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Friedrich Ludwig Gottlob Frege
Gottlob Frege
(/ˈfreɪɡə/;[10] German: [ˈɡɔtloːp ˈfreːɡə]; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language and mathematics. Though largely ignored during his lifetime, Giuseppe Peano
Giuseppe Peano
(1858–1932) and Bertrand Russell (1872–1970) introduced his work to later generations of logicians and philosophers. His contributions include the development of modern logic in the Begriffsschrift
Begriffsschrift
and work in the foundations of mathematics. His book the Foundations of Arithmetic
Foundations of Arithmetic
is the seminal text of the logicist project, and is cited by Michael Dummett
Michael Dummett
as where to pinpoint the linguistic turn. His philosophical papers "On Sense and Reference" ("Über Sinn und Bedeutung") and "The Thought" ("Der Gedanke") are widely cited.

Contents

1 Life

1.1 Childhood (1848–69) 1.2 Studies at University: Jena and Göttingen (1869–74)

2 Work as a logician 3 Philosopher 4 Sense and reference 5 1924 diary 6 Personality 7 Important dates 8 Important works

8.1 Logic, foundation of arithmetic 8.2 Philosophical studies 8.3 Articles on geometry

9 See also 10 References

10.1 Primary 10.2 Secondary

11 External links

Life[edit] Childhood (1848–69)[edit] 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[11] and her father was Johann Heinrich Siegfried Bialloblotzky, a descendant of a Polish noble family who left Poland in the 17th century.[12] 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
Wismar
1850; 3rd ed., Wismar
Wismar
and Ludwigslust: Hinstorff, 1862), the first section of which dealt with the structure and logic of language. Frege studied at a gymnasium in Wismar
Wismar
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. Studies at University: Jena and Göttingen (1869–74)[edit] Frege matriculated at the University of Jena
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
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, analytical geometry of planes, analytical mechanics, optics, physical foundations of mechanics); Hermann Karl Julius Traugott Schaeffer (1824–1900; analytical geometry, applied physics, algebraic analysis, on the telegraph and other electronic machines); and the philosopher Kuno Fischer
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; analytical geometry), Ernst Christian Julius Schering (1824–97; function theory), Wilhelm Eduard Weber
Wilhelm Eduard Weber
(1804–91; physical studies, applied physics), Eduard Riecke (1845–1915; theory of electricity), and Hermann Lotze
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. Work as a logician[edit] Main article: Begriffsschrift Though his education and early mathematical work focused primarily on geometry, Frege's work soon turned to logic. His Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens [Concept-Script: A Formal Language
Language
for Pure Thought Modeled on that of Arithmetic], Halle a/S: Verlag von Louis Nebert, 1879  marked a turning point in the history of logic. The Begriffsschrift
Begriffsschrift
broke new ground, including a rigorous treatment of the ideas of functions and variables. Frege's goal was to show that mathematics grows out of logic, and in so doing, he devised techniques that took him far beyond the Aristotelian syllogistic and Stoic propositional logic that had come down to him in the logical tradition.

Title page to Begriffsschrift
Begriffsschrift
(1879)

