Linked bibliography for the SEP article "Luitzen Egbertus Jan Brouwer" by Mark van Atten

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A full bibliography of Brouwer’s writings can be found in

  • van Dalen, D., 1997, “A bibliography of L.E.J. Brouwer”, Utrecht Logic Group Preprint Series, no. 175 [Available online]. Updated version in van Atten, M., Boldini, P., Bourdeau, M., and Heinzmann, G. (eds.), 2008, One Hundred Years of Intuitionism (1907–2007). The Cerisy Conference, Basel: Birkhäuser, pp. 343–390. (Scholar)

The Brouwer Papers are kept at Noord-Hollands Archief in Haarlem, the Netherlands.

Availability of Brouwer’s writings

Facsimiles of almost all of Brouwer’s published papers can be found in

Full scans and transcriptions of Brouwer’s student notebooks (in Dutch) are available online.

In the Collected Works, papers in Dutch have been translated into English (without naming the translator(s)), but papers in French or German have not. English translations of several of them can be found in

  • van Heijenoort, J., ed., 1967, From Frege to Gödel. A Sourcebook in Mathematical Logic, 1879–1931, Cambridge (MA): Harvard University Press. (Scholar)
  • Mancosu, P., ed., 1998, From Hilbert to Brouwer. The Debate on the Foundations of Mathematics in the 1920s, Oxford: Oxford University Press. (Scholar)

An English translation of Brouwer’s little book Leven, Kunst en Mystiek of 1905, of which the Collected Works contain only excerpts, is

  • Brouwer, L.E.J., 1996, “Life, Art and Mysticism”, Notre Dame Journal of Formal Logic, 37(3):389–429. Translated by Walter van Stigt, who provides an introduction on pp.381–387. (Scholar)

The Berlin lectures of 1927 have been published in

The Cambridge lectures of 1946–1951, which are recommended as Brouwer’s own introduction to intuitionism, have been published as

  • Brouwer, L.E.J., 1981, Brouwer’s Cambridge Lectures on Intuitionism, D. van Dalen (ed.), Cambridge: Cambridge University Press. (Scholar)

A selection of Brouwer’s correspondence has been published as

  • van Dalen, D., ed., 2011, The Selected Correspondence of L.E.J. Brouwer, London: Springer. An online supplement (link and password on the copyright page of the book) presents most of the extant correspondence, but without English translations. (Scholar)

Of particular biographical interest is the correspondence between Brouwer and his friend, the socialist poet C.S. Adama van Scheltema, which covers the years 1898–1924. The Selected Correspondence presents a number of these letters in English. The full correspondence has been published in Dutch, with notes, an introduction, and an appendix on Brouwer, as

  • Brouwer, L.E.J., & Adama van Scheltema, C.S., 1984, Droeve Snaar, Vriend van Mij. Brieven, D. van Dalen (ed.), Amsterdam: De Arbeiderspers. (Scholar)

Cited texts by Brouwer

Brouwer’s writings are referred to according to the scheme in the bibliography van Dalen, 1997.

