Abstract
The two main topics here are Brouwer’s Berlin lectures and the Vienna lectures. The Berlin lectures were held in 1927 on invitation of the math faculty. Reports tell us that Brouwer made furor in Berlin, students form all over the country flocked to Berlin to hear the mysterious great man. Students called themselves putschists, in reaction to a reaction of Hilbert to Weyl’s battle cry ‘And Brouwer, that is the revolution’. The future for intuitionism looked rosy for a while.
A year later Brouwer lectured in Vienna, this was essentially the first public exposition of his philosophy since his dissertation. Wittgenstein attended the lecture, which influenced his return to philosophy.
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Notes
- 1.
- 2.
The reception of the papers was, judging from the review in the Fortschritte, rather nondescript. The reviewer, Arthur Rosenthal, one of Brouwer’s topology friends, restricted himself to a few lines, referring to his earlier review of the old Begründungs-papers. But even that review of more than two pages did little to lift the veil of mystery that covered Brouwer’s writings (Jahrbuch der Fortschritte der Mathematik 47, p. 171, 51, p. 164).
- 3.
Virtuelle und unerweiterbare Ordnung, Brouwer (1927c). A proof of the main theorem of this paper already occurs in Brouwer’s classroom notes of 1925.
- 4.
Cf. p. 316 and Brouwer (1921a).
- 5.
- 6.
Brouwer (1925b).
- 7.
Ibid.
- 8.
Brouwer (1926b).
- 9.
Brouwer (1927b), also cf. pp. 372, 373.
- 10.
Of course, also for later branches of constructive mathematics.
- 11.
‘Congruent’ means roughly ‘identical up to a double negation’.
- 12.
- 13.
Cf. the Denjoy affair, p. 336 ff.
- 14.
Cf. p. 316 ff.
- 15.
Forman (1986), see also p. 316 ff.
- 16.
Reichsverband deutscher mathematischer Gesellschaften und Vereine.
- 17.
For further information and literature, cf. Mehrtens (1984).
- 18.
- 19.
van der Waerden (1928).
- 20.
Brouwer to Curators of the UVA, 10 January 1927.
- 21.
According to Freudenthal, Loewner’s approach was far too complicated—‘In short, a catastrophe’, see Freudenthal (1987a).
- 22.
Weil (1991).
- 23.
Informal meeting after a lecture.
- 24.
Verkrachen Sie sich mit ihm.
- 25.
Brouwer to Alexandrov, 3.II.1927.
- 26.
Henri Borel to Brouwer, 19.I.1927.
- 27.
Frederik Van Eeden to Brouwer, 16.I.1927.
- 28.
Mannoury to Brouwer, 26.I.1927.
- 29.
A somewhat outdated term for ‘symbolic (universal) language’, often used by Mannoury.
- 30.
Just had opened the Spa Jungborn in 1896. The German vicar Felke followed Just’s example and opened in 1915 his own Spa, organised in accordance with Just’s ideas. Brouwer referred to Felke in his ‘Life, Art, and Mysticism’.
- 31.
Brouwer to Hopf, 21.XII.1925. Cf. p. 154 ff.
- 32.
Geschichtliche Entwicklung der Topologie, Feigl (1928).
- 33.
There were more rumours about Brouwer’s behaviour and personality than about most mathematicians, some of them absolutely unfounded. I recall that in the sixties a leading mathematician gave a talk at a monthly meeting of the Dutch Math. Soc., who at one point remarked ‘Brouwer no longer believed in the real numbers, did he?’
- 34.
Brouwer to Hopf, 8.III.1927.
- 35.
Haalmeijer and Schogt (1927).
- 36.
Eva Wernicke to Brouwer, 30.III.1927.
- 37.
Brouwer to Heyting, 17.VII.1928.
- 38.
Brouwer (1992).
- 39.
A partially ordered set is ordered under Brouwer’s definition if a≠b→a<b∨b<a, this is weaker than the trichotomy property. Brouwer (1992), p. 50.
- 40.
Brouwer (1950).
- 41.
Brouwer (1952a).
- 42.
Jubiläumsband I. Aus Anlass des 100 jährigen Bestehens.
- 43.
Henri Borel to Brouwer, 26.III.1927.
- 44.
Brouwer to Eva Wernicke, 22.XII.1927.
- 45.
For the Koebe-affair, see p. 180 ff.
- 46.
Alexandrov to Hopf, 15.II.1927.
- 47.
Alexandrov to Brouwer, 15.III.1927. Shatunovsky may have approached Mrs. Ehrenfest for an introduction to Brouwer.
- 48.
Brouwer to Mrs. Ehrenfest, 3.VII.1927.
- 49.
A gifted ‘Eigenbrötler’.
- 50.
Cf. p. 379.
- 51.
The paper was also published in the reports of the Berlin Academy, Brouwer (1928c).
- 52.
Lize to Louise, 27.XI.1949. Lize spoke of ‘a nitwit of a doctor’.
- 53.
This was indeed an incredible feat, the savings amounted to more than twice the annual income of a full professor.
