Gottlob Frege
For Frege, logic can be written as precisely as mathematics, and a word has both a sense – how it presents something – and a reference – what it picks out.
Placement
Founder of modern logic; distinguished between sense and reference.
Key ideas
- Begriffsschrift
- Sense and reference
- Logicism
Teachers: Hermann Lotze, Kuno Fischer
Students: Rudolf Carnap
Influence
Influenced by 4
Gottfried Wilhelm Leibniz
influenced by
Frege presented his Begriffsschrift (1879) as a step towards Leibniz’s universal characteristic and adopted Leibniz’s definition of identity as substitutability salva veritate (Grundlagen der Arithmetik, 1884). G. Frege, Begriffsschrift (1879), preface; Die Grundlagen der Arithmetik (1884); SEP “Leibniz’s Influence on 19th Century Logic”; SEP “Gottlob Frege”
Evidence: AI draft
Gottfried Wilhelm Leibniz › 1646–1716
Friedrich Adolf Trendelenburg
influenced by
In the preface to the Begriffsschrift Frege refers to Trendelenburg’s essay on Leibniz’s plan for a universal characteristic when he presents his concept-script as a step toward Leibniz’s ideal. Frege, Begriffsschrift (1879), preface and note 2, in van Heijenoort (ed.), From Frege to Gödel (1967), p. 6; cf. SEP “Gottlob Frege” §2.1
Evidence: AI draft
Friedrich Adolf Trendelenburg › 1802–1872
Hermann Lotze studied with
studied with
Frege heard Lotze’s lectures on the philosophy of religion at Göttingen, the only philosophy course he took there, though Potter finds no philosophical teacher of central importance in Frege’s education. M. Potter, “Introduction”, in Potter and Ricketts (eds.), The Cambridge Companion to Frege (2010), p. 1; SEP “Hermann Lotze” (D. Sullivan) names Frege a direct student
Evidence: AI draft
influenced by
Frege’s early set of key sentences about logic is a response to Lotze’s Logic of 1874, taking up the separation of thoughts from ideas but grounding it in the objectivity of truth rather than in value. M. Potter, “Introduction”, Cambridge Companion to Frege (2010), pp. 2–3, after M. Dummett, Frege and Other Philosophers (1991) and F. Hovens, History and Philosophy of Logic 18 (1997)
Evidence: AI draft
Hermann Lotze › 1817–1881
Kuno Fischer studied with
studied with
The only philosophy Frege heard at Jena was Fischer’s lecture course on Kant’s critical philosophy. M. Potter, “Introduction”, Cambridge Companion to Frege (2010), p. 1
Evidence: AI draft
Kuno Fischer › 1824–1907
Influenced 4
Rudolf Carnap taught
taught ✓
Carnap attended Frege’s courses in Jena – Begriffsschrift I and II (1910–11, 1913) and Logic in Mathematics (1914) – as one of very few students; he later recalled them as his introduction to modern logic. R. Carnap, “Intellectual Autobiography”, in P. A. Schilpp (ed.), The Philosophy of Rudolf Carnap (1963)
Evidence: AI draft
Rudolf Carnap › 1891–1970
Michael Dummett
influenced
Dummett read Frege as the founder of analytic philosophy, whose theory of sense makes the theory of meaning the foundation of philosophy (Frege: Philosophy of Language, 1973). M. Dummett, Frege: Philosophy of Language (1973); Origins of Analytical Philosophy (1993); SEP “Gottlob Frege”
Evidence: also in InPhO · InPhO
Michael Dummett › 1925–2011
J. N. Mohanty
influenced
Mohanty used Frege’s distinction of sense and reference to compare him with Husserl, arguing in Husserl and Frege (1982) that Husserl reached it independently. J. N. Mohanty, Husserl and Frege (1982)
Evidence: AI draft
J. N. Mohanty › 1928–2023
John Searle
influenced
Searle developed Frege’s view that proper names have a sense into a cluster theory of names (‘Proper Names’, 1958) and defended a Fregean account of reference (Intentionality, 1983). J. R. Searle, “Proper Names”, Mind 67 (1958); Speech Acts (1969); Intentionality (1983)
