Can Consciousness Be Identified? A Mathematical Theory of What Science Can and Cannot Prove About Experience

Abstract

Consciousness science faces an unusual problem: every report, measurement, experiment, model, and theory used to investigate consciousness is itself accessed through consciousness, while the conscious states of other systems are never directly available to an external observer. This manuscript develops a theory-neutral mathematical framework for determining what consciousness science can actually identify, what cannot be inferred from existing evidence, and what experiments would be required to overcome those limitations. Rather than proposing another neural or computational theory of consciousness, the work treats consciousness as an identifiability problem and derives a sequence of constructive results and impossibility theorems spanning positive unlabeled inference, latent variable identification, intervention equivalence, predictive state reconstruction, causal realization, report censoring, bridge extension, controllability, shadow variables, and multi-route triangulation. The analysis proves, among other results, why behavioral nonresponse cannot constitute evidence of unconsciousness by itself, why disappearance of reports is mathematically unable to distinguish genuine loss of experience from loss of observability without additional assumptions, when multiple independent physiological or neural shadow channels can identify a hidden manifestation state, when a physical phenomenal mapping can be uniquely extended from directly anchored conscious states, and when competing consciousness theories are fundamentally indistinguishable by any possible experiment. These results culminate in a proposed experimental architecture in which first-person phenomenal structure, report-independent latent state inference, and independently identified causal physical realization are constructed separately and then required to converge on the same invariant object under held-out interventions. The manuscript therefore reframes the central scientific question from “Which brain measure correlates with consciousness?” to a stricter one: “Under what mathematical and experimental conditions can consciousness itself be identified?” It provides a formal pathway toward answering that question while also defining the precise boundary beyond which empirical science cannot decide.