  • 1905, Leven, Kunst en Mystiek. Partial English translation in Brouwer, 1975, pp. 1–9. Full English translation (by W. van Stigt) in Notre Dame Journal of Formal Logic, 37(3):389–429.
  • 1907, Over de Grondslagen der Wiskunde, Ph.D. thesis, Universiteit van Amsterdam. English translation in Brouwer, 1975, pp. 11–101.
  • 1908, “De onbetrouwbaarheid der logische principes”, Tijdschrift voor Wijsbegeerte, 2: 152–158. English translation in Brouwer, 1975, pp. 107–111. (Scholar)
  • 1914, “A. Schoenflies und H. Hahn. Die Entwickelung der Mengenlehre und ihrer Anwendungen, Leipzig und Berlin 1913”, Jahresb. D.M.V., 23: 78–83. (Scholar)
  • 1918B, “Begründung der Mengenlehre unabhängig vom logischen Satz vom ausgeschlossenen Dritten. Erster Teil, Allgemeine Mengenlehre”, KNAW Verhandelingen, 5: 1–43. (Scholar)
  • 1919A, “Begründung der Mengenlehre unabhängig vom logischen Satz vom ausgeschlossenen Dritten. Zweiter Teil, Theorie der Punktmengen”, KNAW Verhandelingen, 7: 1–33. (Scholar)
  • 1919D, “ Intuitionistische Mengenlehre ”, Jahresb. D.M.V., 28: 203–208. English translation in Mancosu 1998 pp. 23–27. (Scholar)
  • 1921A, “Besitzt jede reelle Zahl eine Dezimalbruchentwicklung?”, Mathematische Annalen, 83: 201–210. English translation in Mancosu 1998 pp. 28–35. (Scholar)
  • 1924N, “Über die Bedeutung des Satzes vom ausgeschlossenen Dritten in der Mathematik, insbesondere in der Funktionentheorie”, Journal für die reine und angewandte Mathematik, 154: 1–7. English translation in van Heijenoort 1967, pp. 335–341. (Scholar)
  • 1927B, “Über Definitionsbereiche von Funktionen”, Mathematische Annalen, 97: 60–75. English translation of sections 1–3 in van Heijenoort 1967, pp. 457–463. (Scholar)
  • 1928A2, “Intuitionistische Betrachtungen über den Formalismus”, KNAW Proceedings, 31: 374–379. English translation in Mancosu 1998, pp. 40–44. (Scholar)
  • 1929A, “Mathematik, Wissenschaft und Sprache”, Monatshefte für Mathematik und Physik, 36: 153–164. English translation in Mancosu 1998, pp.45–53. (Scholar)
  • 1930A, Die Struktur des Kontinuums, Wien: Komitee zur Veranstaltung von Gastvorträgen ausländischer Gelehrter der exakten Wissenschaften. English translation in Mancosu 1998, pp. 54–63.
  • 1933A2, “Willen, weten, spreken”, in De Uitdrukkingswijze der Wetenschap, L.E.J. Brouwer et al., Groningen: Noordhoff, 45–63. English translation in van Stigt 1990, pp. 418–431. (Scholar)
  • 1946B, “Toespraak van Prof.Dr. L.E.J. Brouwer en antwoord van Prof.Dr. G. Mannoury”, Jaarboek der Universiteit van Amsterdam 1946–1947, II. English translation of Brouwer’s part in Brouwer, 1975, pp. 472–476. English translation of Mannoury’s reply: Synthese, 5: 514–515. (Scholar)
  • 1948A, “Essentieel negatieve eigenschappen”, Indagationes Mathematicae, 10: 322–323. English translation in Brouwer, 1975, pp. 478–479. (Scholar)
  • 1949A, “De non-aequivalentie van de constructieve en de negatieve orderelatie in het continuum”, Indagationes Mathematicae, 11: 37–39. English translation in Brouwer, 1975, pp. 495–496. (Scholar)
  • 1949B, “Contradictoriteit der elementaire meetkunde”, KNAW Proc., 52: 315–316. English translation in Brouwer, 1975, pp. 497–498. (Scholar)
  • 1949C, “Consciousness, philosophy and mathematics”, Proceedings of the 10th International Congress of Philosophy, Amsterdam 1948, 3: 1235–1249. (Scholar)
  • 1954F, “An example of contradictority in classical theory of functions”, Indag. Math., 16: 204–205. (Scholar)
  • 1955, “The effect of intuitionism on classical algebra of logic”, Proceedings of the Royal Irish Academy, 57: 113–116. (Scholar)