In effect, Frege invented axiomatic predicate logic, in large part thanks to his invention of quantified variables, which eventually became ubiquitous in mathematics and logic, and which solved the problem of multiple generality. Previous logic had dealt with the logical constants and, or, if... then..., not, and some and all, but iterations of these operations, especially "some" and "all", were little understood: even the distinction between a sentence like "every boy loves some girl" and "some girl is loved by every boy" could be represented only very artificially, whereas Frege's formalism had no difficulty expressing the different readings of "every boy loves some girl who loves some boy who loves some girl" and similar sentences, in complete parallel with his treatment of, say, "every boy is foolish". A frequently noted example is that Aristotle's logic is unable to represent mathematical statements like Euclid's theorem, a fundamental statement of number theory that there are an infinite number of prime numbers. Frege's "conceptual notation" however can represent such inferences.[13] The analysis of logical concepts and the machinery of formalization that is essential to Principia Mathematica
Principia Mathematica
(3 vols., 1910–13) (by Bertrand Russell, 1872–1970, and Alfred North Whitehead, 1861–1947), to Russell's theory of descriptions, to Kurt Gödel's (1906–78) incompleteness theorems, and to Alfred Tarski's (1901–83) theory of truth, is ultimately due to Frege. One of Frege's stated purposes was to isolate genuinely logical principles of inference, so that in the proper representation of mathematical proof, one would at no point appeal to "intuition". If there was an intuitive element, it was to be isolated and represented separately as an axiom: from there on, the proof was to be purely logical and without gaps. Having exhibited this possibility, Frege's larger purpose was to defend the view that arithmetic is a branch of logic, a view known as logicism: unlike geometry, arithmetic was to be shown to have no basis in "intuition", and no need for non-logical axioms. Already in the 1879 Begriffsschrift
Begriffsschrift
important preliminary theorems, for example a generalized form of law of trichotomy, were derived within what Frege understood to be pure logic. This idea was formulated in non-symbolic terms in his The Foundations of Arithmetic
Arithmetic
(1884). Later, in his Basic Laws of Arithmetic
Arithmetic
(vol. 1, 1893; vol. 2, 1903; vol. 2 was published at his own expense), Frege attempted to derive, by use of his symbolism, all of the laws of arithmetic from axioms he asserted as logical. Most of these axioms were carried over from his Begriffsschrift, though not without some significant changes. The one truly new principle was one he called the Basic Law V: the "value-range" of the function f(x) is the same as the "value-range" of the function g(x) if and only if ∀x[f(x) = g(x)]. The crucial case of the law may be formulated in modern notation as follows. Let xFx denote the extension of the predicate Fx, i.e., the set of all Fs, and similarly for Gx. Then Basic Law V says that the predicates Fx and Gx have the same extension iff ∀x[Fx ↔ Gx]. The set of Fs is the same as the set of Gs just in case every F is a G and every G is an F. (The case is special because what is here being called the extension of a predicate, or a set, is only one type of "value-range" of a function.) In a famous episode, Bertrand Russell
Bertrand Russell
wrote to Frege, just as Vol. 2 of the Grundgesetze was about to go to press in 1903, showing that Russell's paradox
Russell's paradox
could be derived from Frege's Basic Law V. It is easy to define the relation of membership of a set or extension in Frege's system; Russell then drew attention to "the set of things x that are such that x is not a member of x". The system of the Grundgesetze entails that the set thus characterised both is and is not a member of itself, and is thus inconsistent. Frege wrote a hasty, last-minute Appendix to Vol. 2, deriving the contradiction and proposing to eliminate it by modifying Basic Law V. Frege opened the Appendix with the exceptionally honest comment: "Hardly anything more unfortunate can befall a scientific writer than to have one of the foundations of his edifice shaken after the work is finished. This was the position I was placed in by a letter of Mr. Bertrand Russell, just when the printing of this volume was nearing its completion." (This letter and Frege's reply are translated in Jean van Heijenoort
Jean van Heijenoort
1967.) Frege's proposed remedy was subsequently shown to imply that there is but one object in the universe of discourse, and hence is worthless (indeed, this would make for a contradiction in Frege's system if he had axiomatized the idea, fundamental to his discussion, that the True and the False are distinct objects; see, for example, Dummett 1973), but recent work has shown that much of the program of the Grundgesetze might be salvaged in other ways:

Basic Law V can be weakened in other ways. The best-known way is due to philosopher and mathematical logician George Boolos (1940–1996), who was an expert on the work of Frege. A "concept" F is "small" if the objects falling under F cannot be put into one-to-one correspondence with the universe of discourse, that is, unless: ∃R[R is 1-to-1 & ∀x∃y(xRy & Fy)]. Now weaken V to V*: a "concept" F and a "concept" G have the same "extension" if and only if neither F nor G is small or ∀x(Fx ↔ Gx). V* is consistent if second-order arithmetic is, and suffices to prove the axioms of second-order arithmetic. Basic Law V can simply be replaced with Hume's principle, which says that the number of Fs is the same as the number of Gs if and only if the Fs can be put into a one-to-one correspondence with the Gs. This principle, too, is consistent if second-order arithmetic is, and suffices to prove the axioms of second-order arithmetic. This result is termed Frege's theorem because it was noticed that in developing arithmetic, Frege's use of Basic Law V is restricted to a proof of Hume's principle; it is from this, in turn, that arithmetical principles are derived. On Hume's principle and Frege's theorem, see "Frege's Logic, Theorem, and Foundations for Arithmetic".[14] Frege's logic, now known as second-order logic, can be weakened to so-called predicative second-order logic. Predicative second-order logic plus Basic Law V is provably consistent by finitistic or constructive methods, but it can interpret only very weak fragments of arithmetic.[15]

