But you could say the same thing about anything. Concepts obscure the reality in their disclosure of what a thing is. I subscribe to the idea that concepts in no way can encompass their objects, for concepts by their nature reduce, quantify, and ignore what does not fit into established thinking. Or: concepts are abstractions and the world is not an abstraction (Nelson Goodman famously called the "innocent eye," a perception of the world as it is apart from our interpretative inclusion, a myth, but I beg to differ). At any rate, what is biology if not a reduction of the world to pragmatic symbols? There are no "genes" or "DNA" without our presence. We confer those conceptual values on to things, and without this, we have no idea what a thing is.
But this is not to say that biology cannot be defined. It just has its definition lodged in a body of other disciplines. Perhaps the answer lies in what art is not, just as a valid way to say what biology is is by identifying it boundaries with other fields. Art is not a science. What does this mean? What is missing or present in the one that sets it apart form the other? This is a very revealing method, because in showing boundaries, a definition, albeit provisional, rises to the fore as others recede.
For example, art is not a science: what does a science do? It applies,explicitly, the scientific method to observational data to establish principles. laws, and otherwise general rules that are evident. It uses logic to do this. It is an inherently rational process. And so on. Does art do this, at all? Yes: it certainly does require observation, the terms of assessment are grounded in established criteria, logic is used to identify distinctions, similarities; in other words, to see itself IS an exercise in logic. And so on.
But what is different about art? This is, to me, the important question. What sets it apart? What is it, when we have an art experience with some van Gogh painting, Ravel sonata, Jane Austin novel, that makes it art?
As you say, it is a mysterious affair, but that does not mean there is no identifiable common thread.