Hypergendered Logic Source
Hypergendered Logic — Page 122
p does not generally imply □_n p. PH(S) does not generally imply □_n p unless p is specified as invariant across the Γ_n realization-space. 240. Conditional metaexpression rules Γ can encode conditional rules rather than only unconditional trait requirements. □^F_n( puberty_phase_3 -> phenotype_q ). If the actual Stage-n subject reaches puberty_phase_3, T/factivity gives the actual conditional, and ordinary modus ponens can produce phenotype_q. This is a causal/logical deduction only if the conditional rule is explicitly part of Γ^F_n. 241. Stage progression changes a rule-function, not merely a trait list The transition SF^n -> SF^(n+1) can therefore involve a transition Γ^F_n -> Γ^F_(n+1). What changes may be the rules governing phenotype-space, the dimensional vocabulary of phenotype-space, the conditional dependencies among phenotypes, or the modal status of phenotypes. This does not mean every higher stage must visibly alter the body immediately. A stage transition can first alter what is now possible, necessary, or forbidden, with visible realization appearing later when maturity or another trigger supplies the relevant lower-order parameters. 242. Higher stage is not simple set filtering Γ must be generative-transformative as well as constraining. If each higher stage only removed possibilities from a fixed phenotype vocabulary, the ladder could become progressively narrower without revealing genuinely new dimensions. HGL instead allows a higher Γ to introduce new phenotype variables, interactions, or relational structures that did not belong to the lower stage’s expression language. Vocabulary_n ⊂ Vocabulary_(n+1) is permitted. W_(n+1) is not assumed to be a subset or superset of W_n. The relation between stage spaces is intensional and typed. Inherited actual structures persist through IH, while the higher metaexpression function can add genuinely new ways in which those inherited structures may interact or express. 243. No automatic cross-stage modal monotonicity Without an explicit rule, none of the following is universally valid: ◇^F_n p -> ◇^F_(n+1) p □^F_n p -> □^F_(n+1) p NOT ◇^F_n p -> NOT ◇^F_(n+1) p. IH guarantees inheritance of the specified prior state properties; it does not automatically identify the complete modal possibility-space of Γ^F_n with that of Γ^F_(n+1). If HGL later adopts a conservative-extension rule for some phenotype vocabulary, those specific cross-stage inferences become available for that vocabulary. 244. A conservative-extension option for inherited phenotype dimensions A particularly strong but optional refinement is to state that Γ^(n+1) conservatively preserves established Stage-n necessities and exclusions on the inherited phenotype vocabulary while adding new dimensions. This is not assumed globally unless explicitly canonized, because it would constrain how future stages may transform earlier modal rules.
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:122.