Idea theory is the most general and inclusive theory that can possibly exist as it recognizes that all things are ideas if they are considered by the mind. The idea of all possible ideas must therefore exist.
Containment itself is an idea and we see that the set concept cannot be the most general and most inclusive formalism for all possible ideas.
Plato's theory of Forms or theory of Ideas asserts that non-material abstract (but substantial) forms (or ideas), and not the material world of change known to us through sensation, possess the highest and most fundamental kind of reality. When used in this sense, the word form is often capitalized. Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggest that these Forms are the only true objects of study that can provide us with genuine knowledge; thus even apart from the very controversial status of the theory, Plato's own views are much in doubt. Plato spoke of Forms in formulating a possible solution to the problem of universals.
The problem of universals is an ancient problem in metaphysics about whether universals exist. Universals are general or abstract qualities, characteristics, properties, kinds or relations, such as being male/female, solid/liquid/gas or a certain colour, that can be predicated of individuals or particulars, or that individuals or particulars can be regarded as sharing or participating in. For example, Scott, Pat, and Chris have in common the universal quality of being human or humanity. While many standard cases of universals are also typically regarded as abstract objects (such as humanity), abstract objects are not necessarily universals. For example, numbers can be held to be particular yet abstract objects.
Ideas relate to other ideas in a hierarchy, where everywhere in the hierarchy is both top and bottom.
"I think, therefore I exist"
Existence and ideas share ontological status as being the most general and inclusive.
A set is always an idea but an idea is not necessarily always a set. Ideas are therefore more universal than the set concept.
All ideas exist in the abstract sense and all existing things must be expressed as ideas, thus they share ontological primacy.