Why the Unfinished Keeps Returning: Canxianization and the Dynamics of Conscious Priority

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.

We propose uncommon self-knowledge (USK) as a candidate criterion for consciousness: synergistic information a system carries about itself that exists only in the joint of its subsystems and is destroyed by decomposition. Drawing on Gottwald's partition-lattice grounding of Partial Information Decomposition (PID), where redundancy corresponds to Aumann's common knowledge and synergy to the gap between separate and joint observation, we propose the synergistic component of self-directed information as a candidate formal signature for conscious processing. If correct, the framework would (1) offer a clean separation between consciousness and metacognition (synergistic vs. redundant self-knowledge), (2) provide principled resolutions to counterexamples that challenge IIT, GWT, and HOT, (3) be operationalizable via Partial Information Rate Decomposition (PIRD) with self-targeting, and (4) generate distinctive empirical predictions, the strongest being a GWT timing dissociation (consciousness correlates with pre-broadcast synergy formation, not broadcast itself) and a specific dissociation between self-report disruption and task-performance disruption under middle-layer perturbation in LLMs. The proposal is consistent with recent empirical findings that both anaesthesia and Alzheimer's disease specifically reduce synergistic information processing while preserving or increasing redundancy.

A common objection to artificial or simulated consciousness is that a simulated brain is no more conscious than simulated water is wet. We address this from the perspective of Intrinsic Computational Functionalism (ICF): if consciousness is computationally constituted, it depends not on externally imposed descriptions but on the computational structures a system physically realizes in virtue of its own causal-dynamical organization. In previous work we developed Canonical Functionalism as a mathematically precise special case of this anti-interpretivist program, identifying functional states by their complete future input-output roles under a fixed interface. Here we argue that this input-output construction, though important, is incomplete: as a behavioral boundary case of ICF, it makes lookup tables and unfolded systems that preserve the same boundary behavior canonically equivalent. A consciousness-relevant canonical representation must instead include internal mechanisms, interventions, and joint readouts belonging to the relevant intrinsic organization. We therefore define a mechanism-enriched canonical structure and use it to formulate Intrinsic Causal-Computational Realization (ICCR), a realization relation preserving physical implementation, intrinsic state individuation, transition structure, intervention profiles, and the relevant agent-body-world boundary. The central result is conditional: if conscious properties are invariants of intrinsic causal-computational organization, then any system satisfying ICCR realizes the same consciousness-relevant properties, whether biological, artificial, or simulated. We discuss objections including biological naturalism and integrated information theory. We conclude that to deny consciousness to a simulation, one must identify a consciousness-relevant intrinsic causal-computational structure that the simulation fails to realize.