Evidence: also in InPhO · InPhO
John Searle › 1932–2025
Criticism
Mutual critique 2
Georg Cantor ⇄ mutual
criticised
Frege’s 1892 review of Cantor’s collected papers on the transfinite (and an unpublished draft of 1890) objects to Cantor’s appeal to mental abstraction. Frege, review of Cantor, Zeitschrift für Philosophie und philosophische Kritik 100 (1892), 269–272, tr. in Collected Papers (1984), pp. 178–181
Evidence: AI draft
criticised by
Cantor’s 1885 review of Frege’s Grundlagen objected to Frege’s attempt to define number through extensions of concepts. P. Ebert and M. Rossberg, “Cantor on Frege’s Foundations of Arithmetic”, History and Philosophy of Logic 30 (2009), 341–348
Evidence: AI draft
Georg Cantor › 1845–1918
Giuseppe Peano ⇄ mutual
criticised
In 1897 Frege compared Peano’s logical notation with his own and defended the superiority of his concept-script. Frege, “Über die Begriffsschrift des Herrn Peano und meine eigene” (1897), listed in SEP “Frege’s Logic” (R. Cook, 2023)
Evidence: AI draft
criticised by disputed
Peano’s 1895 review of Frege’s Grundgesetze I in the Rivista di matematica prompted Frege’s replies of 1896–97; what exactly Peano objected to was not checked. Bibliographic data from the Frege–Peano literature (G. Besler; Rivista di matematica 5, 1895, 122–128 and 6, 1896–99, 53–61); review text not read
Evidence: AI draft
Giuseppe Peano › 1858–1932
Criticized by 4
Bertrand Russell influenced
influenced ✓
Russell recognised Frege’s logicism as close to his own, expounded it in an appendix to The Principles of Mathematics (1903) and continued it in Principia Mathematica (1910–13). B. Russell, The Principles of Mathematics (1903), appendix A; A. N. Whitehead and B. Russell, Principia Mathematica (1910–13); SEP “Bertrand Russell”
criticised by
In a letter of 16 June 1902 Russell showed that Frege’s Basic Law V yields a contradiction; ‘On Denoting’ (1905) rejected Frege’s distinction of sense and reference. B. Russell to G. Frege, 16 June 1902, in J. van Heijenoort (ed.), From Frege to Gödel (1967); “On Denoting”, Mind 14 (1905); G. Frege, Grundgesetze der Arithmetik II (1903), appendix
Evidence: AI draft
Bertrand Russell › 1872–1970
Ludwig Wittgenstein influenced
influenced ✓
Wittgenstein, who visited Frege (1911), thanked ‘the great works of Frege’ in the Tractatus preface and adopted his principle that names have meaning only in propositions (1921). L. Wittgenstein, Logisch-philosophische Abhandlung (completed 1918; publ. 1921), preface; G. Frege, Die Grundlagen der Arithmetik (1884); SEP “Ludwig Wittgenstein”
criticised by
Wittgenstein rejected Frege’s view that sentences name truth-values and that logical constants represent anything; Frege’s assertion sign he called logically meaningless (Tractatus, 1921, 4.0312, 4.431, 4.442). L. Wittgenstein, Tractatus logico-philosophicus (1921), 3.143, 4.0312, 4.431, 4.442; Philosophische Untersuchungen (1953), § 71
Evidence: AI draft
Ludwig Wittgenstein › 1889–1951
Hilary Putnam
criticised by
Putnam’s Twin Earth case denied that the Fregean sense a speaker grasps fixes a term’s extension: ‘meanings just ain’t in the head’ (‘The Meaning of “Meaning”’, 1975). H. Putnam, “The Meaning of ‘Meaning’”, Minnesota Studies in the Philosophy of Science 7 (1975), 131–193
Evidence: AI draft
Hilary Putnam › 1926–2016
Saul Kripke
criticised by
Kripke rejected the Fregean view that a name’s descriptive sense fixes its reference: names are rigid designators, tied to bearers by a causal chain (Naming and Necessity, 1972/1980). S. Kripke, Naming and Necessity (1972; book 1980), Lectures I–II
Evidence: AI draft
Saul Kripke › 1940–2022
Criticizes 4
Immanuel Kant influenced by
influenced by
