Thank God Frege

from Wikipedia, the free encyclopedia
Thank God Frege (1878)

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

His outstanding achievement in the field of logic is to be the first to develop formal language and, related to it, formal evidence . He thereby created an essential basis for today's computer technology and informatics as well as for formal methods in linguistic semantics .

In the field of philosophy, his reflections on the philosophy of language were extremely influential. He directly influenced, among others, Rudolf Carnap , who studied with him, Bertrand Russell and Ludwig Wittgenstein . Frege is considered to be one of the main pioneers of analytical philosophy , one of the most important currents in 20th century philosophy .

Parents and ancestors

Gottlob Frege's parents were Karl Alexander Frege (* 1809 in Hamburg ; † 1866) and Auguste Wilhelmine Sophia Bialloblotzky (* 1815 in Pattensen ; † 1898). The marriage took place in 1846. Frege's father was a teacher and director of the Wismar Lyceum , a private high school for girls that he himself founded. In particular, elementary classes in New High German were given there (in addition to classes in religion, French, history, natural history, geography and arithmetic) for the daughters who originally spoke Low German (starting age was eight). Karl Alexander Frege also published a New High German grammar in 1862. Frege's mother Auguste had been a teacher there from 1843 and later, after the death of her husband in 1866, successfully ran the girls' school founded by her husband for ten years. Her father was Heinrich Sigmund Bialloblotsky (1757-1828), who was superintendent in Pattensen and from 1822 in Wunstorf . The Bialloblotzky family came from the Polish noble family Ogonceyk, who emigrated from Poland to Germany (Seehausen near Wittenberg) in the 17th century for reasons of faith. Frege's maternal grandmother was the daughter of superintendent Ludwig Wilhelm Ballhorn, who traced her line back to Philipp Melanchthon . Other ancestors of Frege were his maternal uncle the explorer in Africa, headmaster, pastor and missionary Christoph Heinrich Friedrich Bialloblotsky (1799–1869) and his paternal grandfather, the merchant and Saxon consul in Hamburg Christian Gottlob Frege (1779–1811), who with the Daughter of a realtor Printz was married. He came from a well-known Leipzig banking family (see Christian Gottlob Frege )

Frege also had a brother Arnold Frege (* 1852). In 1925, the year Frege died, he is mentioned as a writer in Neudamm near Stettin.

The birthplace in Böttcherstr. 2 in Wismar, which the father bought in 1846, was destroyed in the Second World War. The school was there too.


Frege attended the grammar school Große Stadtschule Wismar . One of his teachers, Leo Sachse, apparently had a great influence on him. The name "Leo Sachse" is later used in examples in Frege's writings. After his father died in 1866, Frege began his studies at the University of Jena in 1869 on Saxon's advice . Among other things, Ernst Abbe , who supported Frege in his scientific career, and the philosopher Kuno Fischer , whose ideas Frege intensively dealt with, taught here.

View of the main building of the University of Jena

In 1871 Frege moved to the University of Göttingen , where he submitted his doctoral thesis in 1873 on a geometric representation of imaginary structures in the plane . Frege returned to Jena , where he in 1874 when Abbe on the subject of accounting methods, which are based on an extension of the term size habilitated . He taught as a private lecturer . In 1879 he was appointed associate professor.

In 1887 Frege married Margarete Lieseberg, daughter of the businessman Heinrich Lieseberg from Grevesmühlen . The marriage remained childless (according to other sources, they had at least two children who died young), and the Frege couple adopted a boy, Paul Otto Alfred Frege (formerly Paul Otto Alfred Fuchs).

In 1895 Frege was elected a member of the Leopoldina . In 1896 Frege was appointed full honorary professor in Jena and taught there - little noticed by students and colleagues - until his retirement in 1917. Frege's only student of importance was Rudolf Carnap , who later continued his work and made it known in many ways. After all, Frege had scientific contact with the Nobel Prize winners Rudolf Eucken and Bertrand Russell .

Frege's scientific work was thrown into a severe crisis by the discovery of Russell's paradox in 1902 (see also the section on mathematics ). In 1903 Frege admitted in the epilogue of his fundamental laws of arithmetic that Russell had "shaken the foundations of his structure".

Frege's wife Margarete died in 1904.

