论文标题
古典推理的悖论
The paradox of classical reasoning
论文作者
论文摘要
从直觉上讲，理论越强大，想法的多样性和数量就可以通过其形式语言来表达。因此，在比较有关同一主题的两种理论时，比较其形式语言的表达能力似乎是合理的。如果量子力学描述是通用的，并且可以应用于宏观系统，则量子理论必须比经典力学更强大。这意味着希尔伯特空间理论的形式语言必须比zermelo-fraenkel set理论（古典形式主义的语言）更具表现力。但是，如论文所示，无法满足这样的要求。结果，古典和量子形式主义不能处于层次之间的关系，即彼此之间。这一事实使量子古典的对应关系质疑，并破坏了对物理世界的简化主义方法。
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.
