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The Paradox of Classical Reasoning

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Abstract

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.

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Acknowledgements

The author wishes to thank the anonymous referee for the productive comments and interesting remarks that helped offset shortcomings of a draft of this paper.

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  1. Ben-Gurion University of the Negev, Beersheba, Israel

    Arkady Bolotin

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Bolotin, A. The Paradox of Classical Reasoning. Found Phys 52, 87 (2022). https://doi.org/10.1007/s10701-022-00604-7

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