Canonical Functionalism: Defining Functional Structure without Observer-Relative Semantic Maps
For philosophers and scientists studying consciousness, this provides a precise framework to formulate functionalist theories without observer relativity, though it is an incremental theoretical refinement.
The paper proposes 'canonical functionalism', a mathematical refinement of computational functionalism that defines consciousness-relevant functional organization via a system's minimal state-transition structure, avoiding observer-relative semantic maps. It reframes objections like lookup tables and simulations as requiring specification of whether canonical structure is preserved.
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.