将不可判定性视为系统结构性约束，揭示其普遍影响。
Systemic Constraints of Undecidability
- 提出因果嵌入概念，证明子系统继承不可判定性
- 不可判定性普遍存在于自然与人工系统中，限制预测与认知
- 挑战通过架构突破计算极限的幻想，适合理论计算机学者
本文提出系统不可判定性的理论，将不可计算性重新定义为系统整体的结构性属性，而非特定函数或问题的局部特征。我们定义了因果嵌入的概念，并证明了一个闭包原理：任何在功能上参与不可判定系统计算的子系统，必然继承其不可判定性。该结果将不可判定性定位为对预测、建模及知识获取的普遍约束，适用于自然与人工系统。本框架削弱了预言机模仿的可能性，挑战了通过架构创新可突破计算极限的观点。通过将经典结果推广至动态系统语境，本文拓展了哥德尔、图灵与查廷的逻辑轨迹，为可计算性的拓扑及其与科学知识边界的关系提供了新视角。
原文摘要 · Abstract (English)
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a closure principle: any subsystem that participates functionally in the computation of an undecidable system inherits its undecidability. This result positions undecidability as a pervasive constraint on prediction, modeling, and epistemic access in both natural and artificial systems. Our framework disarms oracle mimicry and challenges the view that computational limits can be circumvented through architectural innovation. By generalizing classical results into a dynamic systems context, this work augments the logical trajectory of Gödel, Turing, and Chaitin, offering a new perspective of the topology of computability and its interrelation to the boundaries of scientific knowledge.
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