Practical Sector (S_P)

The Practical Sector S_P is the collection of all E_3-admissible contents whose coherence is governed by the Practical Register Reg_P. Formally, S_P = { c ∈ Adm_{E_3} | Coh(c) = Coh_P(c) }. Its sector question is 'What should I do?', its witness bundle is a normative constraint, and its vacuum is a fully coherent ethical framework.

Categorical invariant. Subobject S_P ⊆ Adm_{E_3} cut out by the equation Coh = Coh_P. Second of four pure sectors in the Sector Decomposition Theorem (VII.T03).

Primary registry anchor: VII.D08

Supporting items: VII.D02, VII.D07, VII.D09, VII.D10, VII.D11

1. I.K0 — Universe Postulate
2. VII.D02 — Practical Register Reg_P with codomain Norm
3. VII.D08 — Practical sector S_P — admissible contents whose coherence equals practical coherence

S_P is instantiated wherever a category-error-free claim's coherence is governed by normative consistency: a maxim, an obligation, an institutional norm. The sector question — 'What should I do?' — is the structural ground of categorical ethics (Book VII, Part VII) and categorical societies (Part VIII).

Examples:

• A universalisable maxim — sector S_P content whose vacuum is a contradiction-free obligation set (passes the four ethical tests at VII.D69)
• An institutional anti-corruption policy — sector S_P content read out by Reg_P at the collective level
• A clinical informed-consent obligation — sector S_P content whose witness bundle is the bound obligation on the practitioner

Register codomain: Norm (via Reg_P); the sector itself is a subobject of Adm_{E_3}

Manuscript reference: manuscript-sources/book-07/part01/ch05.tex

Status: Planned

Related glossary entries

• MG-R01-empirical-register Empirical Register (Reg_E)