Gottlob Frege
Według Fregego logikę można zapisać tak precyzyjnie jak matematykę, a słowo ma zarówno sens – sposób, w jaki coś przedstawia – jak i odniesienie – to, co wskazuje.
Umiejscowienie
Twórca nowoczesnej logiki; rozróżnił sens i odniesienie.
Kluczowe idee
- Begriffsschrift
- Sens i odniesienie
- Logicyzm
Nauczyciele: Hermann Lotze, Kuno Fischer
Uczniowie: Rudolf Carnap
Wpływ
Pod wpływem 4
Gottfried Wilhelm Leibniz
pod wpływem
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”
Źródło: szkic AI
Gottfried Wilhelm Leibniz › 1646–1716
Friedrich Adolf Trendelenburg
pod wpływem
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
Źródło: szkic AI
Friedrich Adolf Trendelenburg › 1802–1872
Hermann Lotze nauczyciel(ka)
nauczyciel(ka)
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
Źródło: szkic AI
pod wpływem
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)
Źródło: szkic AI
Hermann Lotze › 1817–1881
Kuno Fischer nauczyciel(ka)
nauczyciel(ka)
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
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Kuno Fischer › 1824–1907
Wpływ na 4
Rudolf Carnap uczeń/uczennica
uczeń/uczennica ✓
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)
Źródło: szkic AI
Rudolf Carnap › 1891–1970
Michael Dummett
wpływ na
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”
Źródło: także w InPhO · InPhO
Michael Dummett › 1925–2011
J. N. Mohanty
wpływ na
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)
Źródło: szkic AI
J. N. Mohanty › 1928–2023
John Searle
wpływ na
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)
Źródło: także w InPhO · InPhO
John Searle › 1932–2025
Krytyka
Wzajemna krytyka 2
Georg Cantor ⇄ wzajemnie
krytykuje
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
Źródło: szkic AI
krytyka ze strony
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
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Georg Cantor › 1845–1918
Giuseppe Peano ⇄ wzajemnie
krytykuje
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)
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krytyka ze strony sporne
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
Źródło: szkic AI
Giuseppe Peano › 1858–1932
Krytyka ze strony 4
Bertrand Russell wpływ na
wpływ na ✓
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”
krytyka ze strony
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
Źródło: szkic AI
Bertrand Russell › 1872–1970
Ludwig Wittgenstein wpływ na
wpływ na ✓
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”
krytyka ze strony
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
Źródło: szkic AI
Ludwig Wittgenstein › 1889–1951
Hilary Putnam
krytyka ze strony
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
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Hilary Putnam › 1926–2016
Saul Kripke
krytyka ze strony
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
Źródło: szkic AI
Saul Kripke › 1940–2022
Krytykuje 4
Immanuel Kant pod wpływem
pod wpływem
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”
Źródło: szkic AI
krytykuje
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
Źródło: szkic AI
Immanuel Kant › 1724–1804
John Stuart Mill
krytykuje
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
Źródło: szkic AI
John Stuart Mill › 1806–1873
Edmund Husserl wpływ na
wpływ na sporne ✓
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”
krytykuje
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
Źródło: szkic AI
Edmund Husserl › 1859–1938
David Hilbert
krytykuje
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”
Źródło: szkic AI
David Hilbert › 1862–1943
Dzieła
- 1879Begriffsschrift
Język formuł czystego myślenia – narodziny nowoczesnej logiki.
Liczby są przedmiotami logicznymi – przeciw psychologizmowi i Kantowi.
- 1892Sens i nominat
Gwiazda Wieczorna to Gwiazda Poranna – ale nie w tym samym sensie.
Stanowisko
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.
Życie i kontekst
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.
Dalsze główne dzieła
- The Foundations of Arithmetic (1884)
- On Sense and Reference (1892)
- Basic Laws of Arithmetic (1893–1903)
- The Thought (1918)
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