TY - JOUR

T1 - The Paradox of Classical Reasoning

AU - Bolotin, Arkady

N1 - Funding Information:
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.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022/8/1

Y1 - 2022/8/1

N2 - 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.

AB - 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.

KW - Copenhagen interpretation

KW - Hierarchy of physics theories

KW - Hilbert space theory

KW - Instrumentalist description

KW - Quantum logic

KW - Set theory

KW - Tarski’s theory of truth

UR - http://www.scopus.com/inward/record.url?scp=85139779484&partnerID=8YFLogxK

U2 - 10.1007/s10701-022-00604-7

DO - 10.1007/s10701-022-00604-7

M3 - Article

AN - SCOPUS:85139779484

SN - 0015-9018

VL - 52

JO - Foundations of Physics

JF - Foundations of Physics

IS - 4

M1 - 87

ER -