Math Forum Discussions

Keith Ramsay

Posts: 1,745
Registered: 12/6/04

Re: intuitionism
Posted: Oct 29, 2009 3:38 AM

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On Oct 28, 3:04 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
|(I'm sure you know all this
|stuff better than I do, but perhaps these random remarks amuse or
|benefit some random reader.)

I think you've made a good observation here about the way
Brouwerian intuitionism is distinctive. In 1970 Bishop
seems to have felt that Brouwer went overboard with his
concern about philosophical minutia about the continuum.
I have a feeling though that for most of us it is our
failure to really "get" Brouwer's point of view that
makes a thing like the theory of free choice sequences
seem like a weird little side-light in Brouwer's thinking
and the thinking of his mathematical descendants. I have
an inkling that the connection between sequences and the
process of a series of notions presenting themselves to
one's intuition, in Brouwer's mind, was quite a deep
thing. I just don't see how to develop it.

I think he might accuse someone like me of being too
technically oriented. I feel looking at some of these
things like there's just not enough noodles in this
broth to make it worth spending a lot of time on it.
Perhaps it is because I have a bias toward mathematics
that is more like classical, 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.

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.

Keith Ramsay