Hypergendered Logic Source
Hypergendered Logic — Page 89
143. Boolean projection versus full HGL identity Define a projection that forgets inheritance provenance while preserving truth consequences: π π 𝐼𝐻𝑆 ( ) ( ) : = π 𝑆 ( ). Then two full HGL states can have overlapping or even equivalent projections while remaining different full states: π 𝑆1 ( ) = π 𝑆2 ( ) ⇏ 𝑆1≡𝐼𝑆2. This is analogous to two causal histories yielding the same current observable value. The output can be extensionally identical while the causal state is not. 144. Why later opposite-side negations can look logically redundant From cumulative nesting, SM10⇒SM1. Therefore ¬SM1⇒¬SM10. So a person already satisfying ¬SM1 automatically satisfies the weaker statement ¬SM10. If the theory recorded only bare negations, no new information would be added. But the higher stage records IH¬SM10, not merely ¬SM10. Its source is a different recursively structured whole and its IH depth is different. This is how the revised theory avoids the false choice between “saturating” and “unbounded but empty.” 145. When provenance would become empty The critique would become correct if HGL made both of the following assumptions: 1. IH source identity has no effect on state identity; and 2. phenotype causation is completely insensitive to IH source/depth. Under those assumptions the higher labels could collapse to Boolean shadows. The present theory rejects the first and permits the causal model to reject the second. Therefore provenance is substantive by definition and potentially substantive biologically. 146. A natural-language test for whether IH is meaningful Ask: “Could two bodies satisfy the same ordinary logical propositions yet be developmentally different because one inherited those propositions through a Stage-20 lineage and the other did not?” If the answer in the fictional world is yes, IH is biologically meaningful. The entire higher ladder is designed around that yes-answer. 147. Female/Male category typing fixes the Stage-1 problem Because SF1 contains the irreducibly joint mode PAx∧¬y rather than being identical to a conjunction of standalone PA routes, PA irreducibility blocks the inference from that joint mode to standalone PAx. Therefore the concept female must not be defined in a way that requires every female-typed state to instantiate that standalone route.
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:89.