Hypergendered Logic Source

Hypergendered Logic — Page 3

HGL Source Framework · Page 3 of 293 · Source: Hypergendered Logic

The third foundational device is the IH Inheritance Operator: 
 
𝐼𝐻𝑍
( )
read: 
the current Hypergendered state inherits the inheritable logical/state properties of source , while 
𝑍
preserving that those properties came from . 
𝑍
HGL permits two source sorts for IH: 
 
𝐼𝐻𝐶φ
( )
for an inner logical/developmental condition , and 
φ
 
𝐼𝐻𝑆𝑆
( )
for an already-formed HGL state . The ordinary notation 
 is used when the operand’s sort is obvious. 
𝑆
𝐼𝐻𝑍
( )
The canonical projection principle is 
 
𝐼𝐻𝑍
( ) ⇒𝑍,
but generally 
 
𝑍 ⇏ 𝐼𝐻𝑍
( ).
Possessing a property is not the same as possessing it by inheritance from that particular source. 
The fourth foundational device is the new PH Phenotype-Possession Operator: 
 
𝑃𝐻𝑍
( ).
Its strengthened reading is: 
the bearer irreducibly possesses the complete Hypergendered phenotype-profile canonically 
associated with source , as the phenotype-profile of considered as a whole. 
𝑍
𝑍
PH is deliberately stronger than saying that some phenotype compatible with happens to occur. It marks 
𝑍
complete profile possession with whole-source identity preserved. If the phenotype-profile of is denoted by 
𝑍
, then 
 says, in effect, that the bearer possesses all traits canonically belonging to 
 as the 
Π 𝑍
( )
𝑃𝐻𝑍
( )
Π 𝑍
( )
irreducible profile of , not merely as an accidental collection of similar traits. 
𝑍
This produces a phenotype analogue of PA irreducibility: 
 
𝑃𝐻𝐴∧𝐵
(
)≢𝑃𝐻𝐴
( ) ∧𝑃𝐻𝐵
( )
in general, and likewise 
 
𝑃𝐻𝐴∨𝐵
(
)≢𝑃𝐻𝐴
( ) ∨𝑃𝐻𝐵
( ).
The phenotype-profile associated with a compound whole may contain properties that arise from the 
compound as a compound. It is therefore not reconstructed merely by placing the profiles of its components 
beside one another. 
The placement of NOT matters for PH just as it matters for PA and IH: 
 
𝑃𝐻¬𝑍
(
)≢¬𝑃𝐻𝑍
( ).
PH(¬Z) is a positive phenotype-possession statement: the bearer irreducibly possesses the complete 
phenotype-profile associated with the logical non- source. ¬PH(Z) says only that the bearer does not 
𝑍
possess the complete phenotype-profile of . The former is vastly more informative. 
𝑍
PH must also remain distinct from developmental causation:

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:3.