Whenever we form concepts, we always form their opposites, such as black and white, male and female, good and evil, beauty and ugliness, synthesis and analysis, art and science, and so on. These opposites, also called poles or duals, provide a map of the bifurcating Universe, constantly splitting forms into two as evolution unfolds in a binary tree.
This map is encapsulated in the Principle of Duality, a proposition D, stating: A complete conceptual model of the manifest Universe consists entirely of dual sets. But is D true? Well, sometimes yes and sometimes not. For instance, a collection of entities without a common attribute does not form a set, which we usually call miscellaneous. But now something quite magical happens!
Those occasions when D is false are the opposite of those occasions when D is true, confirming that D is true. In the terms of Hegel’s dialectical logic, if ‘D is true’ is the thesis and ‘D is false’ is the antithesis, then ‘D is true’ is the synthesis. There is thus a primary-secondary relationship between the truth and falsity of the Principle of Duality. So it is impossible to deny the truth of the Principle of Duality, for any denial confirms its veracity. D is thus a self-verifying proposition, true in all possible worlds, an instance of a class with general attributes A and not-A, called a paradox or self-contradiction.