Going On

As Wittgenstein postulates about learning what the color red is, when we've been shown a red apple, or a red ball, or a red firetruck, we have not learned only to call these things red. But we have learned that common property between these things and are able to 'go on' and call new objects, that we have never seen before, 'red'.
Thus it is, or so we want to think, with art. That with enough exposure to the things others call art, we begin to get a sense of what is this common property, and can thus determine whether new objects are themselves art or not.
On an even more sophisticated level, it seems that we are able to assimilate an idea of art between existing objects that can even rule out current objects that some consider art. Such that once we understand what is really meant by 'art', we can see that we were mistaken call some object art, even though it may have been that very object that helped point us to the idea that in turns rejects its inclusion in the set of 'art'.