The Paradox of Classical Reasoning

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

Original languageAmerican English
Article number87
JournalFoundations of Physics
Issue number4
StatePublished - 1 Aug 2022


  • Copenhagen interpretation
  • Hierarchy of physics theories
  • Hilbert space theory
  • Instrumentalist description
  • Quantum logic
  • Set theory
  • Tarski’s theory of truth

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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