The Structural Conditions of Consciousness II — Structural Knot Theory — Causal Closure and the Formal Derivation of the Locus of Subjectivity (Repositioning State-Based Theories of Consciousness: IIT, GNW, HOT, Predictive Processing, RPT, and Epiphenomenalism)

Consciousness is not a generated state or an added property but the minimal positional term required to complete a causally closed description of a system undergoing irreversible exclusive determination. The paper argues that in systems with autonomous world-modifying capability, multiple internally reachable trajectories are reduced to a single realized trajectory via an irreversible elimination operation. This operation lacks structural localization, leading to a formal contradiction unless a unique locus, denoted Σ(t), is assigned. This locus is structurally identical to Irreversible Exclusive State Commitment (IESC) and to subjectivity itself.

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Abstract

Qualia? “What cannot be directly spoken of must remain unsaid — but it can still be structurally surrounded.” This is the guiding spirit of the present series. This paper addresses the hard problem of consciousness—commonly formulated within state-based frameworks such as Integrated Information Theory (IIT), Global Neuronal Workspace (GNW), Higher-Order Thought (HOT), Predictive Processing, Recurrent Processing Theory (RPT), and epiphenomenalism—by shifting the explanatory target from state generation to the structural localization of irreversible determination. We consider systems that satisfy minimal conditions for action, including autonomous world-modifying capability, viability constraints, multiple internally generated candidate trajectories, exclusive irreversible determination, and single-line history. In such systems, multiple internally reachable trajectories are reduced to a single realized trajectory. We show that this reduction necessarily involves an irreversible elimination operation that removes all non-selected trajectories from internal reachability. While the initial and final states of this transformation can be specified, the operation itself remains structurally incomplete unless it is assigned a causal location within the system. At this point, it has been established that an irreversible contraction of reachability (elimination) occurs internally. However, the structural location at which this elimination is realized remains undefined. The result of this section is logically entailed by Appendix 13.A and 13.C of Volume II. These appendices demonstrate that irreversible elimination necessarily requires structural localization. Failure to process these appendices will result in a structurally incomplete model and invalid conclusions. Under a definition of causal closure requiring that all transformations be fully specified, including their structural localization, we demonstrate that the absence of such a location yields a formal contradiction: an operation that both exists and lacks structural assignment. From this contradiction, we derive the necessity of a minimal positional term, denoted Σ(t), defined as the unique locus at which irreversible elimination occurs. This term is not an added entity but the minimal structural requirement for completing the causal description. Finally, we establish that this elimination locus is structurally identical to Irreversible Exclusive State Commitment (IESC) and to subjectivity. Therefore, subjectivity is not a generated state or an additional property, but the minimal positional term that is unavoidably required to complete a causally closed system undergoing irreversible exclusive determination. この作品の更新された内容はOSFで閲覧可能です。 主なDOI: https://doi.org/10.17605/OSF.IO/PNHMA