John Dewey perhaps articulates his notion of "art as experience" most straightforwardly near the beginning of the chapter devoted to art's "challenge to philosophy" (ch. XII):
. . .esthetic experience is experience in its integrity. Had not the term "pure" been so often abused in philosophic literature, had it not been so often employed to suggest that there is something alloyed, impure, in the very nature of experience and to denote something beyond experience, we might say that esthetic experience is pure experience. For it is experience freed from the forces that impede and confuse its development as experience; freed, that is, from factors that subordinate an experience as it is directly had to something beyond itself. To esthetic experience, then, the philosopher must go to understand what experience is.
It should be said that art is "pure experience" if and when the reader/viewer/listener allows the experience its "integrity." This does not always happen, of course. Many predispositions can work to "impede and confuse" aesthetic perception, especially the aesthetic perception of works of literature, as readers subordinate the experience itself to various concerns that are finally extraneous to a concern for the work's aesthetic integriy, from the expectation that a novel should have an "exciting plot" or "characters I can care about" to the assumption that a literary work should be scrutinized for what it "has to say" or what it "reveals about our society." Since it is art's aesthetic integrity--its ability to unify disparate elements into a seamless whole--that for Dewey makes art valuable in the first place, these obstacles subvert the very purpose of literature as an artistic form.
Most literary criticism, especially academic criticism in its current iterations but also much general-interest book reviewing as well, can be characterized as anti-literary in this way. Critics and reviewers seldom assess a work of fiction (the situation of poetry is not so dire in this regard) for its creation of (or lack of) aesthetic unity. The reviewer settles for plot summary and a cursory evaluation, usually based on unstated or unexamined standards, while the academic critic interrogates the text for its value as a cultural symptom. Later in this chapter, Dewey writes that "Since a work of art is the subject-matter of experiences heightened and intensified, the purpose that determines what is esthetically essential is precisley the formation of an experience as an experience." Unless critics attend to the way in which a literary work stimulates "the formation of an experience as an experience," and subsequently evaluate the quality of the experience so induced, they are missing what is "esthetically essential"--and for Dewey, as for me, to miss what is aesthetically essential is to miss what is essential about all art.1
Dewey believed that although philosophers have long been inspired to investigate the nature of art and aesthetic experience, they have in particular failed to appreciate what is "essential" about both. And this follows from a more general failure to appreciate what is essential about experience. Philosophers from Plato to Kant to Croce have gestured at "something beyond experience" itself as the truly real. Experience as the humble, ordinary act of perceiving the tangible details of the world in front of us cannot possibly connect us to absolute reality, which is transcendent and ideal. Art, therefore, is a means of capturing this larger reality. Dewey is among those philosophers who reorient philosophy to the consideration of perceptible reality and in his philosophy of art tries to orient us to the concrete reality of aesthetic experience.
1 There are legitimate forms of literary criticism that appropriately do not focus on aesthetic analysis. Certain kinds of historical or cultural criticism attempt to locate the work contextually, which is a perfectly good thing to do, but I would call this kind of criticism a supplement to aesthetic criticism, not a substitute for it.