Carving or whittling is just a means to an end, whether that end is art, craft, or design. As such you should not be looking at media as the determining factor of something being art, but concerning yourself with the distillation of ideas or concepts that is endowed into the media whether that is paint, silver halide(photo), wood, concrete, marble, steel, or computer programming (yes it too can be an art).
As for the definition of art, there are many definitions, and the broadest and most generic interpretation that I can give you is that art transforms the ordinary or mundane and it raises its existence to a level beyond its own meaning. Take for example a painting we all know and accept as art, "The Mona Lisa". A description of this work is that it is just a portrait or a woman, which for the most part isn't special, there are billions of painted portraits in existence, but this one is special. Is it because it is oil painting that makes it art? Again dont look a the medium, oil paints can be used to paint a park bench, but does that make it art, not necessarily. The reason it is art is because it does something that other portraits dont do, for example some people say that the eyes follow you, connect with you, reach deep into your soul and have you asking all sorts of questions you wouldnt ask on an everyday basis. This is quite different than grandmas paint-by-numbers oil painting of a dog, the dog is just a dog, nothing special, the artist has not distilled or endowed any special concepts or emotions into the work. And even if the artist tried to endow something in it we dont ask any questions because the artist or shall I say grandma has taken the ordinary, and made it ordinary, and there is nothing special about that. So in this case we can say that grandma is a craftsperson and not truly an artists. Back to whittling, is a person whittles a smoking pipe, is that art? In what way has this pipe become something else that it is not, it is a craft. Conversely, if someone goes into a forrest and say whittles everysingle tree down to a 2x4 without chopping the tree down, so as to prove a point that man manipulates his environment, well this is something else. It serves no function other than to be art,by trying to raise your everyday conciousness to a higher level. Perhaps this wasnt a good example, but hopefully it clarifies some things.