Consistency constraints on mathematical theories of phenomenal consciousness

Summary

The study establishes consistency constraints for mathematical theories describing phenomenal consciousness. It shows that any nontrivial classifier must be discontinuous, and that scores between 0 and a positive value are necessary during continuous deformations. Additionally, it proves that endpoints 0 and 1 cannot be reached under certain conditions, despite symmetries in the configuration space of systems. The findings highlight barriers to computability and suggest that while the theory is descriptive, it does not provide explanations.

Study at a glance

Abstract

We state clean consistency constraints on any descriptive (structural) mathematical theory of phenomenal consciousness. Let the configuration space \(U\) of physically realizable systems be connected (under admissible deformations) and let a descriptive theory deliver a symmetry\-invariant scalar \(p:U [0,1]\) (a ``phenomenality score'') together with an optional crisp classifier \(P= {1}\{p c\}\). We prove: (i) any nontrivial crisp \(P\) must be discontinuous somewhere (Triviality of continuous crisp predicates); (ii) nonzero scores between 0 and a positive value are unavoidable along any continuous deformation (Intermediate\-value necessity); (iii) under mild differential conditions (submersion), endpoints \(0,1\) are excluded from the image of \(p\) even when \(U\) carries symmetries (Endpoint exclusion under submersion). We also note computability barriers (Rice's theorem) and give templates (order parameters, topological invariants) that realize phase boundaries without explanatory import. Conceptually, such a theory is descriptive but not explanatory, consonant with the explanatory gap literature. {Levine 1983}{https://www.informationphilosopher.com/solutions/philosophers/levine/Explanatory_Gap.pdf}, {Chalmers 1995}{https://consc.net/papers/facing.pdf}

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