[FOM] end of my response to Bill Tait's reply to "reading the bible with Bill"
Andrej.Bauer at andrej.com
Sat Mar 11 16:55:25 EST 2006
On Saturday 11 March 2006 01:23, Gabriel Stolzenberg wrote:
> > It is possible to understand both classical and constructive
> > mathematics without wearing the blinkers that you call 'mindsets'.
> As I see it, the only way to know whether your claim is true is
> to check out the mindsets. Until you have lived a while in each,
> you can't rule out the possibility of discovering that there is a
> great deal more to understand than you now suppose.
I do not mean to interfere with the interesting discussion, but I would like
to offer my personal experience in this matter.
I was raised a classical mathematician, of course. Then my Ph.D. was about how
to "do computable topology and analysis better". There seemed to be two
communities doing it, the "constructive" mathematicians, and the "computable"
ones. I could understand the computable ones, as they were classical. The
constructive ones were impossible to understand. It took me about two or
three years (with a lot of help from kind people) to begin to understand what
constructive mathematics was.
I definitely think that it is impossible to understand constructive
mathematics by just "reading a classical translation", as Gabriel puts it
eloquently. One needs to immerse oneself in it and start thinking in a
certain way. All the meta-theorems in the world about the relationship
between classical and intuitionistic logic won't help you get the feel for
it. My current plan is to throw my students in the constructive waters and
watch them learn to swim. If you have a better plan on how to raise students,
please let me know.
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