Frege's work in logic had little international attention until 1903 when Russell wrote an appendix to The Principles of Mathematics stating his differences with Frege. The diagrammatic notation that Frege used had no antecedents (and has had no imitators since). Moreover, until Russell and Whitehead's Principia Mathematica
Principia Mathematica
(3 vols.) appeared in 1910–13, the dominant approach to mathematical logic was still that of George Boole
George Boole
(1815–64) and his intellectual descendants, especially Ernst Schröder
Ernst Schröder
(1841–1902). Frege's logical ideas nevertheless spread through the writings of his student Rudolf Carnap (1891–1970) and other admirers, particularly Bertrand Russell and Ludwig Wittgenstein
Ludwig Wittgenstein
(1889–1951). Philosopher[edit] Frege is one of the founders of analytic philosophy, whose work on logic and language gave rise to the linguistic turn in philosophy. His contributions to the philosophy of language include:

Function–argument analysis of the proposition; Distinction between concept and object (Begriff und Gegenstand); Principle of compositionality; Context principle; Distinction between the sense and reference (Sinn und Bedeutung) of names and other expressions, sometimes said to involve a mediated reference theory.

As a philosopher of mathematics, Frege attacked the psychologistic appeal to mental explanations of the content of judgment of the meaning of sentences. His original purpose was very far from answering general questions about meaning; instead, he devised his logic to explore the foundations of arithmetic, undertaking to answer questions such as "What is a number?" or "What objects do number-words ("one", "two", etc.) refer to?" But in pursuing these matters, he eventually found himself analysing and explaining what meaning is, and thus came to several conclusions that proved highly consequential for the subsequent course of analytic philosophy and the philosophy of language. It should be kept in mind that Frege was employed as a mathematician, not a philosopher, and he published his philosophical papers in scholarly journals that often were hard to access outside of the German-speaking world. He never published a philosophical monograph other than The Foundations of Arithmetic, much of which was mathematical in content, and the first collections of his writings appeared only after World War II. A volume of English translations of Frege's philosophical essays first appeared in 1952, edited by students of Wittgenstein, Peter Geach (1916-2013) and Max Black (1909–88), with the bibliographic assistance of Wittgenstein (see Geach, ed. 1975, Introduction). Despite the generous praise of Russell and Wittgenstein, Frege was little known as a philosopher during his lifetime. His ideas spread chiefly through those he influenced, such as Russell, Wittgenstein, and Carnap, and through work on logic and semantics by Polish logicians. Sense and reference[edit] Main article: Sense and reference 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 unanalyzable whole, and the functional expression "the Prince of Wales", which contains the significant parts "the prince of ξ" and "Wales", have the same reference, namely, the person best known as Prince Charles. But the sense of the word "Wales" is a part of the sense of the latter expression, but no part of the sense of the "full name" of Prince 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". 1924 diary[edit] Frege's published philosophical writings were of a very technical nature and divorced from practical issues, so much so that Frege scholar Dummett expresses his "shock to discover, while reading Frege's diary, that his hero was an anti-Semite."[16] 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 contains extreme right-wing 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.[17] Frege confided "that he had once thought of himself as a liberal and was an admirer of Bismarck", but then sympathized with General Ludendorff and Adolf Hitler. Some interpretations have been written about that time.[18] 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
Gershom Scholem
who much valued his teacher;[19][20] and he encouraged Ludwig Wittgenstein
Ludwig Wittgenstein
to leave for England.[21] The 1924 diary was published posthumously in 1994.[22] Frege apparently never spoke in public about his political viewpoints. Personality[edit] Frege was described by his students as a highly introverted person, seldom entering into dialogue, mostly facing the blackboard while lecturing though being witty and sometimes bitterly sarcastic.[23] Important dates[edit]

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. 1917 or 1918 — retires. Died 26 July 1925 in Bad Kleinen
Bad Kleinen
(now part of Mecklenburg-Vorpommern).

Important works[edit] Logic, foundation of arithmetic[edit] Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens (1879). Halle a. S.

