Advertisement

Abstract

Cut off from his international contacts, in particular Göttingen, Brouwer returned to his foundational research. He lectured on The theory of point sets, a course on constructive set theory. In the 1916/17 course he introduced choice sequences and the continuity principle. Now that he saw how to exploit the apparent weakness of his intuitionistic mathematics, he decided to build his new intuitionism in a systematic way. There were some signs during the war years that something was brewing, but the first papers appeared after the war. Part of his efforts were directed at a project called Significs, a study of language and meaning following Lady Welby and Frederik van Eeden, the author and first psychiatrist in Holland. A considerable effort was made to create a group of people with a common interest in the subject, including an International Academy, etc. In the later years of the war Brouwer proposed, together with colleagues, to found a section of the Dutch Airforce (which was hardly existing at the time) for the study and application of air reconnaissance (photogrammetry). Finally, from now on Brouwer was spending more time on university/faculty/Academy matters.

Keywords

Natural Number Royal Academy Choice Sequence International Academy Fundamental Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Bockstaele, P.: Het intuïtionisme bij de Franse wiskundigen. Verh. K. Vlaam. Acad. Wet. XI(32), 999 (1949) MathSciNetGoogle Scholar
  2. Borel, É.: Sur les principes de la théorie des ensembles. In: Castelnuovo, G. (ed.) Atti IV Congr. Intern. Mat. Roma, vol. 1, pp. 15–17. Accad. Naz. Lincei, Roma (1908b) Google Scholar
  3. Borel, É.: Leçons sur la théorie des fonctions, 3rd edn. Gauthier-Villars, Paris (1928) zbMATHGoogle Scholar
  4. Brouwer, L.E.J.: Intuitionism and formalism. Bull. Am. Math. Soc. 20, 81–96 (1913b) MathSciNetzbMATHCrossRefGoogle Scholar
  5. Brouwer, L.E.J.: A. Schoenflies und H. Hahn. Die Entwickelung der Mengenlehre und ihrer Anwendungen, Leipzig und Berlin 1913. Jahresber. Dtsch. Math.-Ver. 23, 78–83 (1914) Google Scholar
  6. Brouwer, L.E.J.: Luchtvaart en photogrammetrie. Avia 6, 29–30 (1916a) Google Scholar
  7. Brouwer, L.E.J.: Luchtvaart en photogrammetrie. Avia 6, 122–124 (1916b) Google Scholar
  8. Brouwer, L.E.J.: Luchtvaart en photogrammetrie. Avia 6, 223–225 (1916c) Google Scholar
  9. Brouwer, L.E.J.: Addenda en corrigenda over de grondslagen der wiskunde. K. Ned. Akad. Wet. Versl. Gewone Vergad. Afd. Natuurkd. 25, 1418–1423 (1917a). Separate sheet with corrections inserted Google Scholar
  10. Brouwer, L.E.J.: Luchtvaart en photogrammetrie. Het Vliegveld, 142–144, 165–167 (1917b) Google Scholar
  11. Brouwer, L.E.J.: Intuitionistische Mengenlehre. Jahresber. Dtsch. Math.-Ver. 28, 203–208 (1919h). Appeared in 1920 zbMATHGoogle Scholar
  12. Brouwer, L.E.J.: Luchtvaart en photogrammetrie, I. Nieuw Arch. Wiskd. 7, 311–331 (1919l) Google Scholar
  13. Cantor, G.: Ueber eine elementare Frage der Mannigfaltigkeitslehre. Jahresber. Dtsch. Math.-Ver. 1, 75–78 (1892) zbMATHGoogle Scholar
  14. Fontijn, J.: Tweespalt. Het leven van Frederik van Eeden tot 1901. Querido, Amsterdam (1990) Google Scholar
  15. Fontijn, J.: Trots verbrijzeld. Het leven van Frederik van Eeden vanaf 1901. Querido, Amsterdam (1996) Google Scholar
  16. Gutkind, E.: Einwand von Erich Gutkind. Meded. Int. Inst. Wijsb. 2, 33 (1919) Google Scholar
