БЕСКОНЕЧНОСТЬ АКТУАЛЬНАЯ И ПОТЕНЦИАЛЬНАЯ

Infinity, Real and Potential

Two ways of perceiving the infinite. In mathematics, Real Infinity is understood as an infinite multitude, complete and realised (for example, the multitude of all natural numbers). Potential Infinity is understood as an infinite quantity that can increase (decrease) endlessly and become greater (smaller) than any given, predetermined quantity.

The paradoxes of Cantor's theory of sets undermined the instinctive belief of mathematicians in the concept of Real Infinity, and some of them asserted that only Potential Infinity is realisable. These latter consider Real Infinity contradictory because once an infinite quantity is realised it is finite and not infinite. The struggle between the two conceptions is still going on.

The solution to it is to be found in the real world. The material world is infinite in space and time, not potentially but in reality, it is not becoming infinite but has always been such. At the same time it is constantly developing and contains within itself the possibility of unlimited changes. Its infinity is, therefore, also potential. The unity of Real Infinity and Potential Infinity is also observed in the structure of matter. Research methods, to reflect this unity, must be based on a dialectical approach to Real Infinity and Potential Infinity.