English: Concept
Concept
Notation, the Formal Language
Language
of the Pure Thought like that of Arithmetics.

Die Grundlagen der Arithmetik: Eine logisch-mathematische Untersuchung über den Begriff der Zahl (1884). Breslau.

English: The Foundations of Arithmetic: A Logical-Mathematical Investigation of the Concept
Concept
of Number.

Grundgesetze der Arithmetik, Band I (1893); Band II (1903). Jena: Verlag Hermann Pohle.

English: Basic Laws of Arithmetic, translated and edited with an introduction by Philip A. Ebert and Marcus Rossberg. Oxford: Oxford University Press, 2013. ISBN 978-0-19-928174-9.

Philosophical studies[edit] "Function and Concept" (1891)

Original: "Funktion und Begriff"; in Jenaische Gesellschaft für Medizin und Naturwissenschaft, Jena, 9 January 1891; In English: "Function and Concept.

"On Sense and Reference" (1892)

Original: "Über Sinn und Bedeutung", in Zeitschrift für Philosophie und philosophische Kritik C (1892): 25–50; In English: "On Sense and Reference", alternatively translated (in later edition) as "On Sense and Meaning".

" Concept
Concept
and Object" (1892)

Original: "Ueber Begriff und Gegenstand", in Vierteljahresschrift für wissenschaftliche Philosophie XVI (1892): 192–205; In English: " Concept
Concept
and Object".

"What is a Function?" (1904)

Original: "Was ist eine Funktion?", in Festschrift Ludwig Boltzmann gewidmet zum sechzigsten Geburtstage, 20 February 1904, S. Meyer (ed.), Leipzig, 1904, pp. 656–666 (Internet Archive: [1], [2], [3]); In English: "What is a Function?".

Logical Investigations (1918–1923). Frege intended that the following three papers be published together in a book titled Logische Untersuchungen (Logical Investigations). Though the German book never appeared, the papers were published together in Logische Untersuchungen, ed. G. Patzig, Vandenhoeck & Ruprecht, 1966, and English translations appeared together in Logical Investigations, ed. Peter Geach, Blackwell, 1975.

1918–19. "Der Gedanke: Eine logische Untersuchung" ("The Thought: A Logical Inquiry"), in Beiträge zur Philosophie des Deutschen Idealismus I:[24] 58–77. 1918–19. "Die Verneinung" ("Negation") in Beiträge zur Philosophie des Deutschen Idealismus I: 143–157. 1923. "Gedankengefüge" ("Compound Thought"), in Beiträge zur Philosophie des Deutschen Idealismus III: 36–51.

Articles on geometry[edit]

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.

See also[edit]

Philosophy portal Logic
Logic
portal

Frege programming language List of pioneers in computer science

References[edit]

