The isolation of dimensions from a data matrix
has been traditionally formulated in terms of an algebraic
or geometric model. Order analysis was developed
as a method of multidimensional analysis
and scaling based on the theory of Boolean algebra.
The order analytic algorithm utilizes functions of
the propositional calculus in lieu of eigenvalues and
eigenvectors of the general linear model. Also, the
graphic presentation of latent space in coordinates
of the Euclidian space is paralleled in ordering-theoretic models by dendrograms of the test space.
A conceptual outline of order analysis is presented,
followed by an empirical comparison of factor and
order analysis solutions of a sample data problem.
Resulting factor and order analytic structures are
evaluated in terms of meeting criteria of simple
structure and correct reflection of broad cognitive
categories. In addition, the relations of proximity
and dominance are discussed from the perspectives
of both Cartesian and Leibnitzian theories of dimensionality
as pertaining to problems of multivariate
analysis and scaling.