Фридрих Людвиг Готлоб Фреге: Өмір және еңбектері

German philosopher, logician, and mathematician (1848–1925)

|notable works = Begriffsschrift (1879)The Foundations of Arithmetic (1884)Basic Laws of Arithmetic (1893–1903)
|thesis1 title = Ueber eine geometrische Darstellung der imaginären Gebilde in der Ebene (On a Geometrical Representation of Imaginary Forms in a Plane)
|thesis1 url = http://reader. digitale sammlungen. de/de/fs1/object/goToPage/bsb11160343. html?pageNo=2
|thesis1 year = 1873
|thesis2 title = Rechnungsmethoden, die sich auf eine Erweiterung des Größenbegriffes gründen (Methods of Calculation based on an Extension of the Concept of Magnitude)
|thesis2 url = https://www. worldcat. org/title/rechnungsmethoden die sich auf eine erweiterung des groenbegriffes grunden/oclc/314507606
|thesis2 year = 1874
|doctoral advisor = Ernst Christian Julius Schering (PhD thesis advisor)
|academic advisors = Rudolf Friedrich Alfred Clebsch
|notable students = Rudolf Carnap

Friedrich Ludwig Gottlob Frege ('/f//r//eɪ//g//ə/; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever. His contributions include the development of modern logic in the Begriffsschrift and work in the foundations of mathematics. His book the Foundations of Arithmetic is the seminal text of the logicist project, and is cited by Michael Dummett as where to pinpoint the linguistic turn. His philosophical papers "On Sense and Reference" and "The Thought" are also widely cited. The former argues for two different types of meaning and descriptivism. In Foundations and "The Thought", Frege argues for Platonism against psychologism or formalism, concerning numbers and propositions respectively.

Frege was born in 1848 in Wismar, Mecklenburg Schwerin (today part of Mecklenburg Vorpommern). His father Carl (Karl) Alexander Frege (1809–1866) was the co founder and headmaster of a girls' high school until his death. After Carl's death, the school was led by Frege's mother Auguste Wilhelmine Sophie Frege (née Bialloblotzky, 12 January 1815 – 14 October 1898); her mother was Auguste Amalia Maria Ballhorn, a descendant of Philipp Melanchthon and her father was Johann Heinrich Siegfried Bialloblotzky, a descendant of a Polish noble family who left Poland in the 17th century. Frege was a Lutheran. In childhood, Frege encountered philosophies that would guide his future scientific career. For example, his father wrote a textbook on the German language for children aged 9–13, entitled Hülfsbuch zum Unterrichte in der deutschen Sprache für Kinder von 9 bis 13 Jahren (2nd ed., Wismar 1850; 3rd ed., Wismar and Ludwigslust: Hinstorff, 1862) (Help book for teaching German to children from 9 to 13 years old), the first section of which dealt with the structure and logic of language. Frege studied at and graduated in 1869. His teacher Gustav Adolf Leo Sachse (5 November 1843 – 1 September 1909), who was a poet, played the most important role in determining Frege's future scientific career, encouraging him to continue his studies at the University of Jena.

Frege matriculated at the University of Jena in the spring of 1869 as a citizen of the North German Confederation. In the four semesters of his studies he attended approximately twenty courses of lectures, most of them on mathematics and physics. His most important teacher was Ernst Karl Abbe (1840–1905; physicist, mathematician, and inventor). Abbe gave lectures on theory of gravity, galvanism and electrodynamics, complex analysis theory of functions of a complex variable, applications of physics, selected divisions of mechanics, and mechanics of solids. Abbe was more than a teacher to Frege: he was a trusted friend, and, as director of the optical manufacturer Carl Zeiss AG, he was in a position to advance Frege's career. After Frege's graduation, they came into closer correspondence. His other notable university teachers were Christian Philipp Karl Snell (1806–86; subjects: use of infinitesimal analysis in geometry, analytic geometry of planes, analytical mechanics, optics, physical foundations of mechanics); Hermann Karl Julius Traugott Schaeffer (1824–1900; analytic geometry, applied physics, algebraic analysis, on the telegraph and other electronic machines); and the philosopher Kuno Fischer (1824–1907; Kantian and critical philosophy). Starting in 1871, Frege continued his studies in Göttingen, the leading university in mathematics in German speaking territories, where he attended the lectures of Rudolf Friedrich Alfred Clebsch (1833–72; analytic geometry), Ernst Christian Julius Schering (1824–97; function theory), Wilhelm Eduard Weber (1804–91; physical studies, applied physics), Eduard Riecke (1845–1915; theory of electricity), and Hermann Lotze (1817–81; philosophy of religion). Many of the philosophical doctrines of the mature Frege have parallels in Lotze; it has been the subject of scholarly debate whether or not there was a direct influence on Frege's views arising from his attending Lotze's lectures. In 1873, Frege attained his doctorate under Ernst Christian Julius Schering, with a dissertation under the title of "Ueber eine geometrische Darstellung der imaginären Gebilde in der Ebene" ("On a Geometrical Representation of Imaginary Forms in a Plane"), in which he aimed to solve such fundamental problems in geometry as the mathematical interpretation of projective geometry's infinitely distant (imaginary) points. Frege married Margarete Katharina Sophia Anna Lieseberg (15 February 1856 – 25 June 1904) on 14 March 1887.

