Yet, we can find out that Ipq = Hpq & Apq, and we shall realize that the prependency function is the matrix of a transition relationship between conditioning and opposition, marking the concomitance of superalternation and subcontrariety.
Two generic, or truth-fluctuating, propositions, now true, now false, seem to us compatible with one of the following relationships: interference (the weakest conditioning, neither necessary nor sufficient); subalternation (the sufficiently-necessary conditioning); superalternation (the necessarily-sufficient conditioning); equivalence (the necessary and sufficient conditioning); nonrelationality (the weakest opposition, neither contrary nor subcontrary); contrariety (the contrarily-contrary opposition); subcontrariety (the subcontrarily-subcontrary opposition); contradiction (the contrary and subcontrary opposition).
On the contrary, we shall express our reserve in interpreting the valid formula p&q [contains] j p by the phrase "any proposition (p) is sufficiently-necessarily conditioned by its sufficiently-sufficient interconditioning with another proposition (q)," and we shall have reserves in interpreting p [contains] p v q by the phrase "any proposition (p) sufficiently-necessarily conditions its subcontrariety with another proposition (q).
Subcontrariety is the inverse of contrariety: whereas two contrary claims cannot both be true but can both be false, two subcontrary claims cannot both be false, though both, one, or the other, can be true.
Thus, in a sense, subcontrariety can keep contrariety from turning to tyranny.
Urizen's cruciform vision foregrounds contrariety and subcontrariety.