In factor analysis, the idea of multidimensional phenomena comes into play.
In our rational approach to mathematics, we say that the dimensions are length, height, depth, and time.
But in factor analysis, each factor is described as a dimension, and there may be many of them. We are in a sense inventing mental constructs for the purpose of grasping factors which come into play in analyzing a process.
This factor analysis technique is used to detect possible independent influences on a psychological profile. The technique is also used in the study of sociology. Identification of clusters in a continuum that defies separation into categories involves using factor analysis.
Whether there are actual independent factors which determine personality profiles often depends on identifying them. The first step is to determine how many there are. The next step is to define them.
When I was teaching, I graded on the curve, assigning letter grades, A, B, C, D & F. The boundary between each of these letter grades was determined arbitrarily, with no concrete way to distinguish one grade from another. There was no natural breakpoint but using any other technique was too cumbersome.