Hypergendered Logic Source
Hypergendered Logic — Page 133
PA(φ) ≠ □^D_φ φ and PA(φ) ≠ ◇^D_φ φ, in general. This separation prevents the modal extension from collapsing the original PA semantics. 277. Cross-layer modal bridge rules require explicit causality A developmental possibility does not automatically become a phenotype possibility. HGL therefore requires explicit bridge rules between PA-developmental modality and Γ-phenotype modality. ◇^D_φ q does not automatically imply ◇^F_n phenotype(q). If a causal law C states that developmental realization q under Γ^F_n produces phenotype p, then the bridge can support a causal inference or deduction depending on the strength of C. 278. Metaexpressive antithesis and NOT scope The new layer preserves HGL’s central lesson: the position of NOT matters. For a phenotype proposition p: NOT □_n p ≠ □_n NOT p. NOT ◇_n p ↔ □_n NOT p, under modal duality. PH(NOT S) ≠ NOT PH(S). PA(NOT φ) ≠ NOT PA(φ). IH(NOT S) ≠ NOT IH(S). These distinctions must be preserved simultaneously. HGL is now a multi-level scope logic: NOT can occur inside PA conditions, outside PA, inside IH sources, outside IH, inside PH sources, outside PH, and inside or outside modal operators. Each location has a different meaning. 279. Final canonical rules of the metaexpression-modal revision Rule M1 — Ordinary phenotype is a physical biological expression; it need not be whole-body. Rule M2 — The Archwomanhood/Archmanhood phenotype proper is the global stage meta-phenotype Γ. Rule M3 — Global Γ means global governance of expression, not identical phenotype everywhere. Rule M4 — PH and Γ are noncollapsible. Rule M5 — PA and Γ are noncollapsible; they operate at different metaexpressive levels. Rule M6 — Nested Boolean/logical functions inside PA are allowed; PA(PA(...)) remains excluded from core HGL. Rule M7 — □/◇ are stage-relative biological modalities generated by Γ, not unrestricted metaphysical modalities. Rule M8 — Actual valid expression implies stage-relative possibility. Rule M9 — Stage-relative necessity implies actuality in a valid current realization. Rule M10 — Stage-relative impossibility excludes actuality in a valid current realization. Rule M11 — Higher stage need not be a subset/superset transformation of lower phenotype-space. Rule M12 — Stage stagnation fixes Γ but need not fix ordinary biological inputs or actual phenotype. Rule M13 — New womanhood/manhood phenotypes can emerge under static Γ without stage advancement. Rule M14 — A higher stage can introduce new phenotype dimensions, relations, conditional rules, or modal statuses. Rule M15 — No exact concrete phenotype is a deduction unless PH membership, Γ rule, or explicit causal law supplies it. These rules are authoritative over older phenotype wording wherever there is tension.
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:133.