Frege's 1892 paper, "On Sense and Reference" ("Über Sinn und Bedeutung"), introduced his influential distinction between sense ("Sinn") and reference ("Bedeutung", which has also been translated as "meaning", or "denotation"). While conventional accounts of meaning took expressions to have just one feature (reference), Frege introduced the view that expressions have two different aspects of significance: their sense and their reference. Reference (or "Bedeutung") applied to proper names, where a given expression (say the expression "Tom") simply refers to the entity bearing the name (the person named Tom). Frege also held that propositions had a referential relationship with their truth value (in other words, a statement "refers" to the truth value it takes). By contrast, the sense (or "Sinn") associated with a complete sentence is the thought it expresses. The sense of an expression is said to be the "mode of presentation" of the item referred to, and there can be multiple modes of representation for the same referent. The distinction can be illustrated thus: In their ordinary uses, the name "Charles Philip Arthur George Mountbatten Windsor", which for logical purposes is an unanalysable whole, and the functional expression "the King of the United Kingdom", which contains the significant parts "the King of ξ" and "United Kingdom", have the same referent, namely, the person best known as King Charles III. But the sense of the word "United Kingdom" is a part of the sense of the latter expression, but no part of the sense of the "full name" of King Charles. These distinctions were disputed by Bertrand Russell, especially in his paper "On Denoting"; the controversy has continued into the present, fueled especially by Saul Kripke's famous lectures "Naming and Necessity".

Frege's published philosophical writings were of a very technical nature and divorced from practical issues, so much so that Frege scholar Dummett expressed his "shock to discover, while reading Frege's diary, that his hero was an anti Semite." After the German Revolution of 1918–19 his political opinions became more radical. In the last year of his life, at the age of 76, his diary contained political opinions opposing the parliamentary system, democrats, liberals, Catholics, the French and Jews, who he thought ought to be deprived of political rights and, preferably, expelled from Germany. Frege confided "that he had once thought of himself as a liberal and was an admirer of Bismarck", but then sympathized with General Ludendorff. In an entry dated 5 May 1924 Frege expressed agreement with an article published in Houston Stewart Chamberlain's Deutschlands Erneuerung which praised Adolf Hitler. Frege recorded the belief that it would be best if the Jews of Germany would "get lost, or better would like to disappear from Germany." The diary contains a critique of universal suffrage and socialism. Frege had friendly relations with Jews in real life: among his students was Gershom Scholem, who greatly valued his teaching, and it was he who encouraged Ludwig Wittgenstein to leave for England in order to study with Bertrand Russell. The 1924 diary was published posthumously in 1994. Frege apparently never spoke in public about his political viewpoints.

Frege was described by his students as a highly introverted person, seldom entering into dialogues with others and mostly facing the blackboard while lecturing. He was, however, known to occasionally show wit and even bitter sarcasm during his classes.

Born 8 November 1848 in Wismar, Mecklenburg Schwerin. 1869 — attends the University of Jena. 1871 — attends the University of Göttingen. 1873 — PhD, doctor in mathematics (geometry), attained at Göttingen. 1874 — Habilitation at Jena; private teacher. 1879 — Ausserordentlicher Professor at Jena. 1896 — Ordentlicher Honorarprofessor at Jena. 1918 — retires. Died 26 July 1925 in Bad Kleinen (now part of Mecklenburg Vorpommern).

