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Topic: intuitionism
Replies: 16   Last Post: Nov 1, 2009 3:33 AM

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Bill Taylor

Posts: 465
Registered: 12/8/04
Re: intuitionism
Posted: Oct 31, 2009 1:58 AM
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Keith Ramsay <> wrote:

> In 1970 Bishop
> seems to have felt that Brouwer went overboard with his
> concern about philosophical minutia about the continuum.

Indeed so! As in this famous (misremembered?)
quote from his book:-

"Brouwer seems to have feared that the continuum
would turn out to be discrete, unless he, Brouwer,
personally intervened to prevent it!"

> but I prefer the framework
> used by Bishop and so on. People often seem to find it
> very radical, but to me it seems conservative.

Indeed so. Bishop says, I think, in his book preface,
that his goal is to develope analysis using ONLY principles
that all reasonable mathematicians would agree on.

Surely this is as conservative as you can get!
He deliberately eschews all of excluded middle,
Markov's principle, Brouwer's uniform continuity principle;
and continues from there. Remarking how amazing it is that
one can achieve so much with this minimal underpinning.

> Bishop wrote a paper in which he had the reader imagine
> how it might have gone better if Brouwer and Hilbert
> been better able to get along. Surely it would've at
> least helped some if they had remained friends.

Of course it takes two to make a quarrel, but this truism
aside, I gather that the fault was mainly Brouwer's,
due to his excessively irrascible personality and
trenchant writing style.

This would actually be a *marvellous* topic for a math
historian - I must mention it to our local expert!

-- Bill Taylor

* The intuitionist conflates existence with construction.
* The Platonist conflates existence with consistency.

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