Consider the humble square of opposition in logic:
Isn’t it interesting that it illustrates or at least has some minimal resemblance to the 4 human relations and the 4 general social systems?
The human relations, in the order of increasing dignity and sophistication, are:
The social systems in which each of these relations prevails (in the corresponding order) are:
- Autarky / total war
- Feudalism / serfdom
- Laissez-faire capitalism
So, AO would seem to indicate hostility: if one is true, then the other must be false (Xor).
AA is obviously equality and is totally boring (Equivalence).
AI is hierarchy: if A is true, then I is true; but not vice versa (Implication).
And in IO (let’s use the subcontraries for this one), the propositions are complementary: at least one I or O is true, and maybe both are (Or). Each does its proper work in conveying truth, but neither interferes with or determines the other.
NB: these groups of 4 are not actually true quadriformities, because a quadriformity is 4 complementary things that together make up a whole.
The relations themselves are not complementary but rather hierarchical, going from the most primitive and savage to the most sublime.