 In this passage, Wittgenstein is alluding to Brouwer, who, as early as 1907 and 1908, states, first, that “the question of the validity of the principium tertii exclusi is equivalent to the question whether unsolvable mathematical problems exist”, second, that “[t]here is not a shred of a proof for the conviction… that there exist no unsolvable mathematical problems”, and, third, that there are meaningful propositions/‘questions’, such as “Do there occur in the decimal expansion of \(\pi\) infinitely many pairs of consecutive equal digits?”, to which the Law of the Excluded Middle does not apply because “it must be considered as uncertain whether problems like [this] are solvable” (Brouwer, 1908 [1975: 109–110]). “A fortiori it is not certain that any mathematical problem can either be solved or proved to be unsolvable”, Brouwer says (1907 [1975: 79]), “though HILBERT, in ‘Mathematische Probleme’, believes that every mathematician is deeply convinced of it”.