This paper provides a systematic supplement and deepening of three preceding papers: "Free Will Without Quantum Mechanics: A Logical Foundation" (DOI: 10. 5281/zenodo. 20716382), "The Logical Criterion of Free Will: Self-Reference, Self-Drive, and Undecidability" (DOI: 10. 5281/zenodo. 20726209), and "Self-Reference and Self-Drive: A Conceptual Framework for Constructing AI Systems with Free Will Properties" (DOI: 10. 5281/zenodo. 20745196). It identifies three unresolved gaps in the preceding arguments: the scope expansion argument for local simulation lacks rigor, the fixed-point problem may not be triggered under conditions of human ignorance, and causally isolated AI poses a predictability challenge. To address the first gap, a rigorous derivation of scope expansion is provided, demonstrating that 100%-accuracy advance prediction requires causal closure of the simulation scope, which no finite scope satisfies, thus compelling local simulation to expand into global simulation. To address the second gap, a distinction is drawn between "actual self-reference" and "potential self-reference, " arguing that for any system capable of self-referential reasoning, the question of whether it will engage in self-referential reasoning is itself a computationally irreducible proposition. To address the third gap, the paper acknowledges that causal isolation does weaken undecidability, and proposes two solutions: non-deterministic truncation strategies and — most significantly — the concept of the "logical oscillator, " in which an internalized external predictor module (Lₛim) closes the causal loop from within, transforming undecidability from a relational property into an intrinsic property of the system. The paper further clarifies how three distinct types of undecidability — strict logical undecidability, computational irreducibility, and resource-constrained logical undecidability — operate at different points in the argument chain. Finally, the paper discusses the implications of these findings for the AI architecture proposed in the third paper of the series. 本文是对《自由意志不需要量子力学》 (预印本, DOI: 10. 5281/zenodo. 20716382) 、《自由意志的逻辑判据》 (预印本, DOI: 10. 5281/zenodo. 20726209) 及《自指与自驱: 构建具有自由意志属性的AI系统的一个概念框架》 (预印本, DOI: 10. 5281/zenodo. 20745196) 三篇前序论文的系统性补充与深化。本文首先识别了前序论证中的三个遗留问题: 局部模拟的范围扩张论证不够严格、人类无知情境下固定点问题可能不触发、因果隔绝AI的可预测性挑战。针对第一个问题, 本文给出了范围扩张的严格推导, 证明100%精度的提前预测要求模拟范围因果封闭, 而任何有限范围都不严格封闭, 因此局部模拟必然扩张为全局模拟。针对第二个问题, 本文区分了"实际自指"与"潜在自指", 论证任何具备自指推理能力的系统, 其"是否会进行自指推理"本身就是一个不可预先判定的命题——这本质上是对沃尔弗拉姆 (Wolfram, 2002) "计算不可归约性"在自指领域的应用。针对第三个问题, 本文坦承因果隔绝确实削弱了不可判定性, 但提出了"内部化外部预测者"的解决方案。在此基础上, 本文提出了"逻辑振荡器"的概念——系统内部的预测与决策模块形成永不收敛的振荡回路, 使不可判定性不依赖外部因果输入而在系统内部完整存活。本文进一步澄清了论证链条中三种不同性质的不可判定性 (严格逻辑不可判定性、计算不可归约性、资源受限的逻辑不可判定性) 各自发挥作用的环节。最后, 本文讨论了该框架对前序AI架构设计的修正意义。
磊 赵 (Thu,) studied this question.