Let us presume as a working hypothesis that the views expressed in Spinoza's Ethics are in broad strokes metaphysically and ontologically correct. We thus presume that what really exist are relational structures of infinite variety and that these structures everywhere enter in turn into higher-order relations with one another and so on without limit. We and all the things around us are both immersed within relations of these kinds and thoroughly saturated by them. At any particular scale of investigation, then, we may take relatively stable linkages of more or less determinate local relations to constitute ‘things’ or ‘objects’ in a quite general sense, and we may expect to find a variety of relations linking such scare-quoted objects to one another depending upon which we decide to select. Furthermore such relations frequently come packaged together in internally differentiated systems of some common type: chemical, linguistic, military-strategic, stellar-galactic and so forth. Our aim is to develop a workable method for plunging philosophically into this immanent relational sea.

We proceed accordingly at two distinct levels. At an initial level, we will develop an informal diagrammatic notation for representing and analysing arbitrary systems of relations, with objects represented by dots and relations of the relevant type by arrows between dots. At a secondary, reflective level, we will treat the same notation in a more regimented way in order to introduce category theoretical mathematics. At both levels, we will be using systems of partly determined and partly undetermined relations (a variety of dot-and-arrow diagrams) to represent and investigate systems of partly determined and partly undetermined relations (worldly phenomena and mathematical categories). To some extent these representations and patterns of investigation will be reversible, that is, the represented will by virtue of the very form of representation at work serve as a potential representing medium in its own right. It will be a diagram too. The fact that the same notation serves as object, method and mathematical formalism provides the primary link here to Spinoza's philosophy of immanence.