[FOM] philosophical literature on intuitionism
mark van atten
Mark.vanAtten at univ-paris1.fr
Tue Oct 14 10:19:48 EDT 2008
Thomas Forster Mon Oct 13 18:27:15 EDT 2008 wrote:
> I do remember reading that Brouwer was
> hostile to attempts to axiomatise constructive logic..
When Heyting showed Brouwer the manuscript of his (partial)
formalisation of intuitionistic logic, Brouwer wrote to him on July
17, 1928, that he found this `extraordinarily interesting', and
"By now I have already begun to appreciate your work so much, that I
should like to request that you revise it in German for the
Mathematische Annalen (preferably somewhat extended rather than
shortened)." (The paper would instead be published in the proceedings
of the Prussian Academy of Sciences.)
Interestingly, Brouwer also suggested (with an eye on the
formalization of the theory of choice sequences)
"And, with an eye on §13, perhaps also the notion of `law' can be formalized."
Also, in papers from the 1920s Brouwer was quite optimistic about
Hilbert's program for a consistency proof of formalized classical
But, on his conception of the relation between logic and mathematics,
work in logic cannot, as such, lead to new contentual mathematics.
On the other hand, Brouwer was well aware of the practical need for
language, both in order to communicate mathematical results to others
and to help ourselves in remembering and reconstructing our previous
results. Only an ideal mathematician with perfect and unlimited memory
would be able to practice pure mathematics without recourse to
language. Clearly, given these two practical functions of language,
the more precise the language is, the better.
For references and further details, see
in particular sections 2.1, 3.5, and 4.2.
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