But does music really represent feelings in this way, either by reflecting our own or by expressing the composer's? Is it emotion we feel when we listen--anger or sadness or envy or desire? When music brings tears to our eyes, is it because it makes us sad? Some music unquestionably does stir or inspire us; that is the purpose, after all, of national anthems and masses and even some folk songs. Some music also prompts unexpected emotion and thought. But this view of music's purpose is far too limited. The Indian raga serves the function of neither pleasure nor expression, nor does most of the great music of our Western tradition--even the Romantic music that claims to be fundamentally self-expressive. Only products of the pop culture industry unambiguously aim to inspire identification with musical "expression," and seek the avid consumption of such expression through purchase or use.What Rothstein is trying to do for music here mirrors what he has attempted to do (in Chapter 2) for mathematics. He has previously used examples from modern mathematics to problematize the notion that mathematicians mechanically search for objective, universal, "external" truths. Here he is going the other direction: he is trying to dispel the notion that music is merely a subjective experience tied solely to one's personal feelings.
The strength of Rothstein's writing is the way in which he veils the "big ideas" he's getting at, hinting that they are too mysterious to be fully encapsulated in concrete definitions of terms. What does a mathematician really explore when he does mathematics? What does our mind experience when we listen to music? Somehow the two are linked, but it takes patience to really see what the link is, or what the answer to either question might be.
I haven't made it all the way to the end, but one gets the feeling that there's a big payoff waiting.