A GENERAL APPROACH TO THE STUDY OF SPATIAL SYSTEMS;I. The Relational Representation of Measurable Attributes

In this, the First part of a two part work, a general model of spatial organization is introduced. Following a brief synopsis of some of Spinoza's and Leibniz's views regarding natural structure, an extension of the Spinozian model is presented in which the attribute spatial extension is portrayed as a relational system that implicitly underlies the differentiation of sensible space into “modifications” (“natural systems”) and the latter's subdifferentiation into “modes” On the basis of this model, all instances of modal differentiation are understood to take place in a manner explained by this relational structure, the existence (but not the specific characteristics) of which is initially assumed. The nature of the structure is then deduced according to a “most-probable-state” kind of logic; next, it is demonstrated via simulation that the resulting aspatial model of internal relations has a corresponding spatial interpretation (and therefore, in theory, that sensible space structures can be supported by the particular rational ordering posed). The matter of how to apply the model to the study of real world systems is taken up last; discussion focuses on related aspects of the treatment of equilibrium and nonequilibrium systems and the recognition and measurement of modal structures.