Reality (recoverable kernel field)
Reality, in the τ-framework, is the field of NF-addresses that is jointly recoverable across all four registers — the maximal coherent structure that survives the OR1–OR6 narrowing and admits sections in every register's truth-presheaf. Reality is not 'what exists' (that is being, MG-O01) and not 'all possible worlds' (that is the modal frame, VII.D62); it is the joint cross-register recoverable field, anchored at the unique terminal coherence point ω.
τ-Definition
Reality, in the τ-framework, is the field of NF-addresses that is jointly recoverable across all four registers — the maximal coherent structure that survives the OR1–OR6 narrowing and admits sections in every register's truth-presheaf. Reality is not 'what exists' (that is being, MG-O01) and not 'all possible worlds' (that is the modal frame, VII.D62); it is the joint cross-register recoverable field, anchored at the unique terminal coherence point ω.
Categorical invariant. ℛ_τ = the maximal NF-addressed structure satisfying OR1–OR6 jointly across {Reg_E, Reg_P, Reg_D, Reg_C}, with ω as terminal anchor.
Primary registry anchor:
VII.D41
τ-Derivation Chain
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VII.D37— Six Ontic Requirements (OR1–OR6) — the joint admissibility class that defines reality. -
VII.D40— Non-Dualistic Platonism — single ontology with epistemic stratification; reality is one field across registers. -
VII.D41— ω-Uniqueness Principle — the terminal coherence point ω is unique, anchoring the recoverable field. -
VII.D38— Problem Map Classification Scheme — metaphysical problems classified by their relation to the recoverable field (Resolved-Kernel, Resolved-Pattern, Reframed-VM, Open).
Lean modules referenced:
TauLib.BookVII.Meta.Saturation
Phenomenological Correlate
Reality is instantiated whenever we appeal to 'how things really are' — beyond appearance, beyond convention, beyond opinion. The τ-framework reads 'really' as 'recoverable across all four registers under the OR1–OR6 narrowing'. Empirically real (recoverable in Reg_E), normatively real (Reg_P), proof-theoretically real (Reg_D), commitment-theoretically real (Reg_C) — and the joint reality is the intersection: what survives every register's narrowing simultaneously. This is what 'mind-independent reality' should mean once mind-dependence has been disambiguated by register.
Examples:
- Empirical-only: a hallucination is recoverable in one observer's Reg_E but not in others'; it lacks empirical reality.
- Joint cross-register: physical constants are recoverable empirically (measured), proof-theoretically (consequences of admissible kernel structure), and normatively (binding for any coherent agent); they belong to the joint recoverable field.
- Boundary case: aesthetic judgements may be recoverable in some registers (Reg_C, Reg_P) without being recoverable in Reg_E; the τ-framework declines to call them unreal — they are real in their registers, possibly not in Reg_E.
- Anchor: the unique terminal point ω is the maximally recoverable address — what every register's coherence-process converges toward (VII.D41).
Register codomain: Cross-register (reality is the joint recoverable field; register-relative reality is reality-in-that-register; the concept is uniform).
Manuscript reference: manuscript-sources/book-07/part02/ch32.tex
Lean Coverage
Status: Formalized
Module: TauLib.BookVII.Meta.Saturation
Lean kind: structure
Lean symbol: Tau.BookVII.Meta.Registers.UniquenessPrinciple