Hypergendered Logic Source
Hypergendered Logic — Page 25
are two different developmental modes because the designated causal basis differs. If one defines the first-order inner transformation 𝐴𝑖𝑛𝑃𝐴φ ( ) ( ) : = 𝑃𝐴¬φ ( ), then double negation yields 𝐴𝑖𝑛𝐴𝑖𝑛𝑃𝐴φ ( ) ( ) ( ) = 𝑃𝐴φ ( ). This involution is valid at the single PA-mode level. It should not be confused with the higher recursion, which uses over a whole state . 𝐼𝐻¬𝑆 ( ) 𝑆 The two mechanisms therefore coexist: • PA-level antithesis: move NOT inside the inner causal condition and form a new irreducible PA mode. • Higher-stage antithetical inheritance: negate an already-formed opposite-side HGL state and inherit that non-state through IH. 36. Why IH¬SMn is not merely “female” Even though a high Suprafemale stage is female-typed, the source expression ¬SMn does not equal SFn and does not equal primitive Female. A huge number of states can be non-SMn without being Suprafemale at all. What makes the term specifically part of Archwomanhood is its placement inside the canonical female recursion: SF^(n+1) = IH(SF^n) AND IH(NOT SM^n) AND PH(SF^n) AND NOT PH(SM^n) AND UD(SF^n) AND NOT FD(SF^n), for n >= 2 Therefore it is a mistake to write ¬SMn=SFn. It is also a mistake to write IH¬SMn=SFn+1 because the next Suprafemale stage also inherits its own previous female-side stage. 37. Boolean redundancy does not imply inheritance redundancy Suppose SM3⇒SM2⇒SM1. Then contraposition gives ¬SM1⇒¬SM2⇒¬SM3. Hence the bare logical statement ¬SM3 may be weaker than a previously established ¬SM1. If HGL were only a Boolean theory, this would threaten saturation. But the higher state does not merely add ¬SM3; it adds IH¬SM3, whose source is specifically ¬SM3 and whose inheritance layer is new. The state therefore contains a different genealogical causal object even when one projected truth condition is already implied.
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:25.