In the following years Frege fell into a depression , which was expressed, among other things, in the fact that he no longer published any major works. Only after his retirement did a series of three related logical investigations reappear: The Thought (1918), The Negation (1918), and Thoughts (1923). He had at least partially overcome his life crisis. In the part of his diary published in 1994 from the estate (for 1924) there are anti- democratic , anti- Catholic , anti- French and anti-Semitic remarks; however, Frege has probably never made a political appearance in public. Frege spent his twilight years in Bad Kleinen , near his hometown Wismar.

In 2001 the asteroid (21665) Frege was named after him.

Frege's estate came to Münster in 1935 on the initiative of Heinrich Scholz , where a large part of it was destroyed in a bombing raid in March 1945.


The title page of the conceptual writing

After the non-formal syllogistics founded by Aristotle had been considered the most exact form of logical reasoning for more than 2,000 years, Frege's revolutionary “ conceptual writing ” from 1879 began a new era in the history of logic. In this publication he developed a new logic in axiomatic form that already comprised the core of modern formal logic , namely a second level predicate logic with a concept of identity .

Along with George Boole and Ernst Schröder, Frege was one of those nineteenth-century logicians who laid the foundation for research into the foundations of mathematics by improving logic . According to Wilhelm Ackermann and David Hilbert , who often referred to his writings in their work, Frege's most important contribution is the "fulfillment of mathematics' need for exact foundations and strict axiomatic treatment."


In the philosophy of mathematics , Frege emerged as a sharp critic of found approaches: In the foundations of arithmetic there is an extensive and influential analysis, especially of the theories of Immanuel Kant , who understands arithmetic sentences as synthetic a priori judgments , and John Stuart Mills , for the arithmetic Sentences are general laws of nature confirmed by experience .

In addition, Frege was the founder of a new mathematical-philosophical program, logicism , according to which the propositions of arithmetic can be traced back to logical truths. This program is outlined informally in the Fundamentals of Arithmetic and carried out in a strictly formal manner in the later Fundamental Laws of Arithmetic .

The system of logicism, however, contained a contradiction (the so-called Russellian antinomy ), as Frege learned in a famous 1902 letter from Bertrand Russell. Frege saw his life's work failed and resignedly withdrew from logic. Nonetheless, his work had laid the foundations upon which others, especially Russell, could build and complete the logistic program.


Bronze bust of the Frege monument on the tower of St. Mary's Church in Wismar

In the field of linguistic philosophy , Frege differentiates between a sense and a meaning that are assigned to every linguistic sign. Frege's terminology deviates from normal usage and is therefore somewhat misleading, because by meaning he means the reference or reference of an expression, while its meaning is close to what is usually referred to as meaning . Frege basically knows three different types of linguistic expressions: proper names, sentences and conceptual expressions. For each of these types, a distinction can be made between sense and meaning:

  • Proper names: For Frege, proper names are expressions that refer to exactly one object. A proper name can be simple like "Venus" or complex like "the first man on the moon". The meaning of a proper name is the object it designates. The meaning of a proper name lies in the "way it is given", as Frege puts it. The two expressions "3 + 5" and "10 - 2" both designate the number 8, so they have the same meaning according to Frege. But they have different meanings, because they give the number 8 in different forms (once as the result of an addition, once as the result of a subtraction).
  • Sentences: According to Frege, the sense of a sentence is the "thought" expressed by it. This thought is to be understood as objective content, Frege expressly refuses to equate the thought with a mere “idea”. According to Frege, all who understand a sentence grasp the same thought, but nevertheless they can have different ideas.
    When 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 the proper name “Neil Armstrong” in the true sentence “ Neil Armstrong was American” with the same meaning “the first man on the moon”, we get “The first man on the moon was American”, another true sentence. Since the truth or falseness of sentences does not normally change when expressions are replaced by expressions of the same meaning (see below), Frege first defines the so-called "truth values", the true and the false, as the meaning of sentences. According to Frege, all true sentences have the same meaning, as do all false ones. (This initially quite counterintuitive thesis that there are only two possible meanings of sentences is often justified today with recourse to the so-called slingshot argument .)
    As already indicated, the preservation of the truth value when replacing expressions with the same meaning only applies in normal cases . However, the sentences "Frank believes Neil Armstrong is American" and "Frank believes that the first man on the moon is American" do not necessarily have the same truth value (especially if Frank does not know that Neil Armstrong is the first man on the moon), although here too an expression has been replaced by an equivalent. Frege therefore says that subordinate clauses that depend on verbs like "believe" are in " odd speech ". Sentences only have truth values ​​as meanings when they are in direct speech. In odd speech, the meaning of a sentence according to Frege is the thought it expresses. The meaning of a sentence in odd speech is therefore the same as its meaning in even.
  • Conceptual expressions . A term expression arises from the fact that a proper name is omitted from a sentence. By omitting the proper name “Berlin” in the sentence “Berlin is a capital”, the term “() is a capital” arises. Frege also calls such expressions “unsaturated”, which he means to say that they need to be completed with a proper name. The meaning of a term phrase is a concept. For Frege this is a function whose values ​​are truth values. So if the function “() is a capital” is applied to Paris, for example, it delivers the truth value the true (because “Paris is a capital” is true), with Frankfurt it delivers the wrong (because “Frankfurt is a capital” false is). There is not much to be found about the meaning of a term expression in Frege, but one can assume that he understands something like the definition of the corresponding term.


