The problem of how to characterise the properties that would trivialise the principle is one of the hardest problems concerning the principle of identity of indiscernibles and one the problems to which least attention has been paid of.

There are different interpretations of the problem of universals. I understand it as the problem of giving the truthmakers of propositions to the effect that a certain particular is such and such, e.g. propositions like 'this rose is red'. Others have interpreted it as a problem about the ontological commitments of such propositions or a problem about what those propositions mean.

For bundles of universals can be in more than one place at the same time; so a bundle can have more than one instance; so there can be numerically distinct particulars sharing the same universals; so the principle of identity of indiscernibles is false.

Metaphysics is the study of the most general nature and basic structure of reality, and therefore the concepts of metaphysics, concepts like time, space, identity, resemblance, substance, property, fact, event, composition, possibility, etc., are the most fundamental concepts. Thus metaphysics is the most fundamental theoretical discipline.

I do not believe in the bundle theory anyway. The bundle theory postulates universals and I do not believe in them; so I do not believe in the bundle theory.

Knowledge has the form of a tree, and since metaphysics is the most fundamental one of the theoretical disciplines, it represents the roots of the tree.

Those who take knowledge to be a whole zoo of sub-disciplines will react to my giving metaphysics a privileged position in that zoo or to my thinking of knowledge as a tree, with more and less fundamental parts.