Hypergendered Logic Source

Hypergendered Logic — Page 89

HGL Source Framework · Page 89 of 293 · Source: Hypergendered Logic

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.