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


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 sidelight 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



