Hypergendered Logic Source

Hypergendered Logic — Page 116

HGL Source Framework · Page 116 of 293 · Source: Hypergendered Logic

𝑃𝐻𝑍
( ) ⇒𝐻𝑎𝑠𝑇
( ) 𝑓𝑜𝑟 𝑇∈Π 𝑍
( ).
Intensional profile identity: 
 
𝑃𝐻𝑍1
( )≢𝑃𝐻𝑍2
( )
can remain true even when the currently observable trait sets overlap, because the source profiles and 
latent/developmental organization can differ. 
218. Proof that PH(NOT S) does not reduce to NOT PH(S) 
A countermodel is enough. 
Let a subject fail to possess the complete profile because one required trait is absent. Then 
𝑆
 
¬𝑃𝐻𝑆
( )
is true. 
But suppose the subject also fails to possess the complete non- profile. Then 
𝑆
 
𝑃𝐻¬𝑆
(
)
is false. 
Therefore 
 
¬𝑃𝐻𝑆
( ) ⇏ 𝑃𝐻¬𝑆
(
).
Conversely, a theory can stipulate 
 without deriving the syntactically stronger claim that every 
𝑃𝐻¬𝑆
(
)
possible way of 
 failing has been identified with that profile. Hence the operators must remain distinct. 
𝑃𝐻𝑆
( )
219. Proof that PH(A AND B) need not equal PH(A) AND PH(B) 
Choose a phenotype map with 
 
Π 𝐴
( ) = {𝑎},
 
Π 𝐵
( ) = {𝑏},
and 
 
Π 𝐴∧𝐵
(
) = {𝑎, 𝑏, 𝑒},
where is an emergent compound trait. 
𝑒
A bearer can satisfy 
 by possessing and under their respective whole-profile identities 
𝑃𝐻𝐴
( ) ∧𝑃𝐻𝐵
( )
𝑎
𝑏
while lacking . Then 
 is false. Thus distribution fails in at least one admissible HGL model. 
𝑒
𝑃𝐻𝐴∧𝐵
(
)
220. Proof that stage plateau does not imply phenotype plateau 
Construct a model with stage 
SFt=SF4 
for all in 
 years, but maturity variable 
 strictly increasing through puberty. Let a womanhood trait 
𝑡
11, 18
[
]
𝐷𝑡
( )
 be caused when 
 crosses a threshold while SF4 remains constant. 
𝑊
𝐷𝑡
( )
Then 
 
∆𝑆𝐹= 0
but

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:116.