77 (online, PDF, 49 kB)
  • The negation. In: Contributions to the philosophy of German Idealism. Volume I: 1918-1919. Pp. 143-157.
  • Thought structure. In: Contributions to the philosophy of German Idealism. Volume III: 1923rd pp. 36-51.
  • Foundations of Geometry (Second row). In: Annual Report of the German Mathematical Society. 15, 1906 ( the GDZ: I, II, III)
  • Applications of the concept-script. In: Jenaische Journal of Natural Science. 13 Supplement 2, 1879, p.29 (on the Internet Archive )
  • Gottlob Frege: Begriffsschrift. 1879th (reprint: Olms, Hildesheim 1998, ISBN 3-487-00623-5 )
  • Gottfried Gabriel, Frederick Kambartel and Christian Thiel (ed.): Gottlob Frege's correspondence with D. Hilbert, E. Husserl, B. Russell and Frege selected individual letters. Meiner, Hamburg 1980, ISBN 3-7873-0482-7.
  • -. Basic laws of arithmetic. 2 vols 1893-1903. (Reprinted: Olms, Hildesheim 1998, ISBN 3-487-09802-4 )
  • Christian Thiel (ed. ): The Foundations of Arithmetic. 1884th (reprint: Meiner, Hamburg 1988, ISBN 3-7873-0719-2 )
  • Gottfried Gabriel (ed.): writings on logic and philosophy of language: From the estate. 4th edition. Meiner, Hamburg 2001, ISBN 3-7873-1575-6.
  • Max Steck: unknown letters Frege on the foundations of geometry and Hilbert's reply letter to Frege. In: Proceedings of the Heidelberg Academy of Sciences ( Math and Science class), born in 1941, second treatise (reviewed by Heinrich Scholz in Zentralblatt für Mathematik, September 1942 ).
  • Mark Textor (ed. ): Function - Definition - Meaning. Cambridge University Press, Göttingen 2002, ISBN 3-525-30603-2.
  • -. [Diary ]. In: German Journal for Philosophy. [ DZfPh ], Berlin 42 (1994 ) 6, pp. 1067-1098.