Constructivize

These systems can be compared in at least two different ways, depending on whether one's chief concern is to constructivize classical mathematics or, rather, to develop, on its own terms, a completely constructive mathematics.

In classical mathematics the continuum is conceived of as the totality of its points. One might therefore, like Markov and his school, try to constructivize the theory of the continuum by looking upon it as the totality of its constructive points.

In order to constructivize a mathematical notion we consider its classical definition written in terms of the arithmetic of natural numbers. Then we relativize the existential quantifiers according to the following well known scheme.

But just as Ivanov regarded art as one component of a universal philosophy for transforming the world, so the artists of the avant-garde also hoped to "suprematize" and "constructivize" all aspects of reality.

Harmony considerations tend to favour some form of intuitionistic logic over classical logic. That is, harmony constructivizes.

Seeing opportunity to expand the constructivist idea and process to an entire organization, such as a school, or a school district, I suggested strategies to constructivize the total school, as well as the classroom, team, or learning community.