Ranking of Linear Spaces in Generating a Hierarchy Between Concepts

Human perception is composed of fundamental concepts. If we associate these with states in Hilbert spaces such that the fundamental concepts are associated with the spanning sets of the spaces, a composed concept can be defined through the superposition of states within the selected spanning sets. Under these definitions, no particular spanning set can be defined as being fundamental. Therefore, in this article, we describe the concept of a hierarchy of spaces.