^ Hans Sluga, "Frege's alleged realism," Inquiry 20 (1–4):227–242 (1977). ^ a b Michael Resnik, "II. Frege as Idealist and then Realist," Inquiry 22 (1–4):350–357 (1979). ^ Truth – Internet Encyclopedia of Philosophy; The Deflationary Theory of Truth (Stanford Encyclopedia of Philosophy). ^ Willard Van Orman Quine, introduction to "Bausteine der mathematischen Logik", pp. 305–316. Translated by Stefan Bauer-Mengelberg as "On the building blocks of mathematical logic" in Jean van Heijenoort
Jean van Heijenoort
(1967), A Source Book in Mathematical Logic, 1879–1931. Harvard University Press, pp. 355–66. ^ Hans Sluga (1980), Gottlob Frege, Routledge, pp. 53ff. ^ a b Robert Boyce Brandom, "Frege's Technical Concepts", in Frege Synthesized: Essays on the Philosophical and Foundational Work of G. Frege, L. Haaparanta and J. Hintikka, Synthese Library, D. Reidel, 1986, pp. 253–295 ^ Gottfried Gabriel, "Frege, Lotze, and the Continental Roots of Early Analytic Philosophy," in: Erich H. Reck (ed.). From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy, Oxford University Press, 2002, pp. 39–51, esp. 44–48. ^ Tom Ricketts, Michael Potter, The Cambridge Companion to Frege, Cambridge University Press, 2010, p. 179. ^ Sundholm, B. G., "When, and why, did Frege read Bolzano?", LOGICA Yearbook 1999, 164–174 (2000). ^ "Frege". Random House Webster's Unabridged Dictionary. ^ Lothar Kreiser, Gottlob Frege: Leben - Werk - Zeit, Felix Meiner Verlag, 2013, p. 11. ^ Arndt Richter, "Ahnenliste des Mathematikers Gottlob Frege, 1848-1925" ^ Horsten, Leon and Pettigrew, Richard, "Introduction" in The Continuum Companion to Philosophical Logic
Logic
(Continuum International Publishing Group, 2011), p. 7. ^ Frege's Logic, Theorem, and Foundations for Arithmetic, Stanford Encyclopedia of Philosophy at plato.stanford.edu ^ Burgess, John (2005). Fixing Frege. ISBN 0-691-12231-8.  ^ Hersh, Reuben, What Is Mathematics, Really? (Oxford University Press, 1997), p. 241. ^ Michael Dummett: Frege: Philosophy of Language, p. xii. ^ Hans Sluga: Heidegger's Crisis: Philosophy and Politics in Nazi Germany, pp. 99ff. Sluga's source was an article by Eckart Menzler-Trott: "Ich wünsch die Wahrheit und nichts als die Wahrheit: Das politische Testament des deutschen Mathematikers und Logikers Gottlob Frege". In: Forum, vol. 36, no. 432, 20 December 1989, pp. 68–79. ^ "Frege biography".  ^ "Frege, Gottlob – Internet Encyclopedia of Philosophy".  ^ Juliet Floyd, The Frege-Wittgenstein Correspondence: Interpretive Themes ^ 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. ^ Frege's Lectures on Logic, ed. by Erich H. Reck and Steve Awodey, Open Court Publishing, 2004, pp. 18–26. ^ The journal Beiträge zur Philosophie des Deutschen Idealismus was the organ of Deutsche Philosophische Gesellschaft (de).

Primary[edit]

Online bibliography of Frege's works and their English translations (compiled by E. N. Zalta, Stanford Encyclopedia of Philosophy). 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle a. S.: Louis Nebert. Translation: Concept
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
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
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).

Secondary[edit]

Philosophy

Badiou, Alain. "On a Contemporary Usage of Frege", trans. Justin Clemens and Sam Gillespie. UMBR(a), no. 1, 2000, pp. 99–115. Baker, Gordon, and P.M.S. Hacker, 1984. Frege: Logical Excavations. Oxford University Press. — Vigorous, if controversial, criticism of both Frege's philosophy and influential contemporary interpretations such as Dummett's. Currie, Gregory, 1982. Frege: An Introduction to His Philosophy. Harvester Press. Dummett, Michael, 1973. Frege: Philosophy of Language. Harvard University Press. ------, 1981. The Interpretation of Frege's Philosophy. Harvard University Press. Hill, Claire Ortiz, 1991. Word and Object in Husserl, Frege and Russell: The Roots of Twentieth-Century Philosophy. Athens OH: Ohio University Press. ------, and Rosado Haddock, G. E., 2000. Husserl or Frege: Meaning, Objectivity, and Mathematics. Open Court. — On the Frege-Husserl-Cantor triangle. Kenny, Anthony, 1995. Frege — An introduction to the founder of modern analytic philosophy. Penguin Books. — Excellent non-technical introduction and overview of Frege's philosophy. Klemke, E.D., ed., 1968. Essays on Frege. University of Illinois Press. — 31 essays by philosophers, grouped under three headings: 1. Ontology; 2. Semantics; and 3. Logic
Logic
and Philosophy of Mathematics. Rosado Haddock, Guillermo E., 2006. A Critical Introduction to the Philosophy of Gottlob Frege. Ashgate Publishing. Sisti, Nicola, 2005. Il Programma Logicista di Frege e il Tema delle Definizioni. Franco Angeli. — On Frege's theory of definitions. Sluga, Hans, 1980. Gottlob Frege. Routledge. Nicla Vassallo, 2014, Frege on Thinking and Its Epistemic Significance with Pieranna Garavaso, Lexington Books–Rowman & Littlefield, Lanham, MD, Usa. Weiner, Joan, 1990. Frege in Perspective, Cornell University Press.