More texts
  • Gottlob Frege: Conceptual writing. 1879. (Reprint: Olms, Hildesheim 1998, ISBN 3-487-00623-5 )
  • Gottfried Gabriel , Friedrich Kambartel a . Christian Thiel (ed.): Gottlob Frege's correspondence with D. Hilbert, E. Husserl, B. Russell and selected individual letters from Frege. Meiner, Hamburg 1980, ISBN 3-7873-0482-7 .
  • ——. Basic laws of arithmetic. 2 vols. 1893-1903. (Reprint: Olms, Hildesheim 1998, ISBN 3-487-09802-4 )
  • Christian Thiel (ed.): The basics of arithmetic. 1884. (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 from Frege on the fundamentals of geometry and Hilbert's reply to Frege . In: Meeting reports of the Heidelberg Academy of Sciences (mathematical and scientific class) , born in 1941, 2nd treatise (discussed by Heinrich Scholz in the Zentralblatt für Mathematik , September 1942).
  • Mark Textor (Ed.): Function - Concept - Meaning. Vandenhoeck & Ruprecht, Göttingen 2002, ISBN 3-525-30603-2 .
  • ——. [Diary]. In: German magazine for philosophy. [DZfPh], Berlin 42 (1994) 6, pp. 1067-1098.


Web links

Commons : Gottlob Frege  - Collection of images, videos and audio files
Wikisource: Gottlob Frege  - Sources and full texts

Individual evidence

  1. Lothar Kreiser, Gottlob Frege - Life, Work, Time, Felix Meiner Verlag 2001, p. 4. There also the life dates of the mother, for whom 1878 is sometimes wrongly given as the year of death
  2. Lothar Kreiser, Frege's extra-scientific sources of his logical thinking, in: Ingolf Max, Werner Stelzner (ed.), Logic and Mathematics, Frege Colloquium Jena 1993, De Gruyter 1995, p. 219
  3. ^ Lothar Kreiser, in: Frege in Jena. Contributions to the search for traces, Gottfried Gabriel, Wolfgang Kienzler (ed.), Critical Yearbook of Philosophy 2, 1997, Thuringian Society for Philosophy Jena, Würzburg: Königshausen and Neumann, p. 71. He cites the Lower Saxony gender book.
  4. ADB
  5. Hans Hermes, entry Frege in NDB
  6. Johannes Hohlfeld and Volkmar Weiss: About marriage circle and urban ties of the property and educated middle class. The example of Frege in Leipzig 1744–1944 . In: Genealogy, Vol. 52 (2003) pp. 513-530
  7. There were several important members of the family with the first name Christian Gottlob
  8. ^ Kreiser, Frege, p. 41
  9. Hans Hermes, article Frege in NDB, there probably is childless
  10. ↑ Thank God Frege. In: Internet Encyclopedia of Philosophy .
  11. ^ Member entry by Gottlob Frege at the German Academy of Natural Scientists Leopoldina , accessed on April 5, 2015.
  12. Gottlob Frege: [Diary]. In: German magazine for philosophy. [DZfPh], Berlin 42 (1994), pp. 1067-1098.
  13. Yvonne Sherratt: Hitler's philosophers. New Haven, Conn .; Yale University Press, London 2012, ISBN 978-0-300-15193-0
  14. If we now replace a word in [the sentence] with another with the same meaning but with a different meaning, this cannot have any influence on the meaning of the sentence. - Frege: About sense and meaning . In: Frege: function, concept, meaning. Göttingen 1980, p. 47.