Each one has multiple temporal scales and both are mutually irreducible.
They do not hold that all phenomena will support ineliminable pluralism, but that there are some phenomena that will require mutually irreducible or incompatible models.
Rather, the "physical" and "psychic" name two mutually irreducible perspectives from which one and the same world or Being (Sein) may be observed: "nothing occurs in our consciousness that does not find its sensible foundation in certain physical processes," he writes, and all psychological acts (association, apperception, willing) "are accompanied by physiological nerve-actions" (PP II: 644).
The Western understanding of dualism equates to two independent and mutually irreducible substances.
Various formulations of dual-aspect monism also require the mental and the physical to be complementary, mutually irreducible and perhaps inseparable (though distinct).
Madhva's Dvaita differs from the Western definition of dualism in that while he agrees to two mutually irreducible substances that constitute reality, he regards only one – God, as being independent.
It is a further question whether, if statements of a given kind are true or false as a matter of objective, mind-independent fact, those statements record facts of some special irreducible type, distinctive of that discourse.
The other is about a type of minimal submanifold in a rank one symmetric space of irreducible type.
The Manual of Reason raises three questions about this relation: (i) Is it a new and irreducible type or relation, not reducible, that is, to any of the relations already admitted (TSD 66a)?
"In their best performance pieces, the two ritualistically parody male power struggles as an ongoing clash between these opposite, mutually suspicious types".