Begriffsschrift: eine der arithmetischen nachgebildete Formelsprache des reinen Denkens (1879), Halle an der Saale: Verlag von Louis Nebert (online version). In English: Begriffsschrift, a Formula Language, Modeled Upon That of Arithmetic, for Pure Thought, in: J. van Heijenoort (ed. ), From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Harvard, MA: Harvard University Press, 1967, pp. 5–82. In English (selected sections revised in modern formal notation): R. L. Mendelsohn, The Philosophy of Gottlob Frege, Cambridge: Cambridge University Press, 2005: "Appendix A. Begriffsschrift in Modern Notation: (1) to (51)" and "Appendix B. Begriffsschrift in Modern Notation: (52) to (68)." Die Grundlagen der Arithmetik: Eine logisch mathematische Untersuchung über den Begriff der Zahl (1884), Breslau: Verlag von Wilhelm Koebner (online version). In English: The Foundations of Arithmetic: A Logico Mathematical Enquiry into the Concept of Number, translated by J. L. Austin, Oxford: Basil Blackwell, 1950. Grundgesetze der Arithmetik, Band I (1893); Band II (1903), Jena: Verlag Hermann Pohle (online version). In English (translation of selected sections), "Translation of Part of Frege's Grundgesetze der Arithmetik," translated and edited Peter Geach and Max Black in Translations from the Philosophical Writings of Gottlob Frege, New York, NY: Philosophical Library, 1952, pp. 137–158. In German (revised in modern formal notation): Grundgesetze der Arithmetik, Korpora (portal of the University of Duisburg Essen), 2006: Band I and Band II In German (revised in modern formal notation): Grundgesetze der Arithmetik – Begriffsschriftlich abgeleitet. Band I und II: In moderne Formelnotation transkribiert und mit einem ausführlichen Sachregister versehen, edited by T. Müller, B. Schröder, and R. Stuhlmann Laeisz, Paderborn: mentis, 2009. In English: Basic Laws of Arithmetic, translated and edited with an introduction by Philip A. Ebert and Marcus Rossberg. Oxford: Oxford University Press, 2013. .

1903: "Über die Grundlagen der Geometrie". II. Jahresbericht der deutschen Mathematiker Vereinigung XII (1903), 368–375. In English: "On the Foundations of Geometry". 1967: Kleine Schriften. (I. Angelelli, ed.). Darmstadt: Wissenschaftliche Buchgesellschaft, 1967 and Hildesheim, G. Olms, 1967. "Small Writings," a collection of most of his writings (e. g., the previous), posthumously published.

Online bibliography of Frege's works and their English translations (compiled by Edward N. Zalta, Stanford Encyclopedia of Philosophy). 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle a. S.: Louis Nebert. Translation: Concept Script, a formal language of pure thought modelled upon that of arithmetic, by S. Bauer Mengelberg in Jean Van Heijenoort, ed., 1967. From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Harvard University Press. 1884. Die Grundlagen der Arithmetik: Eine logisch mathematische Untersuchung über den Begriff der Zahl. Breslau: W. Koebner. Translation: J. L. Austin, 1974. The Foundations of Arithmetic: A Logico Mathematical Enquiry into the Concept of Number, 2nd ed. Blackwell. 1891. "Funktion und Begriff." Translation: "Function and Concept" in Geach and Black (1980). 1892a. "Über Sinn und Bedeutung" in Zeitschrift für Philosophie und philosophische Kritik 100:25–50. Translation: "On Sense and Reference" in Geach and Black (1980). 1892b. "Ueber Begriff und Gegenstand" in Vierteljahresschrift für wissenschaftliche Philosophie 16:192–205. Translation: "Concept and Object" in Geach and Black (1980). 1893. Grundgesetze der Arithmetik, Band I. Jena: Verlag Hermann Pohle. Band II, 1903. Band I+II online. Partial translation of volume 1: Montgomery Furth, 1964. The Basic Laws of Arithmetic. Univ. of California Press. Translation of selected sections from volume 2 in Geach and Black (1980). Complete translation of both volumes: Philip A. Ebert and Marcus Rossberg, 2013, Basic Laws of Arithmetic. Oxford University Press. 1904. "Was ist eine Funktion?" in Meyer, S., ed., 1904. Festschrift Ludwig Boltzmann gewidmet zum sechzigsten Geburtstage, 20. Februar 1904. Leipzig: Barth: 656–666. Translation: "What is a Function?" in Geach and Black (1980). 1918–1923. Peter Geach (editor): Logical Investigations, Blackwell, 1975. 1924. Gottfried Gabriel, Wolfgang Kienzler (editors): Gottlob Freges politisches Tagebuch. In: Deutsche Zeitschrift für Philosophie, vol. 42, 1994, pp. 1057–98. Introduction by the editors on pp. 1057–66. This article has been translated into English, in: Inquiry, vol. 39, 1996, pp. 303–342. Peter Geach and Max Black, eds., and trans., 1980. Translations from the Philosophical Writings of Gottlob Frege, 3rd ed. Blackwell (1st ed. 1952).