- 54.
Cf. p. 59.
- 55.
Interview, H.J. Looman.
- 56.
Aldert had been very successful in his profession. After his Ph.D. in 1910 (Delft) he worked as a geologist in the Dutch Indies (now Indonesia); in 1918 he got a chair in Delft, and in 1925 he was an exchange professor in Michigan. Utrecht made him an extraordinary professor in 1925. The Royal Academy in Amsterdam elected him a member in 1922. His chair in Amsterdam was in ‘general and practical petrology’.
- 57.
- 58.
Cf. Plisko (1988b, 1988a), Troelstra and van Dalen (1988a), p. 59; Troelstra (1978); van Heijenoort (1967). Another famous Russian, Molotov, also proposed a translation, albeit in a completely different setting. According to Leonard Mosley in Dulles, 1978, Molotov once during a negotiation said ‘I propose that we insert a “not” before every verb in the text’.
- 59.
Cf. Church (1928).
- 60.
Lize ran the pharmacy, but Brouwer was formally the owner. See pp. 53 ff., 195 ff.
- 61.
There were extensive grounds behind the building, stretching all the way into what is now the Vondelpark.
- 62.
Bonger was a through and through socialist. Later he became a violent opponent of national socialism, and at the German invasion of Holland he committed suicide rather than fall in the hands of his arch enemies.
- 63.
Cf. Mannoury (1930), e.g. the executions following the assassination of Wojkof.
- 64.
Prof. Van der Hoeve, the same person who met Urysohn and Alexandrov in Norway.
- 65.
- 66.
Komitee zur Veranstaltung von Gastvorträge ausländischer Gelehrter der exacten Wissenschaften.
- 67.
- 68.
Cf. p. 92 ff.
- 69.
In German Brouwer uses ‘einzelner Mensch’. We will use ‘individual’. It is important to note that in this paper Brouwer does not take a solipsist position.
- 70.
In Brouwer (1933a) Brouwer uses ‘tijdsgewaarwording’ and ‘causale aandacht’, translated as ‘perception of time’ and ‘causal attention’.
- 71.
See pp. 66, 88 ff. and Brouwer (1905), p. 19.
- 72.
Which much later is called the ‘cunning act’, Brouwer (1948b).
- 73.
The terminology may seem confusing. Brouwer had observed that PEM itself is not contradictory. For consider some open problem, e.g. the Riemann hypothesis R. Then if ‘R or not-R’ were contradictory, both R and not-R would yield contradictions, So both not-R and not-not-R would be true, which is impossible. Hence the negation of PEM for a single statement is consistent. The same argument works for finitely many statements, R 1∧R 2∧⋯∧R n . However for an infinite set of statements (the extended case of PEM) this is no longer the case. Consider ‘for all real numbers x, x is rational or x is irrational’. This cannot be true, because it would yield a decomposition of the continuum, which is impossible, cf. p. 375.
- 74.
Menger (1994), Chap. X.
- 75.
- 76.
- 77.
Cf. van Dalen (1999a).
- 78.
Wittgenstein (1984), no. 179.
- 79.
Wittgenstein’s arguments, however, should be distinguished from those of Hilbert, Brouwer, Heyting, and Martin-Löf.
- 80.
pp. 101, 313.
- 81.
Cf. p. 795. Finch to Van Dalen, 10.X.1990.
- 82.
See Köhler (1991). There is however a letter from Gödel to the American Philosophical Society of 19.I.1967 in which he says ‘I have seen Brouwer only on one occasion, in 1953, when he came to Princeton for a brief visit’. If ‘seen’ means ‘met’ there is no contradiction.
- 83.
Gödel über Unerschöpflichkeit der Mathematik. Erst danach Brouwer Wiener Vortrag zu diesen Gedanken angeregt worden’. Carnap 14.II.1928 and 23.XII.1929. See also Wang (1987), p. 50.
- 84.
The Amsterdamer Vorträge were published in Husserl (1997).
- 85.
Husserl to Heidegger, 5.V.1928, Husserl (1994).
- 86.
Hier tummelt sich jetzt Husserl herum, wobei ich stark mit herangezogen werde. Er findet Frä ulein Gawehn den intelligensten Kopf, der er in Holland angetroffen hat.
- 87.
The oral exam was in 1925. Rosenthal and Liebmann examined her in mathematics, Lenard in physics and Jaspers in philosophy.
- 88.
Rector Oslo University to Brouwer, 19.II.1929.
- 89.
For details, see Schmitz (1990a), 6.3.
- 90.
- 91.
Oral communication, C. Vuysje-Mannoury.
- 92.
He got a mortgage of 29,000 guilders.
- 93.
Interview R.A.F. Guasco.
- 94.
Suriname place or square.
- 95.
The transaction was concluded on 2 April 1930.
- 96.
Lize to Louise, 17.V.1935.
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van Dalen, D. (2013). From Berlin to Vienna. In: L.E.J. Brouwer – Topologist, Intuitionist, Philosopher. Springer, London. https://doi.org/10.1007/978-1-4471-4616-2_13
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