But, for scientific exchange and research, this places a great deal of responsibility on the researcher to be explicit about the precise contextual meaning of the nebulous concept. Unfortunately such rigor has been sorely lacking. The tautology is that the supposed dimensions are defined by the same techniques used to detect them. Almost any data set can be subdivided in such a way that subsets have higher internal correlations than their external correlations with one another. To further complicate the issue, there is the effect of data clusters along a single continuum.
Most statistical techniques identify such clusters as different dimensions.
Statistical arguments do not seem to provide a useful answer. The question must be approached conceptually. It is the intention of the researcher which defines the dimension. Further, when a construct is developed which defines a dimension, then the potential for establishing hierarchies of dimensions is opened. One researcher's multidimensional space of incongruities may be another researcher's uni-dimensional line of concern.