For the record, I am feeling quite sick right now and am not exactly awake. That being said, I am not entirely sure if this post will be comprehensive and apologize in advance.
While I recognize that music, for the most part, is about evoking emotion, I don't think we should limit music to only emotions. Yes, music, and art in general, is "holding a mirror up to nature", (I am almost done with the series of Hitchhiker's Guide, by the way, and I think it's a perfectly valid definition. The ideas can be quite philosophical at times.) but nature is not just emotional. Every kid asks, "Why is the sky blue?" for the same reason: nature makes us think. To put it more romantically, it evokes a sense of wonder that not only influences our emotions, but makes us wonder how that something came into being. The simplest thing can come about in the most complicated ways. A smooth pebble was made smooth by millions of years of erosion, but we would never take notice until we stop and wonder, how could something so beautiful happen so simply?
For these reasons, I think all forms of art, including music, are not defined by whether they evoke emotions or not. Art makes us wonder, makes us think how or why something is the way it is. How does a particular sound make us feel the way it makes us feel? Why is it that a piece of Beethoven's music is considered beautiful and emotional, yet the quiet ticking of a clock, or the hum of a fan, or the flow of traffic, is said to be mundane and boring? When sounds we normally overlook because of their common presence in our lives are used by Cage to compose a piece of music, they're called to our attention. We listen, we notice them, and we begin to think. Everyone thinks something different. Daniel, like many others, still considers the sounds mundane, perhaps even insulting to the works of classical composers. Myself, and many others, begin to wonder how a sound we ignore in everyday life can suddenly morph into a decent piece of a musical composition.
Cage's music, though occasionally composed with purposelessness, is still music. As long as it generates some sort of reaction, a form of thought, from its listeners, it can be considered art in my opinion. The main difference, from a purely thought or philisophical view, between a piece of music that evokes emotion and Cage's compositions, is how they reflect nature. An emotional song is composed to reflect our own internal responses to nature--the feelings that are brought out by a sight or situation. Cage's work is a reflection of the external world, the sounds that accompany the sights and the everyday activities of life.