In his famous essay "When is Art?" (in Ways of Worldmaking originally) Nelson Goodman says he has not defined art, but in a way, he has. We find first that art is a form of symbolization, and that this symbolization may be representational, expressive or through exemplification. Of course this does not distinguish art from a rock sample in a Natural History museum. However we are also informed that something is art if and when it is functioning as art. At first, this just seems a circular definition. But Goodman adds that we know it is functioning as art if it has at least some of what he calls the symptoms of the aesthetic. By "symptoms of the aesthetic" he appears to mean "symptoms of art" since he does not talk about these in relation to non-art aesthetic phenomena. He doesn't specify any of these symptoms as either necessary or sufficient for art.
The symptoms, as he lists them, are syntactical density, semantic density, relative repleteness, exemplification, and complex reference. (Note that he does not think that the stone in the Natural History is art even though it does exemplify: so exemplification by itself is not sufficient for art status.) You can go to the essay itself for his explication of each of these symptoms. The important point about all of them for our purposes is that they involve what he calls "nontransparency." That is, in attending to these features we do not look through them to the thing referenced but rather we focus on the symbol itself. Even though the stone in the natural history museum exemplifies it does not do so in a nontransparent way.
So one could say that, for Goodman, something is art if it functions as art, and it functions as art when it works as a nontransparent symbol. Goodman himself does not say this, perhaps because he is worried that in doing so he would be redefining the concept of art. However, as Weitz observed, that's pretty much what each of the classical theories of art does anyway.
Another feature of Goodman's approach is that he is clearly opposed to Danto and Dickie, although his argument against the Purist program is remarkably similar to Danto's in that both think the purist art (like the all-black paintings by Ad Reinhardt) is fine: it is only their claim that their work does not refer to anything outside that is the problem. For Danto they refer to everything else in the style matrix, and thus, really, to all previous art, whereas for Goodman, they refer to all the other objects that have the same property, for example an all-red canvas refers to all other things that have the property of redness, for example roses.
I have already discussed the relation between these philosophers here. In my previous post, however, I did not sufficiently stress the importance of Conceptual Art, and in particular Claes Oldenburg's "Placid Civic Monument" (1967). (Each great philosopher of art has his/her preferred works of art: in Goodman's case it is this particular conceptual piece, and this is largely because it operates as a counterexample to the opposing theories just as Warhol's "Brillo Box" operated as a counterexample for Danto.) In this work, Oldenburg hired grave diggers to dig a hole behind the Metropolitan Museum of Art and then had them fill it up again. The work was the event. Whereas Danto and Dickie require that a work of art be an object or, in Dickie's case, an artifact, Goodman does not require this. But, contra Dickie, Goodman stresses that the artist calling something a work of art is neither necessary nor sufficient for arthood. So, Oldenburg's work might be problematic for Danto and Dickie but not for Goodman.
Danto would probably handle this by saying that someone with sufficient art historical knowledge can see Oldenburg's work as art. Dickie would probably handle it simply by saying that artifactuality is conferred on the event and not on any specific object and that Oldenburg is the representative here of the artworld. All three would agree that it is art, but for different reasons. The work is art for Goodman because it functions as art for a time: it symbolizes, and it does so through exemplification of certain properties, although Goodman does not say which ones these are.
We can say, however, that "Placid Civic Monument" exemplifies the property of monumentality (although this might be problematic for Goodman, as I will note later). It is worth noting that the work was deliberately placed in view of an Egyptian obelisk, "Cleopatra's Needle," also in Central Park. The obelisk reaches upwards whereas, in a mirroring way, the hole reaches downwards. Also the obelisk is about eternity whereas the hole is notably temporary. In brief we can say that what makes it art for Goodman is a nontransparency that causes us to focus on properties that are exemplified (like Bell, in a way, although the number of types of properties to be exemplified are increased from lines, forms and colored shapes to include such things as size and texture) whereas Danto and Dickie call on us to focus on what is not exhibited, in Danto's case on what we see through the atmosphere of artistic theory and, in Dickie's case, on the status gained through the actions of Oldenburg as a representative of the artworld. It is interesting that although all three theories would designate this work as art, each calls on us to focus on quite different features: and each has different implications for how one ought to appreciate avant garde art. Also, whereas Danto and Dickie both think that "once art, always art," Goodman holds that something can lose art status when it no longer functions as art. Yet this is not entirely correct since Danto thinks that Warhol's "Brillo Box" is no longer art if it leaves the gallery and the artworld entirely and returns to the warehouse where it is indistinguishable from industrial brillo cartons: then it just reenters the world of non-art.
By the way, isn't there something strange about a nontransparency that calls on us to note relations to things considered extrinsic to the work of art?
To understand the five symptoms of the aesthetic in Goodman one does best just to focus on relative repleteness (which also, I think, explicates what is meant by "exemplification" or at least exemplification that is artistic). That is, one should focus on the difference between appreciating a Hokusai single-line drawing of a mountain and a stockmarket chart: in the first on focuses on "every feature of shape, line, thickness...counts..." whereas in the second only height counts. So, when the rock is moved to a pedestal in an art museum and treated as art the treatment involves a requirement on viewers to focus on every feature of every physical quality.
What Goodman seems to neglect, however, is other things that can be exemplified. For example, monumentality is exemplified, as I have argued, in Oldenburg's work, but this is not a physical quality (i.e. not of the same sort as color and texture). Goodman may well say that in this case we are symbolizing through expressiveness, but Oldenburg was exemplifying monumentality more than expressing it if expression has to do with an emotion expressed.