Frege kept Kant’s view that geometry rests on a priori intuition and recast his analytic–synthetic distinction as concerning how a truth is justified (Grundlagen der Arithmetik, 1884). G. Frege, Die Grundlagen der Arithmetik (1884); SEP “Gottlob Frege”
Evidence: AI draft
criticised
Frege argued against Kant that arithmetic is analytic, not synthetic a priori, and that Kant underestimated analytic judgements; geometry he left to intuition (Grundlagen der Arithmetik, 1884). G. Frege, Die Grundlagen der Arithmetik (1884), §§ 5, 12–13, 88–90
Evidence: AI draft
Immanuel Kant › 1724–1804
John Stuart Mill
criticised
Frege rejected Mill’s view of numbers as properties of aggregates and of arithmetic as inductive, mocking it as an arithmetic of pebbles and gingerbread (Grundlagen der Arithmetik, 1884, §§ 7–11). G. Frege, Die Grundlagen der Arithmetik (1884), §§ 7–11, 23–25; J. S. Mill, A System of Logic (1843), book II, ch. 6
Evidence: AI draft
John Stuart Mill › 1806–1873
Edmund Husserl influenced
influenced disputed ✓
Husserl discussed Frege’s Grundlagen in Philosophy of Arithmetic (1891); whether Frege’s critical review (1894) prompted his turn against psychologism in the Logical Investigations (1900–01) is disputed. G. Frege, review of E. Husserl, Philosophie der Arithmetik, Zeitschrift für Philosophie und philosophische Kritik 103 (1894); D. Føllesdal, Husserl und Frege (1958); J. N. Mohanty, Husserl and Frege (1982); SEP “Edmund Husserl”
criticised
In his 1894 review of Husserl’s Philosophy of Arithmetic (1891) Frege charged it with psychologism, confusing subjective presentations with objective concepts and numbers. G. Frege, review of E. Husserl, Philosophie der Arithmetik I, Zeitschrift für Philosophie und philosophische Kritik 103 (1894), 313–332
Evidence: AI draft
Edmund Husserl › 1859–1938
David Hilbert
criticised
Frege objected to Hilbert’s Foundations of Geometry (1899) that axioms cannot implicitly define their terms but must be true statements, and that consistency does not prove existence. Frege–Hilbert correspondence, Dec. 1899–1900; G. Frege, “Über die Grundlagen der Geometrie”, Jahresbericht der DMV 12 (1903) and 15 (1906); SEP “The Frege–Hilbert Controversy”
Evidence: AI draft
David Hilbert › 1862–1943
Works
- 1879Begriffsschrift
A formula language of pure thought – the birth of modern logic.
Numbers are logical objects – against psychologism and Kant.
The Evening Star is the Morning Star – but not in the same sense.
Position
Frege is the founder of modern logic and of analytic philosophy of language. In his Begriffsschrift he created a formal language that could express mathematical reasoning without gaps, introducing quantifiers and the analysis of sentences into function and argument. He aimed to show that arithmetic can be derived from logic alone, and that numbers are objective logical objects, not mental images. His distinction between sense and reference explains why “the morning star is the evening star” is informative: both expressions refer to Venus but present it in different ways. His insistence on the objectivity of thought, against psychologism, shaped Russell, Wittgenstein, Carnap and the whole analytic tradition.
Life & context
Frege, born in Wismar on the Baltic, studied mathematics, physics and philosophy in Jena and Göttingen and taught mathematics at Jena for his whole career. His work received little recognition during his lifetime. In 1902 a letter from the young Russell showed that his system contained a contradiction, a blow from which his logicist project never recovered. His diary of 1924, published in 1994, reveals virulent antisemitic and anti-democratic views.
Further main works
- Basic Laws of Arithmetic (1893–1903)
- The Thought (1918)
Appears in
- Journey ‘The Linguistic Turn’ · Stop 1 of 10
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