1. We consider that A is the conceptual ground or
foundation of B when the cognition of B is impossible without the cognition of
A, and A is immediately certain for our intuition. We say that A gives a
semantical self-image, for it does not need further explanation, but B cannot
produce a semantical self-image.
2. Music Theory has developed since Antiquity with
the aid of mathematics, reaching today a fully mathematical status.
3. Mathematics is a formalized symbolic language.
4. Tarski’s theorem states that a formalized
language cannot produce a semantical self-image.
Therefore, music theory could not be the ground
of musical action or of anything else.
In fact, music theory -as well as musical
action- are based on the social life of the human group, which in turn are
based on the homeostatic protocols for survival: emotions.
Proposition 2) requires an explanation. Which music theory does it refer to, and is the theory really mathematical, that is, formal?
ReplyDeleteThank you very much for your comment. You are right proposition 2 needs further explanation. Not only the notion of music theory but also the concept of theory itself would require a philosophical elucidation. I understand by theory a system of logically consistent propositions. Systematization and consistency are better carried on formalizing propositions, cutting off ambiguities and mechanizing the relations among the proposition of the calculus. As you probably know, formalization has not been always the main goal of mathematics (think for a moment in XVIII century analysis), so I would not say that formalism and mathematics are interchangeable concepts. However, I would agree that any theory (defined as above) implies a minimum formalization in its propositions and procedures.
DeleteAll major consistent systems of propositions about music have used arithmetic not only as a tool for its understanding, but also as the better description of the nature of the system, mistaking questions of sound with a much wider phenomenon, which in my opinion is what we call the realm of music. Think for a moment in Rameau’s well known statement: “A knowledge of harmony is sufficient for a complete understanding of all the properties of music” (Treatise on Harmony. Chapter One.).
By full mathematical status of music theory I mean that its social practice at the academic level follow principles of scientific formalization, despite the fact that, since Gödel, mathematics itself has suffered a very serious drawback in its foundational enterprise.
Cordially.
I agree with your premise that music theory itself is not the basis of musical creation. However, we have all heard the work of people with great passion and enthusiasm who take no care to understand basic theoretical principles. Such music (at best) usually lacks substance. Theory is to music as grammar is to language; mastery of it does not guarantee good content, but it does provide a framework upon which many beautiful and important concepts can be grown in an organic way.
ReplyDeleteThank you for your comment. I definitely agree with your statement about the importance of theory. Furthermore, I think that music theory had a major impact in the expansion of the aesthetic horizon of composition. Cordially
ReplyDelete