Brouwer on ‘hypotheses’ and the middle Wittgenstein

Abstract

Wittgenstein returned to Cambridge in January 1929. The earliest manuscripts of that period which we possess, MS 105, date from that month, opening on a few personal remarks, including a comment on his conversations with Ramsey, followed by remarks where we see Wittgenstein exploring new ideas about topics not covered in the Tractatus, such as the nature of irrational numbers or the contrast between a physical and phenomenological description of visual space. Whence these new topics and ideas? It is, exegetically speaking, natural to look for an answer in the prehistory of MS 105. Alas, any earlier manuscript, if any, must be assumed either destroyed or lost. An obvious starting point is Brouwer’s lectures in Vienna in March 1928, ‘Mathematik, Wissenschaft und Sprache’ on the 10th (Brouwer 1929A) and ‘Die Struktur des Kontinuums’ on the 14th (Brouwer 1930A)². It appears that Wittgenstein only attended the first one, but it was reported by a witness, Herbert Feigl, that it spurred him into coming back to philosophy. According to Feigl: When the Dutch mathematician Luitzen Egbertus Jan Brouwer was scheduled to lecture on intuitionism in mathematics in Vienna, Waismann and I managed to coax Wittgenstein, after much resistance, to join us in attending the lecture. When, afterwards, Wittgenstein went to a café with us, a great event took place. Suddenly and very volubly Wittgenstein began talking philosophy—at great length. Perhaps this was the turning point, for ever since that time, 1929, when he moved to Cambridge University Wittgenstein was a philosopher again. (Feigl 1981, p.64)

Ich werde scheinbar, wider meinen Willen, auf die Arthmetik zurückgeworfen. L. Wittgenstein, January 1929¹.

‘It seems that I am thrown back, against my will, to arithmetic.’

English translations under the titles ‘Mathematics, Science, and Language’ and ‘The Structure of the Continuum’ are available in (Ewald 1996, vol. 2, pp. 1175–1185, 1186–1197) and in (Mancosu 1998, pp. 45–53, 54–63); I am using the latter, refer to ‘Mathematics, Science, and Language’ by ‘MSL’, and to the original German by ‘MWS’.