Re the view of my view of classical mathematics that is expressed in "Interview with a Constructive Mathematician."
I do not reject CL (classical) math. Sometimes I accept it, other times I go elsewhere. And far from bemoaning its lack of meaning, I applaud it. That is, I applaud the miracle of being able to create such an astonishing body of mathematics without being able to say what, if anything, it means. To my mind, this is the most remarkable and illuminating feature of CL mathematics. For the practice, meaning doesn't matter. It is created flying blind.
In college, my classmates and I were well aware of this. Math talk sounded intriguingly like a language of objects and their properties. But what were these objects? They didn't seem to be like any others we knew. They were not physical and they were not concepts (understood to reside in the mind). Sometimes, I felt that I almost had them in my grasp but then, like a bar of wet soap, they would slip away. But remarkably, as I already have said, this seemed to have no bearing on mathematical practice.
So, for me, the lack of ordinary meaning (nothing fancy) in CL math is one of its greatest charms. Try squaring this with what was said to be my view of CL in the interview.
When I shift out of the CL mindset, it's because I want to see how certain things appear from the CO (constructive) one, where I am nearly all the time. Why? It's because there are fascinating signs that, by the traditional standards of clarity, beauty, simplicity, explanatory power and application to physics, CO may be superior to CL for the role of mathematics simpliciter: what math majors major in. However, whether or not this is true, there is not a shred of evidence that working CL is, as is universally believed, superior to working CO as judged by any of the same criteria.