FOM: Wittegenstein and Brouwer (fwd)

Stephen Ferguson srf1 at
Fri Feb 6 11:06:29 EST 1998

  Bill Tait writes:

   >The influence of Brouwer, often refered to, puzzles me. The analysis of 
   >`following a rule' in _Phil Investigations_ would seem, whether 
   >accidently or not, to be aimed precisely at Brouwer's doctrine of 
   >mathematics as a lnanguage-less activity.

Torkel Franzen replied:

>  Undoubtedly Wittgenstein's thinking about rules is incompatible with
>Brouwer's doctrines. Nevertheless, (i) there is much that is
>reminiscent of Brouwer in Wittgenstein's earlier writings, in
>particular in the Philosophical Grammar and the Philosophical Remarks,
>and (ii) according to contemporary sources, Brouwer made a considerable
>impression on Wittgenstein. Thus, in Monk's biography:
>     In March 1928 Brouwer came to Vienna to deliver a lecture entitled
>     'Mathematics, Science and Language', which Wittgenstein attended,
>     together with Waismann and Feigl, and, reports Feigl:
> was fascinating to behold the change that had come over
>     Wittgenstein that evening...he became extremely voluble and began
>     sketching ideas that were the beginnings of his later writings..."

I always took Wittgenstein's reaction to Brouwer's talk to be as B.T puts
it, a negative reaction. Sure, Wittgenstein agrees with Brouwer that
mathematics is a creation of man, but his anti-platonist line looks for
all the world like an account of what Brouwer *should have said*, i.e. it
gives the proper shape to an objection to platonism, which Brouwer's
clearly isn't. Wittgenstein never mentions Brouwer by name in his
discussion of rule following, but then he never refers to Kant in the
Tractatus, when he is critcising his views there: so lack of naming his
does not seem to be much of a clue. But the time of writing (especially
RFM) and the concentration on language and community are just too much of
a coincidence for Wittgenstein's ideas not to be aimed at Brouwer. 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.

There is, as far as I can tell, no English translation of the talk that
Brouwer gave (Mathematik, Wissenschaft und Sprache, in collected works
pp417-28). I think it is very important, if not for Brouwer scholarhisp,
but for Wittgenstein scholars. Anyone interested?

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

All the best,

Stephen Ferguson
			27, North St, St Andrews, KY16 9PW
			(01334) 474437
			Logic and Metaphysics, The University, 
			St Andrews, KY16 9AL
			(01334) 462484

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