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Gottlob Frege (1848–1925)

Gottlob Frege was a German mathematician, logician, and philosopher whose ideas revolutionized modern logic and paved the way for the reconsideration of the foundations of mathematics that occupied European thinkers in the first decades of the twentieth century. Frege spent most of his career teaching at the University of Jena, the same institution where he pursued his initial studies, after receiving his doctorate from the University of Göttingen in 1873. Though not a public or political figure himself, Frege’s legacy has been marred by revelations of his virulent anti-Semitism and his professed admiration of Adolf Hitler, a support conditioned by Frege’s long-standing anti-liberalism and anti-socialism. Whatever his personal and political failings, Frege’s reputation as a thinker and his centrality to modern philosophy generally remains uncompromised.

His first major work was the Begriffschrift (Concept-Script, 1879), which made significant advances over Aristotelian syllogistic logic in the development of an axiomatic predicate logic that, Frege believed, could ‘ground’ mathematics. Frege’s commitment to the idea that arithmetic was a branch of logic was further developed in Die Grundlagen der Arithmatik (The Foundations of Arithmetic, 1884), a work of crucial importance to the Cahiers pour l’Analyse. In addition to a brief presentation by Yves Duroux of the ‘successor function’ in this work and its anti-psychologistic import, the article at the heart of the Cercle d’Épistémologie’s investigation of a formalised theory of the subject - Jacques-Alain Miller’s ‘La Suture’ - takes the form of Lacanian reading of the Grundlagen and its case for the generation of the natural numbers out of the concept of the zero. Frege’s later efforts to develop the Grundlagen further in a more ambitious work, published in two volumes as the Grundgesetz der Arithmatik (Basic Laws of Arithmatic, 1893, 1903), were stymied by a letter from Bertrand Russell. in which the latter shared his famous paradox concerning the membership of sets who are not members of themselves, itself another crucial episode in the history of logic that was important for Lacan. and the editors of the Cahiers. Despite its problems, Frege’s logicism nonetheless lay at the source of twentieth-century analytic philosophy, inspiring the logical positivism of Rudolf Carnap and the Vienna Circle as well as the inquiries into semnatics produced by Alfred Tarski and other Polish logicians.

In the Cahiers pour l’Analyse

Yves Duroux, ‘Psychologie et logique’, CpA 1.2 [HTML] [PDF] [SYN]
Jacques-Alain Miller, ‘La suture (Éléments de la logique du signifiant)’, CpA 1.3 [HTML] [PDF] [SYN]
Serge Leclaire, ‘L’analyste à sa place?’, CpA 1.4 [HTML] [PDF] [SYN]
Alain Badiou, ‘Marque et manque: à propos du zéro’, CpA 10.8 [HTML] [PDF] [SYN]

Select bibliography

  • Begriffschrift, a formula language, modeled upon that of arithmetic, for pure thought’ (1879). In From Frege to Gödel: A Sourcebook in Mathematical Logi, 1879-1931, ed. Jean van Heijenoort. Cambridge, MA: Harvard University Press, 1967.
  • Foundations of Arithmetic (1884), trans. J.L. Austin. Oxford: Basil Blackwell, 1980.