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Complexity is the foundation of the ordinal theory, which is why that theory can provide an adequate basis for a theory of art. Art is built upon complexity and inexhaustibility even in its simplest and purest works. Only the theory of contrast as delineated here can explain this feature of art: that the simplest works are sometimes pregnant with the most sublime, profound, and complex qualities. The theory of contrast is closely related to Kant's theory of purposiveness and finality given by the free play of the cognitive faculties Page 8 without the reference to the subject that his analytic of aesthetic judgment requires.

The fundamental principle of an ordinal theory is that whatever is is an order of constituents, whatever is relevant to it in a particular location, and every order functions as a constituent in other orders. The theory is functional in that what an order is, the constituents it has, are a function of its location in another order, a sphere of relevance. Page 11 Thus every work of art is an order with constituents relevant to it, every component of a work is an order inhabiting many spheres of relation with its particular constituents, and an immense variety of human orders provide relevant locations for works of art.

So that the discussion of art may be as rigorous and precise as possible, I develop the systematic basis of the theory in Chapter 3, after a discussion of some of the major traditional views of art. The discussion of the major types of contrast in art, in Chapters 4 and 5, is built upon the general theory, but is written to be as intelligible as possible independent of the more technical discussion. The final chapter, on the theory of interpretation and criticism, rests on principles developed in earlier discussions, but is also written to be as independent as possible.

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