Logic
Logic
and mathematics

Anderson, D. J., and Edward Zalta, 2004, "Frege, Boolos, and Logical Objects," Journal of Philosophical Logic
Logic
33: 1–26. Blanchette, Patricia, 2012, Frege's Conception of Logic. Oxford: Oxford University Press, 2012 Burgess, John, 2005. Fixing Frege. Princeton Univ. Press. — A critical survey of the ongoing rehabilitation of Frege's logicism. Boolos, George, 1998. Logic, Logic, and Logic. MIT Press. — 12 papers on Frege's theorem and the logicist approach to the foundation of arithmetic. Dummett, Michael, 1991. Frege: Philosophy of Mathematics. Harvard University Press. Demopoulos, William, ed., 1995. Frege's Philosophy of Mathematics. Harvard Univ. Press. — Papers exploring Frege's theorem and Frege's mathematical and intellectual background. Ferreira, F. and Wehmeier, K., 2002, "On the consistency of the Delta-1-1-CA fragment of Frege's Grundgesetze," Journal of Philosophic Logic
Logic
31: 301–11. Grattan-Guinness, Ivor, 2000. The Search for Mathematical Roots 1870–1940. Princeton University Press. — Fair to the mathematician, less so to the philosopher. Gillies, Donald A., 1982. Frege, Dedekind, and Peano on the foundations of arithmetic. Methodology and Science Foundation, 2. Van Gorcum & Co., Assen, 1982. Gillies, Donald: The Fregean revolution in logic. Revolutions in mathematics, 265–305, Oxford Sci. Publ., Oxford Univ. Press, New York, 1992. Irvine, Andrew David, 2010, "Frege on Number Properties," Studia Logica, 96(2): 239-60. Charles Parsons, 1965, "Frege's Theory of Number." Reprinted with Postscript in Demopoulos (1965): 182–210. The starting point of the ongoing sympathetic reexamination of Frege's logicism. Gillies, Donald: The Fregean revolution in logic. Revolutions in mathematics, 265–305, Oxford Sci. Publ., Oxford Univ. Press, New York, 1992. Heck, Richard G., Jr: Frege's Theorem. Oxford: Oxford University Press, 2011 Heck, Richard G., Jr: Reading Frege's Grundgesetze. Oxford: Oxford University Press, 2013 Wright, Crispin, 1983. Frege's Conception of Numbers as Objects. Aberdeen University Press. — A systematic exposition and a scope-restricted defense of Frege's Grundlagen conception of numbers.

Historical context

Everdell, William R. (1997), The First Moderns: Profiles in the Origins of Twentieth Century Thought, Chicago: University of Chicago Press 

External links[edit]

Find more aboutGottlob Fregeat's sister projects

Media from Wikimedia Commons Quotations from Wikiquote Texts from Wikisource

Works by or about Gottlob Frege
Gottlob Frege
at Internet Archive Frege at Genealogy Project A comprehensive guide to Fregean material available on the web by Brian Carver. Stanford Encyclopedia of Philosophy:

"Gottlob Frege" — by Edward Zalta. "Frege's Logic, Theorem, and Foundations for Arithmetic" — by Edward Zalta.

Internet Encyclopedia of Philosophy:

Gottlob Frege — by Kevin C. Klement. Frege and Language — by Dorothea Lotter.

Metaphysics Research Lab: Gottlob Frege. Frege on Being, Existence and Truth. O'Connor, John J.; Robertson, Edmund F., "Gottlob Frege", MacTutor History of Mathematics
Mathematics
archive, University of St Andrews . Begriff, a LaTeX
LaTeX
package for typesetting Frege's logic notation, earlier version grundgesetze, a LaTeX
LaTeX
package for typesetting Frege's logic notation, mature version Frege's Basic Laws of Arithmetic, info website, incl. corrigenda and LaTeX
LaTeX
typesetting tool — by P.A. Ebert and M. Rossberg

