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. In such a relationship are, for example, the statements "some people are poets" and "some people are mortal." Also, the function of postpendency can promote a subalternation-subcontrariety relationship (Fpq = Cpq & Apq), like the one between the statement "some rhombs are square" and "some rhombs are parallelograms." In both cases we have to deal with dyads of propositions where the truth of one of them bears the stamp of necessity.
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).
Negations can express a contradiction, a contrariety, or a subcontrariety
; see Aristotle, De interpretatione, 6.17a25-8.18a27.
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. Identifying the tree's "wisdom" as a vertical relation, an upright axis reaching "high & deep," Urizen would naturally situate the reasoning brain at the head of the cross and its opposite love, desire or energy at the base which suggestively penetrates and is enveloped by the earth.