ABSTRACT
Constructivisability of a mathematical theory signifies the possibility of isolating the constructions of objects from their existence proofs. Consequently, classical logic cannot lead us to the non-constructivisability of the theorems proved either in geometry, or in geometry supplemented with algebraic operations on the real numbers, but without the explicit mention of the integers as a set. In any classical proof of these theorems one may mark out the construction and its substantiation, which may be carried out, in particular, also by the method of “indirect proof”. While examining the problem of constructivisability, it is possible to mark out three major trends: pseudo-classical, non-classical and significative. Constructivism tries to unite constructivisability with maximum retention of the classical mathematical paradigm. To some extent constructivism is as Platonist, as classical mathematics. The intuitionist theories are more abstract and they too can give rise to an entire family of more concrete constructivist theories.
