The Paradox of Classical Reasoning

Intuitively, the more powerful a theory is, greater variety and quantity of ideas can be expressed through its formal language. Therefore, when comparing two theories concerning same subject, it seems only reasonable to compare expressive powers their languages. On condition that quantum mechanical description is universal so applied macroscopic systems, required than classical mechanics. This implies language Hilbert space must Zermelo-Fraenkel set (the formalism). However, as shown in paper, such requirement cannot met. As result, formalisms hierarchical relation, include one another. fact puts doubt quantum-classical correspondence undermines reductionist approach physical world.