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A theory of art is intended to contrast with a definition of art. Traditionally, definitions are composed of necessary and sufficient conditions, and a single counterexample overthrows such a definition. Theorizing about art, on the other hand, is analogous to a theory of a natural phenomenon like gravity. In fact, the intent behind a theory of art is to treat art as a natural phenomenon that should be investigated like any other. The question of whether one can speak of a theory of art without employing a concept of art is also discussed below.
The motivation behind seeking a theory, rather than a definition, is that our best minds have not been able to find definitions without counterexamples. The term "definition" assumes there are concepts, in something along Platonic lines, and a definition is an attempt to reach in and pluck out the essence of the concept and also assumes that at least some people have intellectual access to these concepts. In contrast, a 'conception' is an individual attempt to grasp at the putative essence behind this common term while nobody has "access" to the concept.
A theory of art presumes that each of us employs different conceptions of this unattainable art concept and as a result we must resort to worldly human investigation.