Is there an essence of Art that all art shares, or is art just a category into which we lump a contingent collection of cultural pursuits?

Excellent question! There are a number of theories of art over the centuries that philosophers have proposed. For Plato and Aristotle art involved what they called techne (technique) and imitation (mimisis), for romantics (and this was especially advanced by Tolstoy), art involved the expression of emotions under certain conditions, for others works of art involve the embodiment of emotions, and there are still other theories. A view of art that comes closest to your suggestion about our lumping together "a contingent collection of cultural pursuits" is called the institutional theory of art --introduced in different forms by George Dickie and Arthur Danto. A very crude version is that a work of art is whatever is identified as a work of art by the artworld.

I personally think the latter is not the best way to go philosophically, as it leaves one without any guidance as to what someone in the art world should recognize as a work of art, and it also seems somewhat circular, like defining science as that which scientists do. I gravitate toward what is called an aesthetic theory of art. An object (event, thing, process....) is a work of art if it is made (or framed) to be the object of an aesthetic experience. By 'aesthetic experience' I mean (essentially) the emotive qualities of an object (its sadness, joy, solitariness, moodiness, beauty, ugliness, etc). The theory faces dozens of objections and there are (I believe) good replies to them. I defend this account and face objections in Aesthetics: A Beginner's Guide (Oneworld Press).

Read another response by Charles Taliaferro
Read another response about Art