I think that a musical composition is different from a text asserting logical and semantic content. There still might be a “correct interpretation” of musical compositions, but I don’t think the issue here is one of a true theory about the semantic and logical content of a text, but of the aesthetic value of different musical compositions, or of different performances of the same musical score. I think we can ask the question of whether one or another performance of a musical score has more or less aesthetic value, and that people can answer this question by rating musical performances. In fact, it is possible for each person rating such performances to develop a measurement model creating a ratio-scaled set of numerical ratings of the relative aesthetic value of any comparison set of such performances. Of course, each of these models will be the conjecture of a single individual, so you can ask what all of these conjectures have to do with knowledge? Well, first of all, each of these measurement models can be tested for logical inconsistency. And second, we can use neural networking or other models to derive the patterns of coherence among alternative models generated by different people, and we can decide whether to accept a measurement model as the “best one” based on such an analysis of the pattern of coherence.
The model produced in this way is “objective” in the sense that it is sharable and criticizable. We cannot know for sure whether the scores produced by such a model actually correspond to “aesthetic value.” However, and once again, we can never be sure that any of our models, descriptive or otherwise, correspond to what they’re supposed to correspond to. All we can ever do is to compare competing models, evaluate what’s best according to our critical frameworks, and get on with growing our knowledge. If our efforts improve our lives over time, then we will know eventually, whether our knowledge has helped us to adapt to the challenges posed by our environment. If it has, then it truly was knowledge, whether of fact or value. If it hasn’t, then something is wrong with our frameworks for evaluating our knowledge claims, and we had better improve both the originality of our ideas and these evaluative frameworks.
Finally, what we should not do, I think, is what we have done in the field of value theory, including ethics, normative theory, and aesthetics. That is, we should not accept the epistemological perspectives of relativism and subjectivity which assert that our knowledge is always and everywhere a matter of individual, ethnic, moral, or cultural subjectivity. To make that assumption is to give up the game before we have played it. It is to give up the possible growth of knowledge and the attainment of objective knowledge in return for the comfortable feeling that arises from thinking we are sophisticated and realistic because we have recognized the diversity of human perspectives and have concluded from this diversity that we can, of course, create nothing but an arbitrary unity. This assumption is nothing but a basic axiom of a particular epistemology, which however sensible it may seem, may be a false theory of knowledge. And if it is false, and if we in our “sophistication” act in accordance with this theory, we will give away any possibility of the growth of our knowledge, and with that growth, our future world itself.