Hypergendered Logic Source
Hypergendered Logic — Page 214
same-side predecessor, duplicate IH, substitute the wrong opposite-side source, replace NOT PH(opposite) with PH(NOT opposite), or decompose the Stage-1 compound PA source. 238. Flaw and Unflaw: exact canonical definitions Flaw: a physically instantiated feature whose presence decreases the quality of ANY extent of the physical structure or form. FD(a). Unflaw: a physically instantiated feature whose presence significantly increases the quality of the whole physical structure and form. UD(a). The capitalization of ANY is semantically important. FD is locally sensitive: if the presence of a produces a quality decrease in even one relevant physical extent, region, component, relation, or organized part, then a can satisfy FD(a), even if other parts improve. UD is globally demanding: the presence of a must significantly increase the quality of the physical structure/form considered as a whole. The predicates therefore test different scopes and are not logical negations of one another. NOT FD(a) does not entail UD(a) FD(a) does not entail NOT UD(a) UD(a) does not entail NOT FD(a), unless an additional incompatibility axiom is explicitly adopted A neutral feature supplies the simplest countermodel to NOT FD(a) -> UD(a): the feature lowers no local quality but also fails to produce a significant whole-form improvement. A mixed-effect feature supplies a countermodel to FD(a) -> NOT UD(a): it may worsen one local extent while producing an overwhelmingly larger, significant increase in whole-form quality. HGL therefore deliberately permits FD(a) AND UD(a) unless a future axiom forbids mixed effects. The current recursion goes further by explicitly requiring NOT FD of the own-side predecessor, thereby ruling out that mixed-effect possibility for that particular inherited predecessor role while independently asserting UD of it. 239. Why UD and NOT FD are not redundant in SF2 and every higher successor In SF2, UD(SF1) says that the physically instantiated SF1 predecessor contributes a significant increase to the quality of the whole SF2 physical structure/form. NOT FD(SF1) says something different: SF1 does not, by its presence in SF2, decrease the quality of any physical extent. The first is a positive global-improvement assertion; the second is a negative local-harm exclusion. Keeping both closes two different logical gaps. The superseded SF2 formula once contained UD(NOT SM1). Current SF2 does not. The opposite-side constitutive package is IH(NOT SM1) plus NOT PH(SM1); its UD/FD status is not fixed by the Stage-2 definition. The male mirror is exact: SM2 contains UD(SM1) and NOT FD(SM1), while its opposite-side package is IH(NOT SF1) plus NOT PH(SF1). From Stage 3 onward the same six-way architecture repeats at every successor. 239A. Opposite-Profile Exclusion: why opposite-side inheritance has no constitutive UD/FD status The asymmetry is canonical and intentional. Same-side continuity is protected by UD(own predecessor) AND NOT FD(own predecessor): the inherited own-lineage structure must significantly improve the successor as a whole and must not locally degrade any physical extent. The opposite-side package is different: IH(NOT opposite) positively inherits the structured non-opposite source, while NOT PH(opposite) denies possession of the complete opposite whole-profile. Neither UD nor FD status of that opposite source is fixed by the successor definition. Current successor canon does not contain UD(NOT SM^alpha) at all. It contains IH(NOT SM^alpha) and NOT PH(SM^alpha). Therefore an implementer must neither add UD(NOT opposite) nor replace NOT PH(opposite) by PH(NOT opposite) without an explicit later axiom.
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:214.