The Algebra of Experience — Recursive Semantic Operator Theory: Process, Affect, Reflection, and the Measurement of Consciousness

Abstract

This paper develops Recursive Semantic Operator Theory (RSOT), a physicalist, graded, and substrate-neutral account of consciousness. Its central claim is constitutive rather than additive: a conscious episode is not a further property produced by cognition, but the temporally extended, self-inclusive organisation of a system whose semantically grounded operations construct a counterfactual world-model, represent the system within that model, and recursively use that self-representation to reorganise perception, memory, valuation, inference, and action. The proposal therefore begins from process rather than static representation. Representations are treated as time-indexed stabilisations within an ongoing causal process; concepts are treated primarily as empirically identifiable families of transformations; and cognition is described as the context-dependent algebra generated by those transformations. The paper adds two linked theses to earlier formulations of recursive semantic integration. First, affect is formalised as a family of meta-operators that reparameterise the active semantic algebra by changing gain, attention, attractor structure, action thresholds, temporal horizon, memory consolidation, and learning. On this account, feeling is not a second property applied to cognition: the affect-induced change in the geometry and availability of grounded semantic operations is the feeling. The world inferred and learned under fear is therefore not the same operational world as the one inferred and learned under safety. Second, introspection is treated as an endogenous, state-changing operation. A report about an episode is generated from a successor state that has already selected, compressed, labelled, and frequently altered the episode it purports to describe. The explanatory gap is consequently reframed as a reflexive measurement residual: a system compares an external description of a prior process with an internally reconstructed successor-state representation and mistakes the mismatch for evidence of an additional ontological property. Together with the Identity Postulate, this yields a dissolution of the hard problem as a category error and measurement error rather than a bridge from physical process to an extra phenomenal object. Formally, RSOT distinguishes the physically executable language of context-conditioned operations from the analytical operator algebra used to study it. It uses intervention-defined concept clusters, Markov and Koopman operators on observables, local Jacobians, Hilbert-Schmidt operator spaces, commutators, invariant subspaces, spectral and attractor structure, causal abstraction, partial information decomposition, and matched causal interventions. Consciousness is operationalised first as a multidimensional Recursive Semantic Integration Profile, not a single scalar. Eligibility requires a causally coherent candidate boundary and genuine counterfactual world-model capacity; the primary profile measures causal recursion, reciprocal cross-level influence, synergistic integration, semantic grounding, self-model closure, temporal continuity, and differentiated complexity. A separate operator/content/affect signature describes qualitative organisation. The resulting framework integrates philosophical argument, affective science, consciousness research, mechanistic interpretability, artificial agents, extended cognition, and hybrid human-AI systems while specifying concrete experiments, limitations, and falsification conditions.