- Comments
- 67 pages, 1 table, Lean 4 verification appendix (machine-checked). v2: substantially expanded from v1; adds formal-verification and identifiability sections and corrects references
AI中文摘要
本文形式化了一类广泛使用的动力学——复制者-突变动力学和价格式选择与传输——并明确了决定该类动力学跨领域实例化的建模选择(尺度、原子单位、交互拓扑、传输核)。其主干是已知的;我们不声称发现了选择。新颖贡献有三方面:(i)一种尺度相对的核参数化,其中原子单位本身是参数,使得在物理学、生物学、经济学、认知和社会组织中系统实例化成为可能;(ii)一种用于政治哲学的同意-摩擦实例化,其中摩擦是原始量,合法性作为生存概率,信念传递作为突变核;(iii)一条从社会契约论而非生物学或物理学出发的推导路径,通过独立途径到达相同的正式结构。我们提供了一个连接描述性动力学与工具性规范性的桥梁原则:如果主体偏好更低的预期摩擦,那么“应当”主张就是减少指定动力学下预期摩擦的策略的简写。这种条件结构避免了实然-应然谬误,同时将规范性话语建立在经验上可处理的动力学基础上。我们通过显式建模潜在摩擦与观察摩擦来处理病态情况(威权稳定性、被抑制的摩擦)。该框架通过摩擦、合法性和信念传递动力学的操作化产生可检验的预测,并且在测量装置层面而非正式结构层面是可证伪的。
英文摘要
This paper formalizes a widely used dynamical class--replicator-mutator dynamics and Price-style selection-and-transmission--and makes explicit the modeling choices (scale, atomic unit, interaction topology, transmission kernel) that determine how this class instantiates across domains. The backbone is known; we do not claim to have discovered selection. The novel contributions are threefold: (i) a scale-relative kernel parameterization where atomic units are themselves parameters, enabling systematic instantiation across physics, biology, economics, cognition, and social organization; (ii) a consent-friction instantiation for political philosophy, where friction is the primitive, legitimacy functions as survival probability, and belief-transfer functions as mutation kernel; and (iii) a derivation path from social contract theory rather than from biology or physics, arriving at the same formal structure via an independent route. We provide a bridge principle connecting descriptive dynamics to instrumental normativity: if agents prefer lower expected friction, then "ought" claims are shorthand for policies that reduce expected friction under the specified dynamics. This conditional structure avoids the is-ought fallacy while grounding normative discourse in empirically tractable dynamics. We address pathological cases (authoritarian stability, suppressed friction) through explicit modeling of latent versus observed friction. The framework generates testable predictions through operationalization of friction, legitimacy, and belief-transfer dynamics, and is falsifiable at the level of measurement apparatus rather than formal structure.