[FOM] end of my response to Bill Tait's reply to "reading the bible with Bill"

[Andrej Bauer]

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.

Andrej