Hypergendered Logic Source

Hypergendered Logic — Page 11

HGL Source Framework · Page 11 of 293 · Source: Hypergendered Logic

𝑃𝐻¬𝑍
(
)≢¬𝑃𝐻𝑍
( ),
 
𝑃𝐻𝑍
( )≢𝑃𝐴𝑍
( ),
and 
 
𝑃𝐻𝑍
( )≢𝐼𝐻𝑍
( ).
The location of NOT, the identity of the operator, and the source type all matter. 
8. No nested PA, no self-referential same-stage PH 
The phrase “no nested PA” is a type restriction on PA as an operator, not a restriction on logical depth inside 
the PA argument. HGL permits nested propositional/logical functions inside a single PA whenever the inner 
expression is a well-formed developmental condition. 
Allowed: PA(NOT((x AND NOT y) OR (NOT x AND y))). 
Noncanonical in core HGL: PA(PA(x)). 
The allowed form is especially important under Biological Metaexpressability. A logically complex inner 
condition can specify a correspondingly complex rule/constraint basis for what anatomy and physiology are 
developmentally expressible, while PA irreducibility prevents that basis from being automatically 
decomposed into separate PA modes. 
Core HGL deliberately rejects 
 
𝑃𝐴𝑃𝐴φ
( )
(
).
It also avoids defining a stage by 
 of that same stage, such as 
𝑃𝐻
SFn:=⋯∧PHSFn, 
because that would introduce unnecessary self-reference. 
Instead the hierarchy is stage-lagged: SFn+1 may contain PHSFn, and SMn+1 may contain PHSMn, 
because the lower stage has already been defined. This makes the phenotype recursion well founded. 
Part II — The deontic epiphany and scope of negation 
5. Why deontic logic was the crucial analogy 
Suppose 
 means “it is obligatory that .” Then 
𝑂𝑝
( )
𝑝
 
¬𝑂𝑝
( )
means “it is not obligatory that ,” while 
𝑝
 
𝑂¬𝑝
(
)
means “it is obligatory that not- .” 
𝑝
These are not equivalent: 
 
¬𝑂𝑝
( ) ≠𝑂¬𝑝
(
).
A person may be under no obligation to open a door without being obligated to keep it closed. In other 
words, removing an obligation is not the same operation as placing an obligation on the opposite content. 
HGL applies the same structural insight: 
 
¬𝑃𝐴φ
( ) ≠𝑃𝐴¬φ
(
).

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:11.