I suspect art can be defined, but what counts as a piece of art is subject to debate. Notice that it is a significant claim that 'what counts as a piece of art is subject to debate'. It indicates that the old adage, "There's no disputing about taste" is incorrect. We can, and often do, argue about whether or not something is a work of art. This seems to indicate that there are rational criteria for whether or not something is a work of art.
I tend to subscribe to a Kantian theory of art, though you should take that with a grain of salt, since I'm hardly an aethetician. He has what I think is a pretty good definition. It's been a while, so I apologize if this isn't entirely accurate. Art is something which gives rise to the free play of ideas. I'll try to look it up in his third Critique later.
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"Die Deutschen meinen, daß die Kraft sich in Härte und Grausamkeit offenbaren müsse, sie unterwerfen sich dann gerne und mit Bewunderung:[...]. Daß es Kraft giebt in der Milde und Stille, das glauben sie nicht leicht."
"The Germans believe that power must reveal itself in hardness and cruelty and then submit themselves gladly and with admiration[...]. They do not believe readily that there is power in meekness and calm."
-- Friedrich Nietzsche
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