Computational functionalism about consciousness is often criticized for relying on observer-relative interpretations of physical systems. This paper proposes a mathematical refinement of functionalism that avoids this problem. The central idea is that consciousness-relevant functional organization should be identified not with arbitrary input-output mappings, semantic labels, or externally imposed computational descriptions, but with a system's canonical functional structure: the minimal state-transition structure obtained by identifying internal states that have identical future behavior under all possible continuations. On this view, a state is functionally defined by its complete counterfactual role: how the system would evolve and respond from that state under possible future interactions. We call this position canonical functionalism. The framework does not claim to identify which systems are conscious, nor to show that functional organization is sufficient for consciousness. Rather, it identifies the canonical object over which functionalist theories of consciousness should be formulated: the task is to specify consciousness-relevant invariants, measures, or structural conditions over canonical functional structures, rather than over arbitrary semantic interpretations or superficial behavioral profiles. This reframes familiar objections about lookup tables, simulations, unfolding, and observer-relative computation: such cases do not by themselves refute functionalism, but force the functionalist to specify whether the relevant canonical structure is preserved, and if not, which additional structural features are missing.

翻译：关于意识的计算功能主义常因依赖对物理系统的观察者相对性解释而受到批评。本文提出了一种避免该问题的功能主义数学精炼方案。核心思想在于，与意识相关的功能组织不应被认定为任意的输入输出映射、语义标签或外部强加的计算描述，而应被认定为系统的规范功能结构：即通过识别在一切可能延续下具有相同未来行为的内部状态，所获得的最小状态转移结构。基于此观点，一个状态由其完整的反事实角色功能性地定义：即系统在可能的未来交互作用下，从该状态出发如何演化与响应。我们将这一立场称为规范功能主义。该框架并非旨在识别哪些系统具有意识，也非证明功能组织足以构成意识，而是指出功能主义意识理论应构建于其上的规范对象：任务在于明确规范功能结构上具有意识相关性的不变量、度量或结构条件，而非任意语义解释或表层行为特征。这重新框定了关于查找表、模拟、展开与观察者相对计算等常见批评：此类案例本身并不否定功能主义，而是迫使功能主义者明确相关规范结构是否得以保持，若未保持，则缺少哪些附加结构特征。