Gottlob Frege
Pour Frege, la logique peut être écrite aussi précisément que les mathématiques, et un mot a à la fois un sens – la manière dont il présente quelque chose – et une référence – ce qu’il désigne.
Repères
Fondateur de la logique moderne ; a distingué le sens et la référence.
Idées clés
- Begriffsschrift
- Sens et référence
- Logicisme
Maîtres: Hermann Lotze, Kuno Fischer
Élèves: Rudolf Carnap
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Influence
Influences reçues de 4
Gottfried Wilhelm Leibniz
influencé par
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”
Attestation: brouillon IA
Gottfried Wilhelm Leibniz › 1646–1716
Friedrich Adolf Trendelenburg
influencé par
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
Attestation: brouillon IA
Friedrich Adolf Trendelenburg › 1802–1872
Hermann Lotze élève de
élève de
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
Attestation: brouillon IA
influencé par
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)
Attestation: brouillon IA
Hermann Lotze › 1817–1881
Kuno Fischer élève de
élève de
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
Attestation: brouillon IA
Kuno Fischer › 1824–1907
A influencé 4
Rudolf Carnap a enseigné à
a enseigné à ✓
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)
Attestation: brouillon IA
Rudolf Carnap › 1891–1970
Michael Dummett
a influencé
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”
Attestation: aussi dans InPhO · InPhO
Michael Dummett › 1925–2011
J. N. Mohanty
a influencé
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)
Attestation: brouillon IA
J. N. Mohanty › 1928–2023
John Searle
a influencé
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)
Attestation: aussi dans InPhO · InPhO
John Searle › 1932–2025
Critique
Critique réciproque 2
Georg Cantor ⇄ réciproque
a critiqué
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
Attestation: brouillon IA
critiqué par
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
Attestation: brouillon IA
Georg Cantor › 1845–1918
Giuseppe Peano ⇄ réciproque
a critiqué
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)
Attestation: brouillon IA
critiqué par contesté
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
Attestation: brouillon IA
Giuseppe Peano › 1858–1932
Critiques reçues de 4
Bertrand Russell a influencé
a influencé ✓
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”
critiqué par
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
Attestation: brouillon IA
Bertrand Russell › 1872–1970
Ludwig Wittgenstein a influencé
a influencé ✓
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”
critiqué par
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
Attestation: brouillon IA
Ludwig Wittgenstein › 1889–1951
Hilary Putnam
critiqué par
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
Attestation: brouillon IA
Hilary Putnam › 1926–2016
Saul Kripke
critiqué par
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
Attestation: brouillon IA
Saul Kripke › 1940–2022
Critiques adressées à 4
Emmanuel Kant influencé par
influencé par
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”
Attestation: brouillon IA
a critiqué
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
Attestation: brouillon IA
Emmanuel Kant › 1724–1804
John Stuart Mill
a critiqué
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
Attestation: brouillon IA
John Stuart Mill › 1806–1873
Edmund Husserl a influencé
a influencé contesté ✓
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”
a critiqué
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
Attestation: brouillon IA
Edmund Husserl › 1859–1938
David Hilbert
a critiqué
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”
Attestation: brouillon IA
David Hilbert › 1862–1943
Œuvres
- 1879Idéographie
Un langage formulaire de la pensée pure – la naissance de la logique moderne.
Les nombres sont des objets logiques – contre le psychologisme et contre Kant.
L’étoile du soir est l’étoile du matin – mais pas dans le même sens.
Position
Frege est le fondateur de la logique moderne et de la philosophie analytique du langage. Dans son Idéographie, il créa un langage formel capable d’exprimer le raisonnement mathématique sans lacune, en introduisant les quantificateurs et l’analyse des phrases en fonction et argument. Il visait à montrer que l’arithmétique peut être dérivée de la seule logique, et que les nombres sont des objets logiques objectifs, non des images mentales. Sa distinction entre sens et dénotation explique pourquoi « l’étoile du matin est l’étoile du soir » est instructif : les deux expressions renvoient à Vénus, mais la présentent de façons différentes. Son insistance sur l’objectivité de la pensée, contre le psychologisme, a marqué Russell, Wittgenstein, Carnap et toute la tradition analytique.
Vie et contexte
Frege, né à Wismar, sur la Baltique, étudia les mathématiques, la physique et la philosophie à Iéna et à Göttingen et enseigna les mathématiques à Iéna pendant toute sa carrière. Son œuvre reçut peu de reconnaissance de son vivant. En 1902, une lettre du jeune Russell montra que son système contenait une contradiction, un coup dont son projet logiciste ne se remit jamais. Son journal de 1924, publié en 1994, révèle des vues antisémites et antidémocratiques virulentes.
Autres œuvres principales
- Grundgesetze der Arithmetik (traduction propre : « Lois fondamentales de l’arithmétique », 1893–1903)
- La Pensée (1918)
Apparaît dans
- Voyage « Le tournant linguistique » · Étape 1 sur 10
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