Hypergendered Logic Source

Hypergendered Logic — Page 78

HGL Source Framework · Page 78 of 293 · Source: Hypergendered Logic

Therefore an SF5 Archfemale can remain at SF5 while biological consequences associated with her 
inherited SF4 structure, inherited non-SM4 structure, and deeper inherited ancestors become more mature 
or more integrated. She does not need to acquire IH¬SM5 until she actually transitions to SF6. 
This is another reason provenance must be preserved: a new anatomical change during an SF5 plateau can 
be caused by maturation of already-present inherited architecture rather than by acquisition of the next 
stage. 
121. Temporal logic notation for specialists 
A temporal-logical formulation can make the distinction compact. Let 
 mean “throughout interval ” and 
 
𝐺𝐼
𝐼
𝐹𝐼
mean “at some time in interval .” To avoid confusing temporal with the Female symbol , this document 
𝐼
𝐹
𝐹
always typesets temporal operators in bold. 
Temporary stage stagnation can be represented as 
 
𝐺𝐼𝑆𝐴, 𝑡
(
) = 𝑆𝐹
𝑛
[
].
Continued development somewhere in the same interval is 
 
𝐹𝐼𝐷𝐴, 𝑡
(
) ≠𝐷𝐴, 𝑡0
(
)
[
].
The new canon explicitly permits their conjunction: 
 
𝐺𝐼𝑆𝐴, 𝑡
(
) = 𝑆𝐹
𝑛
[
] ∧𝐹𝐼𝐷𝐴, 𝑡
(
) ≠𝐷𝐴, 𝑡0
(
)
[
].
Permanent stagnation beginning at can be represented as 
𝑡0
 
𝐺[𝑡0,∞) 𝑆𝐴, 𝑡
(
) = 𝑆𝐹
𝑛
[
].
Again, this does not entail 
 
𝐺[𝑡0,∞) 𝐷𝐴, 𝑡
(
) = 𝐷𝐴, 𝑡0
(
)
[
].
122. A model-theoretic proof of non-entailment 
To prove formally that stage stagnation does not entail developmental stagnation, construct two models 
satisfying the same stage facts. 
Model 1 
 
𝑆𝐴, 𝑡1
(
) = 𝑆𝐴, 𝑡2
(
) = 𝑆𝐹
3,
 
𝐷𝐴, 𝑡1
(
) = 𝐷𝐴, 𝑡2
(
) = 𝑑1.
Model 2 
 
𝑆𝐴, 𝑡1
(
) = 𝑆𝐴, 𝑡2
(
) = 𝑆𝐹
3,
 
𝐷𝐴, 𝑡1
(
) = 𝑑1,
 
𝐷𝐴, 𝑡2
(
) = 𝑑2,   𝑑1 ≠𝑑2.
Both models satisfy the same stage-stagnation premise. Only Model 1 satisfies developmental constancy. 
Therefore developmental constancy is not true in every model of stage stagnation, so 
 
𝑆𝑡𝑎𝑔𝑒𝑆𝑡𝑎𝑔𝑛𝑎𝑡𝑖𝑜𝑛 ⊭ 𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑚𝑒𝑛𝑡𝑎𝑙𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑐𝑦.
This is not merely an analogy; it is the standard model-theoretic form of a non-entailment proof.

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:78.