Trait theorists conceptualize the self as a series of attributes. Individuals receive a set of scores based on the degree to which they possess the attribute in question: conscientiousness level 22, neuroticism level 15, etc. But can the self be reduced to a series of dimensions? There is an argument to be made that it cannot. The self as a collection of attributes is inert, passive, still. But, after all, consciousness is dynamic and protean; it can conceive of attributes and then decide to embody/imitate them.
But perhaps there are limits to the self's mutability. Individual differences exist that can be extrapolated from the self's movements and behaviors, even if they don't strictly bind the "I" like a rigid protocol or list of ingredients. Attributes can be inferred.
The question is, what do our "attributes" actually describe. Do they refer to a pattern of behaviors? Or do they point to qualities of consciousness, qualities of subjectivity? Does it feel different to inhabit a neurotic mind than it does to occupy a non-neurotic mind (o.k. the answer to that one is easy)? If we were to express an individual's instantaneous consciousness as a picture, would the picture look different if we increased his or her extraversion score by a couple of points?
Of course, the answer is that our attributes have both an external and an internal component. Still, I think we each have an idea of there being a "self" that's held in reserve, a self that's free of descriptors: the self as force, or will. The thought that even this self can be hemmed in and pinned down by a set of "attributes", I think, is somehow difficult to fathom.