[FOM] Re: Constructive analysis

[Ayan Mahalanobis]

On Thu, 5 Sep 2002, Bas Spitters wrote:


I don't like your interpretation that BISH is the common core of INT RUSS 
... because whatever one can prove in BISH is simultaneously proved in 
INT. 
You know better than me on this topic, so correct me if I am wrong, the spirit 
of BISH is completely different than that of INT and  they have very 
little common interaction except in meta theory. 

As I understand it (again correct me if I am wrong) BISH is more like 
doing classical mathematics constructively and I sometime wonder why would 
a constructivist be interested in that. The fundamental reason of doing 
constructive mathematics is meaning as I understood it which is a product 
of dissatisfaction from classical math. Then to embrace it as a guideline 
is self-defeating to me.

--Ayan


> Dear Steve,
> 
> 
> May I suggest to look at:
> Bridges & Richman, "Varieties of constructive mathematics"
> to start with.
> 
> 
> The picture that is painted there is the following:
> 
> 
> CLASS   INT      RUSS
>      \         |           /
>             BISH
> 
> 
> Where 
> CLASS is classical mathemathics
> INT is intuitionistic mathematics
> RUSS is Russian recursive constructive mathematics
> BISH is Bishop-style mathematics
> 
> 
> So BISH is the common core.