The thing is, the definition of a concept, is the axiom that it exists outside of human understanding.

I don't agree with that definition of a concept.

Idea = mental representation of an object, or a set of objects and their interactions.

Concept = generalization of an idea.

wherein 'mental' justifiably implicates the working of a brain. It is very much tied to what we call brain understanding. Sorry for taking this discussion to the definition of words.