Cited primary texts by others

Secondary Literature

  • Dubucs, J.-P., 1988, “L.E.J. Brouwer : Topologie et constructivisme”, Revue d’histoire des sciences, 41(2): 133–155.
    • An analysis of the relation between Brouwer’s topological work and his constructivist foundations. (Scholar)
  • Dummett, M., 1977, Elements of Intuitionism, Oxford: Oxford University Press. 2nd, revised edition, 2000, Oxford: Clarendon Press.
    • An overview of intuitionism. Philosophically, it seems closer to Wittgenstein than to Brouwer. (Scholar)
  • Franchella, M., 2015, “Brouwer and Nietzsche: Views about Life, Views about Logic”, History and Philosophy of Logic, 36(4): 367–391.
    • A comparison of Nietschze’s and Brouwer’s critical views on the role of logic. (Scholar)
  • Hesseling, D.E., 2003, Gnomes in the Fog. The Reception of Brouwer’s Intuitionism in the 1920s, Basel: Birkhauser.
    • A detailed historical discussion of the reactions to Brouwer’s mature intuitionism during the foundational debate. (Scholar)
  • Heyting, A., 1956, Intuitionism. An introduction, Amsterdam: North-Holland. 2nd, revised edition, 1966. 3rd, revised edition, 1971.
    • Probably the most influential book on the subject ever written. In a style that is more down-to-earth and oecumenical than Brouwer’s, Heyting presents the intuitionistic versions of various basic subjects in everyday mathematics. Brouwer and Heyting have some philosophical disagreements that make a difference in their appreciation of some aspects of intuitionistic mathematics. No comments of Brouwer on this book are known. (Scholar)
  • Kirkels, M., 2019, Gerrit Mannoury (1867–1956). Een Relativistisch Denker, Rotterdam: Erasmus Universiteit.
    • A thorough biography of the remarkable man who was Brouwer’s teacher and then lifelong close friend; in Dutch. (Scholar)
  • Largeault, J., 1993, Intuition et Intuitionisme, Paris: Vrin.
    • An overview of intuitionism, staying close to Brouwer, and showing a good sense of the historical background of Brouwer’s notion of intuition. (Scholar)
  • Placek, T., 1999, Mathematical Intuitionism and Intersubjectivity, Dordrecht: Kluwer.
    • A comparison of the arguments for intuitionism advanced by, respectively, Brouwer, Heyting, and Dummett, in particular with respect to the possibility of intersubjective validity of intuitionistic mathematics. (Scholar)
  • Schmitz, H.W., 1990, De Hollandse Significa. Een Reconstructie van de Geschiedenis van 1892 tot 1926, Assen: van Gorcum.
    • A detailed monograph on the development of the Signific Movement in the Netherlands, in Dutch (translated from the author’s German Habilitationsschrift). (Scholar)
  • Schmitz, H.W., ed., 1990, Essays on Significs: Papers Presented on the Occasion of the 150th Anniversary of the Birth of Victoria Lady Welby, 1837–1912, Amsterdam: John Benjamins.
    • Historical and systematical essays on Lady Welby, the relations between significs and semiotics, and the Signific Movement in the Netherlands. (Scholar)
  • Troelstra, A., 1969, Principles of Intuitionism, Heidelberg: Springer.
    • The first exposition of intuitionism after those by Brouwer and Heyting. While strongly mathematically oriented, it shows a strong appreciation of philosophical aspects. Written as lectures notes for the conference on Intuitionism and Proof Theory, Buffalo, 1968, after the author spent the academic year 1966–1967 with Kreisel. (Scholar)
  • van Atten, M., 2004, On Brouwer, Belmont (CA): Wadsworth.
    • A philosophical introduction to intuitionism as conceived by Brouwer, with extensive treatments of the proof of the bar theorem, the creating subject, and intersubjectivity. (Scholar)
  • van Atten, M., 2018, “The Creating Subject, the Brouwer-Kripke Schema, and infinite proofs”, Indagationes Mathematicae, 29(6): 1565–1636.
    • A discussion of philosophical, mathematical, and historical aspects of Brouwer’s Creating Subject arguments. Issues 29(1) and 29(6) of Indagationes make up a voluminous virtual special issue in commemoration of the 50th anniversary of Brouwer’s death. (Scholar)
  • van Atten, M., Boldini, P., Bourdeau, M., and Heinzmann, G., eds., 2008, One Hundred Years of Intuitionism (1907–2007). The Cerisy Conference, Basel: Birkhäuser.
    • Part I consists of a number of historical and systematical papers on Brouwer and Brouwerian intuitionism. Part II contains, among others, two papers on Brouwer in relation to French recursors of intuitionism. Part III includes a paper on the Hilbert-Brouwer controversy from a historical-mathematical perspective. (Scholar)
  • van Atten, M. and Tragesser, R., “Mysticism and Mathematics: Brouwer, Gödel and the Common Core Thesis”, in Klarheit in Religionsdingen, Deppert, W. & Rahnfeld, M., eds., Leipzig: Leipziger Universitatsverlag, 145–160.
    • A comparison of Brouwer’s and Gödel’s interest in mysticism and of their views on its relation to mathematics. (Scholar)
  • van Dalen, D., 1999/2005, Mystic, Geometer, and Intuitionist, 2 volumes, Oxford: Clarendon Press.
    • The standard biography of Brouwer. Volume 1, The Dawning Revolution, covers the years 1881–1928, volume 2, Hope and Disillusion, covers 1929–1966. (Scholar)
  • van Dalen, D., 2001, L.E.J. Brouwer 1881–1966. Een Biografie. Het Heldere Licht van de Wiskunde, Amsterdam: Bert Bakker.
    • A popular biography in 1 volume, in Dutch. (Scholar)
  • van Dalen, D., 2013, L.E.J. Brouwer—Topologist, Intuitionist, Philosopher. How Mathematics Is Rooted in Life, London: Springer.
    • A somewhat revised version in 1 volume of the biography (van Dalen 1999/2005). (Scholar)
  • van Stigt, W., 1990, Brouwer’s Intuitionism, Amsterdam: North-Holland.
    • Contains interesting philosophical discussions and gives English translations of material from the Brouwer archive. The biographical sketch has now been superseded by (van Dalen, 1999/2005) and (van Dalen, 2001). Van Stigt also contributed to the introductions to the papers on intuitionism in Mancosu 1998 (see above). (Scholar)

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