FOM: Wittegenstein and Brouwer (fwd)

Torkel Franzen torkel at
Sat Feb 7 07:13:11 EST 1998

Stephen Ferguson says:

  >Isn't it more plausible to think that Wittgenstein started writing
  >because he was irritated by people feteing Brouwer and what he
  >must have considered wrong ideas, rather than thinking that he was
  >in agreement with those thoughts? Wittgenstein was after all,
  >non-revisionist about mathematics (and indeed all practices) contra Brouwer.

  Not, it's not at all plausible. Nor is it true that "Wittgenstein was
a non-revisionist about mathematics", simpliciter. As I mentioned before,
in his earlier writings he made quite explicitly revisionist remarks.
It mustn't be assumed that Wittgenstein, at the time when he was
writing about rules in PI, had the same outlook as when he was writing
the Philosophical Grammar or the Philosophical Remarks.

  >ps I'm pretty certain Go/"del was also supposed to have been at this
  >lecture of Brouwer's (Wang mentions it, I think)

  Yes, according to Wang, Brouwer gave two talks in Vienna that spring,
"Mathematik, Wissenschaft und Sprache" and "Die Struktur des
Kontinuums". According to Wang, "It appears certain that Godel must have
heard the two lectures." Godel also saw Wittgenstein once, probably
at the first of the two lectures.

  Bill Tait says:

   >As for (i), I carefully referred only to _Philsophical
   >Investigations_. There is good evidence that W changed his views about
   >mathematics through the 30's.

  Yes. I mistakenly took your comment that "The influence of Brouwer,
often referred to, puzzles me" to mean that you were puzzled by the
assertion that there is such an influence. This influence, if it
exists, is to be found in his pre-PI writings.

   >It is hard in the face of this to think that W was consciously
   >advocating a revisionist conception of mathematics.

  Wittgenstein's comments in this regard were ambiguous and varying. In
the Grammar (or possibly the Remarks - I'm sorry to say that I no longer
have these books available, and so can't substantiate my references)
he makes explicitly revisionist remarks. In his "discussions" with
Turing in 1939, on the other hand, he is careful not to suggest that
anything in mathematics is wrong, but it isn't altogether easy to uphold
the distinction between claiming that set theory is wrong and claiming
that mathematicians present it in a completely misleading way.

  >True, the Feigl report concerns a lecture in 1929; but I see W's
  >critique of rule following in his later writings as a development of
  >Frege's critique of psychologism; and W certainly know of that in
  >1929. Even if he had not begun to think about rule following the
  >psychologistic element in Brouwer's is very explicit (even though it
  >is played down by later exponents of intuitionism).

  We needn't assume that everything in Brouwer's exposition appealed
to Wittgenstein. Indeed a large part of the appeal of the lectures
lay, I suspect, in their passion and originality. But when we consider
Wittgenstein's remarks about infinity and about such classics as the
occurrences of sevens in the decimal expansion of pi, there is much in
those remarks that, to put the matter in more or less neutral terms,
would have been very congenial to Brouwer.

Torkel Franzen

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