Is it fair/possible for Weitz to apply logical reasoning to art and aesthetic theory in his argument?

One of the reasons Morris Weitz gives for his assertion that one cannot and should not define art, is that the very processes of defining art are illogical.

"Aesthetic theory- all of it- is wrong in principle in thinking that a correct theory is possible because it radically misconstrues the logic of the concept of art...a logically vain attempt to define what cannot be defined, to state the necessary and sufficient properties of that which has no necessary and sufficient properties, to conceive the concept of art as closed when its very use reveals and demands its openness" (Weitz, 410-11).

Weitz does make a reasonably strong argument; it is true that attempting to define something that is undefinable would be contradictory, and therefore, illogical.  However, his argument of the illogical nature of defining art and aesthetic theory rests solely on this premise, that it is impossible to define the undefinable.  This begs the question though, is art truly undefinable?  Weitz focuses the central theme of his paper on the concept of the inability to define art, or at least that all prior definitions have failed, and should not be attempted in the future.  It would follow, that he would have reasonable grounds to use this contradictory style premise in his argument.  Is that enough, though?  Despite the fact that he spends much of his writing discussing this contradictory principle, the inference to the premise that, "art is undefinable," is surely questionable, or at the very least, circular in reason, regardless of the content of the premise.

As we discussed in class, I would agree that art can be defined, in a way that the definition is sufficient, yet preserves the ambiguity required for art and artists to create whatever products they wish, and present them in any medium they can imagine.