  17. Gutkind, E.: Von Freundschaft. In: Liber Amicorum Dr. Frederik van Eeden aangeboden ter gelegenheid van zijn 70ste verjaardag 3 april 1930, pp. 68–69. Maatschappij tot verspreiding van goede en goedkope literatuur, Amsterdam (1930) Google Scholar
  18. Heijerman, E., van der Hoeven, M.J.: Filosofie in Nederland. De Internationale School voor Wijsbegeerte als ontmoetingsplaats 1916–1986. Boom, Meppel (1986) Google Scholar
  19. Hölder, O.: Die mathematische Methode. Logisch erkenntnisstheoretische Untersuchungen im Gebiete der Mathematik, Mechanik und Physik. Springer, Berlin (1924) Google Scholar
  20. Kellermann, H. (ed.): Der Krieg der Geister: eine Auslese deutscher und ausländischer Stimmen. Alexander Dunker Verlag, Weimar (1915) Google Scholar
  21. Mannoury, G.: De Schoonheid der wiskunde als signifisch probleem. Synthese 2, 197–201 (1937) zbMATHCrossRefGoogle Scholar
  22. Mannoury, G.: Handboek der Analytische Significa. Geschiedenis der Begripskritiek. Kroonder, Bussum (1947) Google Scholar
  23. Mannoury, G.: Handboek der Analytische Significa. Hoofdbegrippen en Methoden der Significa. Ontogenese en Fylogenese van het verstandhoudingsapparaat. Kroonder, Bussum (1948) Google Scholar
  24. Mauthner, F.: Beiträge zu einer Kritik der Sprache. J.G. Cotta, Stuttgart (1906). 3 vols. Google Scholar
  25. Richard, J.: Les principes des mathématiques et le probleme des ensembles. Rev. Gén. Sci. Pures Appl. 16, 541 (1905). Transl. in van Heijenoort (1967) Google Scholar
  26. Schmitz, H.W.: Tönnies’ Zeichentheorie zwischen Signifik und Wiener Kreis. In: Clausen, L., Borries, V. (eds.) Tönnies heute. Zur Aktualität von Ferdinand Tönnies, vol. 999, pp. 73–93. Mülau Verlag, Kiel (1985) Google Scholar
  27. Schmitz, H.W.: Frederik van Eeden and the introduction of significs into the Netherlands: from Lady Welby to Mannoury. In: Schmitz, H.W. (ed.) Essays on Significs. Papers Presented on the Occasion of the 150th Birtday of Victoria Lady Welby (1837–1912), vol. 23, pp. 219–246. Benjamins, Philadelphia (1990a) Google Scholar
  28. Schmitz, W.H.: De Hollandse Significa. Van Gorcum, Assen (1990b) Google Scholar
  29. Tönnies, F.: Philosophical terminology (I). Mind 8, 289–332 (1899a) CrossRefGoogle Scholar
  30. Tönnies, F.: Philosophical terminology (II). Mind 8, 467–491 (1899b) CrossRefGoogle Scholar
  31. Tönnies, F.: Philosophical terminology (III). Mind 9, 46–61 (1900) CrossRefGoogle Scholar
  32. Tönnies, F.: Philosophische Terminologie in psychologisch-soziologischer Ansicht. Thomas, Leipzig (1906) Google Scholar
  33. Troelstra, A.S.: On the origin and development of Brouwer’s concept of choice sequence. In: Troelstra, A.S., van Dalen, D. (eds.) The L.E.J. Brouwer Centenary Symposium, vol. 999, pp. 465–486. North-Holland, Amsterdam (1982) CrossRefGoogle Scholar
  34. van Eeden, F.: Dagboek 1878–1923. van Tricht, H.W. (ed.). Tjeenk Willink, Culemborg (1971). 4 vols. Google Scholar
  35. van Eeden, F., Gutkind, E.: Welt–Eroberung durch Helden–Liebe. Schuster & Loeffler, Berlin (1911) Google Scholar
  36. van Everdingen, E.: Zestig Jaar Internationale School van Wijsbergeerte. Van Gorcum, Assen (1976) Google Scholar
  37. Volker (pseud. E. Gutkind). Siderische Geburt. Seraphische Wanderungen vom Tode der Welt zur Taufe der Tat. Karl Schnabel, Berlin (1910) Google Scholar
  38. Zermelo, E.: Beweis dasz jede Mengen wohlgeordnet werden kann. Math. Ann. 59, 514–516 (1904) MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Dirk van Dalen
    • 1
  1. 1.Department of PhilosophyUtrecht UniversityUtrechtNetherlands

Personalised recommendations