v t e

Analytic philosophy

Philosophers

J. L. Austin A. J. Ayer G. E. M. Anscombe Nick Bostrom Robert Brandom C. D. Broad Patricia Churchland David Chalmers Noam Chomsky James F. Conant Alice Crary Donald Davidson Daniel Dennett Cora Diamond Michael Dummett Paul Feyerabend Antony Flew Bas van Fraassen Gottlob Frege Jerry Fodor Philippa Foot Peter Geach Paul Grice Ian Hacking R. M. Hare Carl Gustav Hempel Peter van Inwagen Christine Korsgaard Saul Kripke Thomas Kuhn David Lewis Alasdair MacIntyre J. L. Mackie Norman Malcolm John McDowell G. E. Moore Ernest Nagel Thomas Nagel Robert Nozick Derek Parfit Alvin Plantinga Karl Popper Hilary Putnam W. V. O. Quine John Rawls Hans Reichenbach Richard Rorty Bertrand Russell Gilbert Ryle Moritz Schlick John Searle Wilfrid Sellars Peter Singer Richard Swinburne Charles Taylor Michael Walzer Bernard Williams Timothy Williamson Ludwig Wittgenstein

Theories

Actualism Analytical feminism Analytical Marxism Anti-realism Berlin Circle Descriptivist theory of names Emotivism Functional contextualism Linguistic turn Logical positivism Modal realism Model-dependent realism Neopragmatism Neurophilosophy Ordinary language philosophy Postanalytic philosophy Pragmatic theory of truth Verificationism Vienna Circle

Concepts

Analysis Analytic–synthetic distinction Causal / Deductive / epistemic closure Concept Counterfactual Denotation / reference Definite description Factive Family resemblance Intuition Meaning (Proposition) Modality Natural kind / projectability Necessary–sufficient conditions Paradox of analysis Possible world Reduction Reflective equilibrium Rigid–flaccid designators Sense data Supervenience Thought experiment Truth function Truthmaker Truth-bearer Type–token distinction

Related articles

Aretaic turn Australian realism Communitarianism Ordinary language philosophy Philosophical logic Philosophy of language Philosophy of science Postanalytic philosophy

Index Category

v t e

Philosophy of language

Philosophers

Plato
Plato
(Cratylus) Gorgias Confucius Xunzi Aristotle Stoics Pyrrhonists Scholasticism Ibn Rushd Ibn Khaldun Thomas Hobbes Gottfried Wilhelm Leibniz Johann Herder Ludwig Noiré Wilhelm von Humboldt Fritz Mauthner Paul Ricœur Ferdinand de Saussure Gottlob Frege Franz Boas Paul Tillich Edward Sapir Leonard Bloomfield Zhuangzi Henri Bergson Lev Vygotsky Ludwig Wittgenstein

Philosophical Investigations Tractatus Logico-Philosophicus

Bertrand Russell Rudolf Carnap Jacques Derrida

Of Grammatology Limited Inc

Benjamin Lee Whorf Gustav Bergmann J. L. Austin Noam Chomsky Hans-Georg Gadamer Saul Kripke A. J. Ayer G. E. M. Anscombe Jaakko Hintikka Michael Dummett Donald Davidson Roger Gibson Paul Grice Gilbert Ryle P. F. Strawson Willard Van Orman Quine Hilary Putnam David Lewis John Searle Joxe Azurmendi Scott Soames Stephen Yablo John Hawthorne Stephen Neale Paul Watzlawick

Theories

Causal theory of reference Contrast theory of meaning Contrastivism Conventionalism Cratylism Deconstruction Descriptivist theory of names Direct reference theory Dramatism Expressivism Linguistic determinism Logical atomism Logical positivism Mediated reference theory Nominalism Non-cognitivism Phallogocentrism Quietism Relevance theory Semantic externalism Semantic holism Structuralism Supposition theory Symbiosism Theological noncognitivism Theory of descriptions Verification theory

Concepts

Ambiguity Linguistic relativity Meaning Language Truth-bearer Proposition Use–mention distinction Concept Categories Set Class Intension Logical form Metalanguage Mental representation Principle of compositionality Property Sign Sense and reference Speech act Symbol Entity Sentence Statement more...

Related articles

Analytic philosophy Philosophy of information Philosophical logic Linguistics Pragmatics Rhetoric Semantics Formal semantics Semiotics

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Authority control

WorldCat Identities VIAF: 51689723 LCCN: n79117996 ISNI: 0000 0001 2132 6294 GND: 118535161 SELIBR: 187415 SUDOC: 026874229 BNF: cb119035228 (data) BIBSYS: 90079249 MGP: 46166 NLA: 35102466 NDL: 00440110 NKC: jn20000700561 BNE: XX933058 CiNii: DA00328

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